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Constant-pressure calorimetry | https://www.youtube.com/watch?v=SkMeY6RBJZY | vtt | https://www.youtube.com/api/timedtext?v=SkMeY6RBJZY&ei=6VWUZZqzHpq7p-oPx_-UuA0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6BD83B5EBAEB3D820DF0E72BBC7C17E2D546DF7A.B83BA1BCB1EA2944C19B1CC712D21859DA108368&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.080 --> 00:00:02.400
- [Instructor] Calorimetry
refers to the measurement
00:00:02.400 --> 00:00:03.460
of heat flow.
00:00:03.460 --> 00:00:05.790
And a device that's used
to measure heat flow
00:00:05.790 --> 00:00:07.863
is called a calorimeter.
00:00:08.870 --> 00:00:13.690
An easy way to make a calorimeter
is to use two coffee cups.
00:00:13.690 --> 00:00:16.010
So at the base here,
we have one coffee cup,
00:00:16.010 --> 00:00:18.580
and then we can also
use another coffee cup
00:00:18.580 --> 00:00:20.800
as a loose fitting lid.
00:00:20.800 --> 00:00:23.800
And since this top coffee
cup is loose fitting,
00:00:23.800 --> 00:00:26.760
our calorimeter is exposed
to the constant pressure
00:00:26.760 --> 00:00:28.280
of the atmosphere.
00:00:28.280 --> 00:00:31.090
Therefore, we could use
this coffee cup calorimeter
00:00:31.090 --> 00:00:33.783
for constant-pressure calorimetry.
00:00:34.710 --> 00:00:38.720
Other components of our
calorimeter include some water
00:00:39.720 --> 00:00:43.060
and then we also have a stir
bar to stir up the water,
00:00:43.060 --> 00:00:46.530
and a thermometer to measure
the temperature change
00:00:46.530 --> 00:00:47.453
of the water.
00:00:48.670 --> 00:00:51.810
Let's say we have 150.0 grams of water
00:00:51.810 --> 00:00:56.650
at an initial temperature
of 25.0 degrees Celsius.
00:00:56.650 --> 00:01:01.650
Next, let's take a block of
copper, 120.0 grams of it,
00:01:01.710 --> 00:01:03.530
and let's heat up that block of copper
00:01:03.530 --> 00:01:07.500
to 100.0 degrees Celsius.
00:01:07.500 --> 00:01:09.860
Once the copper has
reached that temperature,
00:01:09.860 --> 00:01:14.063
we add the copper block
to our calorimeter.
00:01:15.320 --> 00:01:17.530
Here, we can see the
copper block has been added
00:01:17.530 --> 00:01:20.220
to the calorimeter, and since the copper
00:01:20.220 --> 00:01:22.660
is at a higher temperature than the water,
00:01:22.660 --> 00:01:26.680
heat flows from the
copper block to the water,
00:01:26.680 --> 00:01:30.010
and therefore the temperature
of the water will increase,
00:01:30.010 --> 00:01:32.860
which we will see on the thermometer.
00:01:32.860 --> 00:01:35.873
So we'll see the temperature
increase on the thermometer.
00:01:37.070 --> 00:01:40.210
Heat is transferred from the
copper block to the water
00:01:40.210 --> 00:01:43.150
until thermal equilibrium
has been reached.
00:01:43.150 --> 00:01:45.540
And we know when thermal
equilibrium has been reached
00:01:45.540 --> 00:01:46.800
by looking at the thermometer
00:01:46.800 --> 00:01:49.730
and measuring the highest
temperature that's reached.
00:01:49.730 --> 00:01:52.720
Let's say the final temperature is equal
00:01:52.720 --> 00:01:57.560
to 30.0 degrees Celsius.
00:01:57.560 --> 00:02:01.170
So at thermal equilibrium,
both the pieces of copper,
00:02:01.170 --> 00:02:03.050
both the copper block and the water
00:02:03.050 --> 00:02:05.463
are at the same final temperature.
00:02:06.500 --> 00:02:08.840
Next, let's calculate the
heat gained by the water
00:02:08.840 --> 00:02:12.660
by using the equation q
is equal to mc delta T.
00:02:12.660 --> 00:02:15.290
So q is what we're trying to calculate,
00:02:15.290 --> 00:02:17.010
the heat gained by the water.
00:02:17.010 --> 00:02:21.310
M is the mass of the water,
which is 150.0 grams.
00:02:21.310 --> 00:02:25.310
So we can write in 150.0 grams.
00:02:25.310 --> 00:02:30.310
C is the specific heat of
water, which is 4.18 joules
00:02:31.450 --> 00:02:35.230
per gram degrees Celsius.
00:02:35.230 --> 00:02:38.150
And delta T is the change
in the temperature,
00:02:38.150 --> 00:02:40.080
which would be the final temperature,
00:02:40.080 --> 00:02:43.183
so Tf minus the initial temperature Ti.
00:02:44.140 --> 00:02:48.760
The final temperature of the
water is 30.0 degrees Celsius,
00:02:48.760 --> 00:02:50.630
and the initial temperature of the water
00:02:50.630 --> 00:02:53.540
was 25.0 degrees Celsius.
00:02:53.540 --> 00:02:58.540
So 30.0 minus 25.0 is equal
to 5.0 degrees Celsius.
00:03:01.230 --> 00:03:03.050
So we can write that in.
00:03:03.050 --> 00:03:07.170
And next, we look at units
and see what cancels out here.
00:03:07.170 --> 00:03:12.170
So the grams cancel out,
degrees Celsius cancels out,
00:03:12.370 --> 00:03:14.740
and we're left with joules as our unit.
00:03:14.740 --> 00:03:19.740
So q is equal to, when we go
to two significant figures,
00:03:20.680 --> 00:03:25.680
this is positive 3.1 times
10 to the third joules.
00:03:28.200 --> 00:03:33.200
The positive sign means that
this was the energy gained
00:03:33.410 --> 00:03:34.583
by the water.
00:03:35.460 --> 00:03:38.270
Next, let's do the same
calculation for copper.
00:03:38.270 --> 00:03:40.970
So we're trying to find q.
00:03:40.970 --> 00:03:45.150
The mass of the copper was 120.0 grams.
00:03:45.150 --> 00:03:47.760
So we can plug that in.
00:03:47.760 --> 00:03:52.760
The specific heat of copper is .39 joules
00:03:53.580 --> 00:03:57.320
per gram degrees Celsius.
00:03:57.320 --> 00:03:58.690
And let's think about the change
00:03:58.690 --> 00:04:00.980
in the temperature of the copper.
00:04:00.980 --> 00:04:02.710
The final temperature of the copper
00:04:02.710 --> 00:04:05.590
was 30.0 degrees Celsius,
00:04:05.590 --> 00:04:07.870
and the initial temperature of the copper
00:04:07.870 --> 00:04:11.480
was 100.0 degrees Celsius.
00:04:11.480 --> 00:04:15.813
So the change in the temperature
would be 30.0 minus 100.0,
00:04:17.980 --> 00:04:21.830
which of course is negative 70.0.
00:04:21.830 --> 00:04:26.830
So let's plug in negative
70.0 degrees Celsius.
00:04:28.700 --> 00:04:32.030
Once again, we see what
cancels for our units.
00:04:32.030 --> 00:04:35.370
Grams will cancel, degrees
Celsius will cancel,
00:04:35.370 --> 00:04:38.060
and our answer will be in joules.
00:04:38.060 --> 00:04:43.060
So q is equal to, using
two significant figures,
00:04:45.977 --> 00:04:49.290
negative 3.3 times 10 to the third joules.
00:04:53.100 --> 00:04:54.800
And the negative sign,
00:04:54.800 --> 00:04:57.860
so this negative sign
means this is the energy
00:04:57.860 --> 00:05:00.353
that was lost by the copper.
00:05:02.090 --> 00:05:04.040
Next, let's look at these
two numbers that we got
00:05:04.040 --> 00:05:05.350
from our calculations.
00:05:05.350 --> 00:05:09.020
Let's think about the
magnitude of these two numbers.
00:05:09.020 --> 00:05:12.480
If our coffee cup calorimeter
were a perfect insulator,
00:05:12.480 --> 00:05:15.580
the magnitude of these two
numbers would be the same.
00:05:15.580 --> 00:05:17.670
So it could be something like 3.3 times 10
00:05:17.670 --> 00:05:20.760
to the third joules for both of them.
00:05:20.760 --> 00:05:23.720
But since these two numbers
are not the same, right?
00:05:23.720 --> 00:05:27.330
We can see that we've lost
more heat from the copper
00:05:27.330 --> 00:05:30.010
than we've gained in terms
of energy for the water,
00:05:30.010 --> 00:05:32.980
which means we could have
lost some of the energy
00:05:32.980 --> 00:05:34.930
to the environment.
00:05:34.930 --> 00:05:38.810
So not all of the heat
was transferred directly
00:05:38.810 --> 00:05:39.870
to the water.
00:05:39.870 --> 00:05:43.313
Some of it could have escaped
our coffee cup calorimeter.
00:05:44.530 --> 00:05:48.920
Next, let's think about calorimetry
for a chemical reaction.
00:05:48.920 --> 00:05:50.010
So before we do that,
00:05:50.010 --> 00:05:53.110
let's review some terms
for thermodynamics.
00:05:53.110 --> 00:05:56.170
So the system is the part of the universe
00:05:56.170 --> 00:05:58.070
that we are studying.
00:05:58.070 --> 00:06:00.090
So in the case of a chemical reaction,
00:06:00.090 --> 00:06:03.960
the reactants and the
products make up the system.
00:06:03.960 --> 00:06:06.483
The surroundings are everything else,
00:06:07.680 --> 00:06:11.410
which would include the
water in the calorimeter,
00:06:11.410 --> 00:06:14.050
the coffee cup itself, the thermometer,
00:06:14.050 --> 00:06:15.720
the environment outside,
00:06:15.720 --> 00:06:17.460
so the surroundings are everything else.
00:06:17.460 --> 00:06:20.120
And finally, the universe
would be the system
00:06:20.120 --> 00:06:22.400
plus the surroundings.
00:06:22.400 --> 00:06:24.870
So the reactants and the
products make up the system.
00:06:24.870 --> 00:06:28.420
So that's what the S stands
for here in our calorimeter.
00:06:28.420 --> 00:06:29.690
That's our system.
00:06:29.690 --> 00:06:31.710
And let's say we run a reaction,
00:06:31.710 --> 00:06:35.880
and in the reaction, heat is given off.
00:06:35.880 --> 00:06:37.070
So in that case,
00:06:37.070 --> 00:06:40.740
heat would flow from the
system to the surroundings,
00:06:40.740 --> 00:06:43.940
and so the temperature of
the water would increase.
00:06:43.940 --> 00:06:47.500
So we would see that as
the temperature increases
00:06:47.500 --> 00:06:49.210
on the thermometer.
00:06:49.210 --> 00:06:51.640
Next, we could calculate
the heat gained by the water
00:06:51.640 --> 00:06:56.640
by using our q is equal
to mc delta T equation.
00:06:57.240 --> 00:07:02.240
And let's say q is equal
to positive 1.0 times 10
00:07:03.400 --> 00:07:06.180
to the second joules.
00:07:06.180 --> 00:07:11.180
The positive sign means that
the water gained energy.
00:07:12.770 --> 00:07:15.910
If we assume a perfect transfer of heat
00:07:15.910 --> 00:07:17.880
from the system to the surroundings,
00:07:17.880 --> 00:07:21.340
if the surroundings gained
positive 1.0 times 10
00:07:21.340 --> 00:07:22.630
to the second joules,
00:07:22.630 --> 00:07:27.533
that means the system must
have lost negative 1.0 times 10
00:07:29.210 --> 00:07:31.130
to the second joules.
00:07:31.130 --> 00:07:34.390
So the same magnitude, but
we changed the sign here,
00:07:34.390 --> 00:07:36.360
because if we're talking about
00:07:36.360 --> 00:07:38.550
the energy lost by the system,
00:07:38.550 --> 00:07:41.833
it's the same in magnitude,
but opposite in sign.
00:07:42.690 --> 00:07:46.370
Next, remember that our lid
over here is loose fitting,
00:07:46.370 --> 00:07:50.030
which makes this constant
pressure calorimetry,
00:07:50.030 --> 00:07:53.240
and therefore this heat that
was transferred is the heat
00:07:53.240 --> 00:07:55.150
that's transferred at constant pressure.
00:07:55.150 --> 00:07:59.580
So we can write a
subscript p in here, so qp.
00:07:59.580 --> 00:08:02.700
The heat transfer at a constant
pressure is the definition
00:08:02.700 --> 00:08:05.840
for the change in the enthalpy delta H,
00:08:05.840 --> 00:08:10.800
so we can write that
qp is equal to delta H.
00:08:11.820 --> 00:08:15.140
And when delta H is negative,
00:08:15.140 --> 00:08:18.383
we're talking about an
exothermic reaction.
00:08:22.940 --> 00:08:24.810
So when a reaction is exothermic,
00:08:24.810 --> 00:08:27.800
heat is transferred from the
system to the surroundings,
00:08:27.800 --> 00:08:29.680
and therefore we see an increase
00:08:29.680 --> 00:08:32.190
in the temperature of the water.
00:08:32.190 --> 00:08:35.280
Finally, let's think about
an endothermic reaction.
00:08:35.280 --> 00:08:36.710
In an endothermic reaction,
00:08:36.710 --> 00:08:39.940
heat is transferred from the
surroundings to the system.
00:08:39.940 --> 00:08:41.630
So here we can show heat flowing
00:08:41.630 --> 00:08:44.200
from the surroundings to the system.
00:08:44.200 --> 00:08:48.090
Since energy is leaving the surroundings,
00:08:48.090 --> 00:08:51.640
the temperature of the water will decrease
00:08:51.640 --> 00:08:54.430
for an endothermic reaction.
00:08:54.430 --> 00:08:57.640
And since heat is being
transferred to the system,
00:08:57.640 --> 00:09:00.860
we can go ahead and write heat over here,
00:09:00.860 --> 00:09:03.990
we can go ahead and write
heat on the reactants side,
00:09:03.990 --> 00:09:08.990
and delta H would be positive
for an endothermic reaction.
00:09:09.960 --> 00:09:11.910
So for an endothermic reaction,
00:09:11.910 --> 00:09:15.560
energy is transferred from the
surroundings to the system,
00:09:15.560 --> 00:09:19.123
and therefore the temperature
of the water will decrease.
|
Heat capacity | https://www.youtube.com/watch?v=QlusUNM1ehA | vtt | https://www.youtube.com/api/timedtext?v=QlusUNM1ehA&ei=6VWUZcGTAuvFhcIPysmJ0Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2151BBE2DD8CBD64C723C7A0E032C60163EE9648.D6C67FF39C0C6991EBD8C3DDA28F5A43AFE292AA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.200 --> 00:00:03.430
- [Instructor] The heat capacity
of an object is the amount
00:00:03.430 --> 00:00:05.640
of heat necessary to raise the temperature
00:00:05.640 --> 00:00:10.230
of the object by one degree
Celsius or one Kelvin.
00:00:10.230 --> 00:00:12.820
The specific heat capacity, which is often
00:00:12.820 --> 00:00:16.310
just called specific
heat is the heat capacity
00:00:16.310 --> 00:00:18.640
of one gram of a substance
00:00:18.640 --> 00:00:21.890
while the molar heat
capacity is the heat capacity
00:00:21.890 --> 00:00:24.313
for one mole of a substance.
00:00:25.170 --> 00:00:28.630
We symbolize specific
heat with a capital C
00:00:28.630 --> 00:00:31.000
and a subscript s for specific,
00:00:31.000 --> 00:00:34.250
and molar heat capacity
is symbolized by capital C
00:00:34.250 --> 00:00:36.430
with a subscript m.
00:00:36.430 --> 00:00:38.510
First let's look at specific heat.
00:00:38.510 --> 00:00:40.390
The specific heat of water is equal
00:00:40.390 --> 00:00:43.897
to 4.18 joules per gram degrees Celsius.
00:00:43.897 --> 00:00:48.750
And what this means is if we
have one gram of liquid water,
00:00:48.750 --> 00:00:50.030
and let's say the initial temperature
00:00:50.030 --> 00:00:53.540
is 14.5 degrees Celsius,
00:00:53.540 --> 00:00:58.380
it takes positive 4.18 joules
00:00:58.380 --> 00:01:00.880
of energy to increase the temperature
00:01:00.880 --> 00:01:05.640
of that one gram of water
by one degree Celsius.
00:01:05.640 --> 00:01:07.760
Therefore the final
temperature of the water
00:01:07.760 --> 00:01:12.760
would be 15.5 degrees Celsius
after we add 4.18 joules.
00:01:14.950 --> 00:01:17.360
Next let's calculate
the molar heat capacity
00:01:17.360 --> 00:01:20.160
of water from the specific heat.
00:01:20.160 --> 00:01:22.030
If we multiply the specific heat
00:01:22.030 --> 00:01:24.710
of water by the molar mass of water
00:01:24.710 --> 00:01:29.710
which is 18.0 grams per mole,
00:01:31.000 --> 00:01:36.000
the grams will cancel out
and that gives us 75.2 joules
00:01:39.149 --> 00:01:43.560
per mole degree Celsius.
00:01:43.560 --> 00:01:48.560
And so this is the molar
heat capacity of water.
00:01:49.250 --> 00:01:52.190
Let's say we had 18.0 grams of water.
00:01:52.190 --> 00:01:54.340
If we divide by the molar mass of water
00:01:54.340 --> 00:01:59.210
which is 18.0 grams per
mole, the grams cancel
00:01:59.210 --> 00:02:03.770
and that gives us one
mole of liquid water.
00:02:03.770 --> 00:02:06.300
So one mole of H2O.
00:02:06.300 --> 00:02:09.364
Using the molar heat capacity of water,
00:02:09.364 --> 00:02:14.364
it would take positive 75.2 joules
00:02:14.650 --> 00:02:17.470
of energy to increase the temperature
00:02:17.470 --> 00:02:22.470
of that 18.0 grams of water
by one degree Celsius.
00:02:22.890 --> 00:02:25.640
Next let's calculate how
much heat is necessary
00:02:25.640 --> 00:02:30.000
to warm 250 grams of water
from an initial temperature
00:02:30.000 --> 00:02:32.840
of 22 degrees Celsius
to a final temperature
00:02:32.840 --> 00:02:35.590
of 98 degrees Celsius.
00:02:35.590 --> 00:02:38.830
Using the units for specific heat,
00:02:38.830 --> 00:02:42.420
which are joules per gram degree Celsius.
00:02:42.420 --> 00:02:45.580
We can rewrite the specific heat is equal
00:02:45.580 --> 00:02:50.120
to joules is the quantity
of heat that's transferred.
00:02:50.120 --> 00:02:52.580
So we could just write q for that.
00:02:52.580 --> 00:02:55.690
Grams is the mass of the substance
00:02:55.690 --> 00:02:57.920
and degree Celsius is talking
00:02:57.920 --> 00:03:00.520
about the change in temperature delta T.
00:03:00.520 --> 00:03:04.360
So if we multiply both sides by m delta T,
00:03:04.360 --> 00:03:07.010
we arrive at the following equation
00:03:07.010 --> 00:03:12.010
which is q is equal to mC delta T.
00:03:12.500 --> 00:03:15.160
And we can use this equation
to calculate the heat
00:03:15.160 --> 00:03:17.370
transferred for different substances
00:03:17.370 --> 00:03:20.030
with different specific heats.
00:03:20.030 --> 00:03:23.220
However, right now we're only
interested in our liquid water
00:03:23.220 --> 00:03:26.160
and how much heat it takes
to increase the temperature
00:03:26.160 --> 00:03:29.880
of our water from 22 degrees
Celsius to a final temperature
00:03:29.880 --> 00:03:32.440
of 98 degrees Celsius.
00:03:32.440 --> 00:03:34.370
To find the change in temperature,
00:03:34.370 --> 00:03:36.860
that's equal to the final temperature
00:03:36.860 --> 00:03:39.610
minus the initial temperature
00:03:39.610 --> 00:03:42.480
which would be 98 degrees Celsius
00:03:42.480 --> 00:03:47.480
minus 22 which is equal
to 76 degrees Celsius.
00:03:49.470 --> 00:03:52.210
Next, we can plug everything
into our equation.
00:03:52.210 --> 00:03:54.410
Q is what we're trying to find.
00:03:54.410 --> 00:03:57.887
M is the mass of the
substance, which is 250 grams.
00:03:59.810 --> 00:04:02.410
C is the specific heat of water
00:04:02.410 --> 00:04:06.070
which is 4.18 joules per
gram degrees Celsius,
00:04:06.070 --> 00:04:10.490
and delta T we've just
found is 76 degrees Celsius.
00:04:10.490 --> 00:04:13.830
So let's plug everything
into our equation.
00:04:13.830 --> 00:04:18.830
Q would be equal to,
the mass is 250 grams.
00:04:19.410 --> 00:04:24.410
The specific heat of water is 4.18 joules
00:04:24.880 --> 00:04:28.900
per gram degree Celsius.
00:04:28.900 --> 00:04:33.570
And the change of temperature
is 76 degrees Celsius.
00:04:33.570 --> 00:04:37.720
So looking at that, we can
see that grams will cancel out
00:04:37.720 --> 00:04:42.030
and degrees Celsius will
cancel out and give us,
00:04:42.030 --> 00:04:47.030
q is equal to 79,420 joules
or to two significant figures,
00:04:51.910 --> 00:04:56.910
q is equal to 7.9 times
10 to the fourth joules.
00:04:59.266 --> 00:05:02.810
So 7.9 times 10 to the
fourth joules of energy
00:05:02.810 --> 00:05:05.260
has to be transferred to the water
00:05:05.260 --> 00:05:08.170
to increase the temperature of the water
00:05:08.170 --> 00:05:13.110
from 22 degrees Celsius
to 98 degrees Celsius.
00:05:13.110 --> 00:05:15.670
The specific heat can vary
slightly with temperature.
00:05:15.670 --> 00:05:18.590
So the temperature is often
specified when you're looking
00:05:18.590 --> 00:05:21.180
at a table for specific heats.
00:05:21.180 --> 00:05:22.930
For example, in the left column
00:05:22.930 --> 00:05:24.250
we have different substances,
00:05:24.250 --> 00:05:26.220
on the right column we
have their specific heats
00:05:26.220 --> 00:05:29.090
at 298 Kelvin.
00:05:29.090 --> 00:05:31.030
So we could use for our units
00:05:31.030 --> 00:05:35.220
for specific heat joules
per gram degrees Celsius,
00:05:35.220 --> 00:05:38.920
or we could use joules per gram Kelvin.
00:05:38.920 --> 00:05:43.920
For liquid water, the specific
heat is 4.18 at 298 Kelvin.
00:05:45.180 --> 00:05:50.180
For aluminum, solid aluminum,
the specific heat is 0.90.
00:05:50.430 --> 00:05:54.227
And for solid iron the
specific heat is 0.45
00:05:55.520 --> 00:05:58.310
joules per gram Kelvin.
00:05:58.310 --> 00:06:01.490
Let's compare the two
metals on our table here.
00:06:01.490 --> 00:06:04.780
Let's compare a solid
aluminum and solid iron.
00:06:04.780 --> 00:06:08.053
So we're gonna add 1.0 times 10
00:06:08.053 --> 00:06:13.053
to the second joules of
energy to both metals
00:06:13.560 --> 00:06:17.760
and see what happens in terms
of change in temperature.
00:06:17.760 --> 00:06:20.240
First, let's do the
calculation for aluminum.
00:06:20.240 --> 00:06:22.360
We're doing Q is equal to mC delta T
00:06:22.360 --> 00:06:27.360
and we're adding 1.0 times
10 to the second joules.
00:06:28.140 --> 00:06:32.970
And let's say we had 10
grams of both of our metals.
00:06:32.970 --> 00:06:36.870
So this would be 10.0 grams of aluminum.
00:06:36.870 --> 00:06:39.910
And then we multiply that by
this specific heat of aluminum,
00:06:39.910 --> 00:06:41.565
which is 0.90.
00:06:41.565 --> 00:06:46.565
So 0.90 joules per gram
Kelvin times delta T.
00:06:49.620 --> 00:06:51.500
When we do the math for this,
00:06:51.500 --> 00:06:55.010
the joules will cancel out,
the grams will cancel out
00:06:55.010 --> 00:06:58.100
and we would find that
delta T would be equal
00:06:58.100 --> 00:07:01.800
to 11 Kelvin or 11 degrees Celsius.
00:07:01.800 --> 00:07:05.040
It doesn't really matter
which units you're using here
00:07:05.040 --> 00:07:07.230
for the specific heat.
00:07:07.230 --> 00:07:10.630
Next let's do the same
calculation for iron.
00:07:10.630 --> 00:07:13.380
So we're adding the same amount of heat.
00:07:13.380 --> 00:07:16.410
So 1.0 times 10 to the
second joules of energy.
00:07:16.410 --> 00:07:20.450
So we can plug that in, 1.0 times 10
00:07:20.450 --> 00:07:22.370
to the second joules.
00:07:22.370 --> 00:07:24.090
We're dealing with the same mass
00:07:24.090 --> 00:07:27.710
so we have 10.0 grams of iron
00:07:27.710 --> 00:07:30.280
but this time we're using
these specific heat of iron
00:07:30.280 --> 00:07:35.280
which is 0.45 joules per
gram Kelvin times delta T.
00:07:39.450 --> 00:07:43.380
So once again, joules cancels
out, grams cancels out
00:07:43.380 --> 00:07:48.380
and we get that delta T
is equal to 22 Kelvin,
00:07:49.080 --> 00:07:52.890
or 22 degrees Celsius.
00:07:52.890 --> 00:07:55.380
What we can learn from
doing these two calculations
00:07:55.380 --> 00:07:58.270
is we had the same amount of heat added
00:07:58.270 --> 00:08:00.300
to our two substances
00:08:00.300 --> 00:08:01.980
with the mass of the two substances
00:08:01.980 --> 00:08:05.850
was the same, the difference
was their specific heats.
00:08:05.850 --> 00:08:10.850
So iron has a lower
specific heat than aluminum.
00:08:10.850 --> 00:08:13.840
And since iron has a lower specific heat,
00:08:13.840 --> 00:08:16.540
it's easier to change the
temperature of the iron.
00:08:16.540 --> 00:08:18.870
So the lower the value
for the specific heat,
00:08:18.870 --> 00:08:21.850
the higher the change in the temperature,
00:08:21.850 --> 00:08:24.440
or you could also say the higher the value
00:08:24.440 --> 00:08:25.860
for the specific heat,
00:08:25.860 --> 00:08:28.230
the smaller the change in the temperature,
00:08:28.230 --> 00:08:30.423
and going back to our chart,
00:08:31.651 --> 00:08:35.150
water, liquid water has a
relatively high specific heat
00:08:35.150 --> 00:08:36.960
which means the temperature of water
00:08:36.960 --> 00:08:39.953
is relatively resistant to change.
|
Heat transfer and thermal equilibrium | https://www.youtube.com/watch?v=7jAPitc0bkY | vtt | https://www.youtube.com/api/timedtext?v=7jAPitc0bkY&ei=6VWUZdP4IOzWxN8PyZupyAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=12F81AD19D63AFD9AC84687C1474CCAFDFC328E2.AB71906AB898455C8DA172E9CDB4F13B55CE43A2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.450 --> 00:00:03.360
- [Instructor] Let's say we
have two samples of helium gas.
00:00:03.360 --> 00:00:05.730
One sample of helium
gas is at temperature T1
00:00:06.910 --> 00:00:09.973
and the other sample of helium
gas is at temperature T2.
00:00:10.840 --> 00:00:13.600
If T2 is greater than T1,
00:00:13.600 --> 00:00:15.080
that means on average,
00:00:15.080 --> 00:00:18.780
the particles of helium
gas in the second box
00:00:18.780 --> 00:00:22.550
are moving faster than the
particles of helium gas
00:00:22.550 --> 00:00:24.170
in the first box.
00:00:24.170 --> 00:00:26.020
We can tell the particles
in the second box
00:00:26.020 --> 00:00:28.320
are moving faster because on average,
00:00:28.320 --> 00:00:32.460
the length of these arrows
indicating the velocity vector
00:00:32.460 --> 00:00:34.620
in the box and the right are longer
00:00:34.620 --> 00:00:38.130
than the length of the
arrows in the first box.
00:00:38.130 --> 00:00:40.660
The equation for kinetic energy
00:00:40.660 --> 00:00:44.420
is equal to 1/2 mv squared,
00:00:44.420 --> 00:00:46.450
where m is the mass of a particle
00:00:46.450 --> 00:00:49.330
and v is the velocity of a particle.
00:00:49.330 --> 00:00:51.990
Since the gas particles
in the box on the right
00:00:51.990 --> 00:00:55.660
are on average traveling faster
and have higher velocities,
00:00:55.660 --> 00:00:58.170
the average kinetic energy
00:00:58.170 --> 00:01:01.130
of the particles in the box on the right
00:01:01.130 --> 00:01:03.800
is higher than the average kinetic energy
00:01:03.800 --> 00:01:06.980
for the particles in the box on the left.
00:01:06.980 --> 00:01:08.880
And so the average kinetic energy
00:01:08.880 --> 00:01:11.160
is proportional to the temperature.
00:01:11.160 --> 00:01:12.760
The higher the temperature,
00:01:12.760 --> 00:01:16.993
the higher the average kinetic
energy of the particles.
00:01:18.090 --> 00:01:21.180
Instead of gases, let's
look at two metal blocks
00:01:21.180 --> 00:01:23.050
made of the same material.
00:01:23.050 --> 00:01:25.670
So one of the metal blocks
is at temperature T1
00:01:25.670 --> 00:01:28.890
and the other metal block
is at temperature T2.
00:01:28.890 --> 00:01:32.800
Let's say the temperature
T2 is greater than T1.
00:01:32.800 --> 00:01:36.230
What that means is the
particles in the metal box
00:01:36.230 --> 00:01:39.170
on the right are on average moving faster
00:01:39.170 --> 00:01:42.530
than the particles in the
metal box on the left.
00:01:42.530 --> 00:01:44.970
And that means that the
average kinetic energy
00:01:44.970 --> 00:01:47.620
of the particles in the
box on the right is greater
00:01:47.620 --> 00:01:48.980
than the average kinetic energy
00:01:48.980 --> 00:01:52.393
in the particles in the box on the left.
00:01:53.340 --> 00:01:55.680
Also notice, right now
are two pieces of metal
00:01:55.680 --> 00:01:57.150
are not touching each other.
00:01:57.150 --> 00:01:59.450
So there's a little bit
of space between them.
00:02:00.450 --> 00:02:01.980
Next, we bring the two objects
00:02:01.980 --> 00:02:04.040
and we put them in
contact with each other.
00:02:04.040 --> 00:02:07.410
So now there are collisions
between the particles that touch
00:02:07.410 --> 00:02:10.170
and this results in the transfer of energy
00:02:10.170 --> 00:02:13.550
from the hotter object
to the cooler object.
00:02:13.550 --> 00:02:17.310
So heat flows from the object
at the higher temperature
00:02:17.310 --> 00:02:20.480
to the object at the lower temperature.
00:02:20.480 --> 00:02:24.410
And so the hot atoms in the
metal object on the right
00:02:24.410 --> 00:02:25.860
start to move a little slower,
00:02:25.860 --> 00:02:28.580
whereas the colder atoms
in the metal on the left
00:02:28.580 --> 00:02:30.710
start to move a little bit faster.
00:02:30.710 --> 00:02:33.810
And the transfer of energy continues
00:02:33.810 --> 00:02:38.350
until both objects have
the same final temperature.
00:02:38.350 --> 00:02:42.653
And we say that thermal
equilibrium has been reached.
00:02:43.620 --> 00:02:45.640
So here we have our two objects,
00:02:45.640 --> 00:02:50.070
and the two objects are at
the same final temperature,
00:02:50.070 --> 00:02:53.870
which means we have reached
thermal equilibrium.
00:02:53.870 --> 00:02:55.750
And since we've reached
thermal equilibrium,
00:02:55.750 --> 00:02:58.530
there's no more flow of heat
between the two objects,
00:02:58.530 --> 00:03:02.000
and since both objects are at
the same final temperature,
00:03:02.000 --> 00:03:04.190
that means the average kinetic energy
00:03:04.190 --> 00:03:07.663
of the particles in both
objects is now the same.
|
Representing endothermic and exothermic processes using energy diagrams | https://www.youtube.com/watch?v=LYrpdeXbvdk | vtt | https://www.youtube.com/api/timedtext?v=LYrpdeXbvdk&ei=6VWUZbjXDrukvdIPoc6_uAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=53AD1C077AA21EC83CFCBEC1A4F7FEE7D2C43BA9.064FE4F6467FFD03B973F6B07186287A2D2B0182&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.021 --> 00:00:01.730
- [Instructor] Let's
say we run an experiment
00:00:01.730 --> 00:00:05.510
to determine if a reaction
is endo or exothermic.
00:00:05.510 --> 00:00:10.510
For our hypothetical reaction,
A reaction would B to form C.
00:00:10.580 --> 00:00:13.290
And let's say this reaction
takes place in aqueous solution
00:00:13.290 --> 00:00:15.180
in a beaker.
00:00:15.180 --> 00:00:18.259
We can define our system as
the reactants and products
00:00:18.259 --> 00:00:20.850
that make up our chemical reaction,
00:00:20.850 --> 00:00:23.130
and everything else is
part of the surroundings,
00:00:23.130 --> 00:00:25.475
for example, the water and also the beaker
00:00:25.475 --> 00:00:28.630
the reaction is taking place in.
00:00:28.630 --> 00:00:30.100
Let's say we run the reaction
00:00:30.100 --> 00:00:31.667
and we put our hand on the beaker
00:00:31.667 --> 00:00:34.710
and we feel that the beaker is warm.
00:00:34.710 --> 00:00:35.860
If the beaker is warm
00:00:35.860 --> 00:00:38.700
since the beaker is part
of the surroundings,
00:00:38.700 --> 00:00:41.130
energy must've been
transferred from the system
00:00:41.130 --> 00:00:42.920
to the surrounding.
00:00:42.920 --> 00:00:45.790
So heat flowed from the
system to the surroundings.
00:00:45.790 --> 00:00:49.160
And that's an example of
an exothermic reaction.
00:00:49.160 --> 00:00:53.280
So Delta H is negative.
00:00:53.280 --> 00:00:54.938
We can determine the amount
of energy that flowed
00:00:54.938 --> 00:00:56.700
from the system to the surroundings
00:00:56.700 --> 00:00:58.177
by looking at the energy profile
00:00:58.177 --> 00:01:01.670
for our hypothetical reaction.
00:01:01.670 --> 00:01:04.680
In an energy profile, potential
energy is in the y-axis
00:01:04.680 --> 00:01:06.733
in kilojoules per mole
and reaction to progress
00:01:06.733 --> 00:01:08.980
is on the x-axis.
00:01:08.980 --> 00:01:12.230
So as we move to the right on the x-axis,
00:01:12.230 --> 00:01:14.820
the reaction is occurring.
00:01:14.820 --> 00:01:16.810
Our reactants, which are A and B
00:01:16.810 --> 00:01:18.750
have a certain amount of potential energy.
00:01:18.750 --> 00:01:21.780
So that's right here
on our energy profile.
00:01:21.780 --> 00:01:25.350
So that part represents the
energy of our reactants.
00:01:25.350 --> 00:01:28.000
Our reactants react
together to form our product
00:01:28.000 --> 00:01:30.840
which is C and that's at the very end.
00:01:30.840 --> 00:01:34.480
So over here, this line
represents the energy
00:01:34.480 --> 00:01:37.533
the potential energy of our products.
00:01:38.530 --> 00:01:41.320
Notice how the potential
energy of our reactants
00:01:41.320 --> 00:01:43.800
is higher than the potential
energy of the product.
00:01:43.800 --> 00:01:46.900
So if we were to find
the change in energy,
00:01:46.900 --> 00:01:49.070
that would be the final minus the initial.
00:01:49.070 --> 00:01:52.760
So the energy of the
products minus the energy
00:01:52.760 --> 00:01:56.120
of the reactance for this energy profile,
00:01:56.120 --> 00:02:00.100
the energy of the products is
about 50 kilojoules per mole,
00:02:00.100 --> 00:02:03.310
and the potential energy
of our reactance is at 100.
00:02:03.310 --> 00:02:06.946
So this would be 50 minus 100
00:02:06.946 --> 00:02:11.946
which is equal to negative
50 kilojoules per mole.
00:02:15.470 --> 00:02:18.470
So on our energy profile,
we could show Delta E
00:02:18.470 --> 00:02:20.940
which would be this difference right here.
00:02:20.940 --> 00:02:23.300
So that represents Delta E
00:02:23.300 --> 00:02:27.374
and the change in energy Delta
E is also equal to the change
00:02:27.374 --> 00:02:32.374
in the enthalpy Delta H for this reaction.
00:02:32.730 --> 00:02:34.530
So we know that the change in enthalpy
00:02:34.530 --> 00:02:37.900
is equal to negative 50
kilojoules per moles.
00:02:37.900 --> 00:02:41.660
Let's go ahead and plug that
in over here on the left.
00:02:41.660 --> 00:02:44.180
So by feeling the outside of the beaker,
00:02:44.180 --> 00:02:47.150
we knew that the reaction was exothermic,
00:02:47.150 --> 00:02:49.100
but the energy profile
allowed us to figure out
00:02:49.100 --> 00:02:53.220
how much energy was
transferred from the system
00:02:53.220 --> 00:02:55.510
to the surroundings.
00:02:55.510 --> 00:02:58.560
So for an energy profile, when
the energy of the reactants
00:02:58.560 --> 00:03:01.180
is higher than the energy of the products,
00:03:01.180 --> 00:03:05.300
this is the energy profile
for an exothermic reaction.
00:03:05.300 --> 00:03:07.460
Let's say we ran a similar reaction
00:03:07.460 --> 00:03:10.090
where A plus B turned into C,
00:03:10.090 --> 00:03:11.780
but this time when we felt the beaker,
00:03:11.780 --> 00:03:14.620
the beaker felt cool to the touch.
00:03:14.620 --> 00:03:16.400
If that's the case, it's because energy
00:03:16.400 --> 00:03:21.150
was being transferred from the
surroundings to the system.
00:03:21.150 --> 00:03:23.920
And since these surroundings
was losing energy,
00:03:23.920 --> 00:03:27.000
that's why the beaker felt cool.
00:03:27.000 --> 00:03:29.840
So heat flows from the
surroundings to the system,
00:03:29.840 --> 00:03:33.400
and this occurs in an endothermic reaction
00:03:33.400 --> 00:03:36.940
and the change in entropy,
Delta H is positive
00:03:36.940 --> 00:03:39.810
for an endothermic process.
00:03:39.810 --> 00:03:41.123
When we look at the energy profile
00:03:41.123 --> 00:03:43.740
for an endothermic reaction.
00:03:43.740 --> 00:03:46.280
The energy of the reactants.
00:03:46.280 --> 00:03:48.300
So go ahead and write reactants in here.
00:03:48.300 --> 00:03:50.990
The energy of the reactants is lower
00:03:50.990 --> 00:03:54.083
than the energy of the products.
00:03:56.343 --> 00:03:59.313
So this time, if we find Delta E
00:03:59.313 --> 00:04:03.000
that would be the energy of our products
00:04:03.000 --> 00:04:06.210
minus the energy of our reactants.
00:04:06.210 --> 00:04:07.710
And the energy of our products
00:04:07.710 --> 00:04:11.050
is about 100 kilojoules per mole
00:04:11.050 --> 00:04:13.528
and the energy of our
reactants is about 50.
00:04:13.528 --> 00:04:16.600
So let's say it's 100 minus 50,
00:04:16.600 --> 00:04:21.513
which would be positive
50 kilojoules per mole.
00:04:24.890 --> 00:04:28.840
So on our diagram if we represent Delta E,
00:04:28.840 --> 00:04:32.520
that would be this difference
here on the energy profile.
00:04:32.520 --> 00:04:36.998
And once again, Delta E
is equal to the change
00:04:36.998 --> 00:04:41.600
in the enthalpy Delta H for the reaction.
00:04:41.600 --> 00:04:44.230
So Delta H for this hypothetical reaction
00:04:44.230 --> 00:04:48.583
is positive 50 kilojoules per mole.
00:04:51.310 --> 00:04:52.369
Since Delta H is positive,
00:04:52.369 --> 00:04:54.794
we know that energy was
transferred from the surroundings
00:04:54.794 --> 00:04:56.690
to the system.
00:04:56.690 --> 00:04:58.550
And that's the reason why the products
00:04:58.550 --> 00:05:01.890
have a higher potential
energy than the reactants
00:05:01.890 --> 00:05:03.663
in our energy diagram.
|
Endothermic and exothermic processes | https://www.youtube.com/watch?v=JPxTgtUx9sE | vtt | https://www.youtube.com/api/timedtext?v=JPxTgtUx9sE&ei=6VWUZYr7Grysp-oPuuW7OA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=11EE172BBDCB3CDC152BA939FA6D3941DD691171.92B98263E2266C37DA3FD169359537443E64ECE2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.400 --> 00:00:02.660
- [Educator] Before we get into the terms,
00:00:02.660 --> 00:00:04.090
endo and exothermic,
00:00:04.090 --> 00:00:06.480
We need to look at some
other thermodynamics terms
00:00:06.480 --> 00:00:07.590
that are used.
00:00:07.590 --> 00:00:09.060
For example, system.
00:00:09.060 --> 00:00:12.520
The system refers to
the part of the universe
00:00:12.520 --> 00:00:14.270
that we are studying.
00:00:14.270 --> 00:00:17.770
For our example, we're going
to consider a monatomic gas.
00:00:17.770 --> 00:00:21.460
Let's say we have some helium
particles in a container.
00:00:21.460 --> 00:00:24.970
And the helium gas represents our system.
00:00:24.970 --> 00:00:28.440
The surroundings are everything
else in the universe.
00:00:28.440 --> 00:00:31.548
So that would include this piston here
00:00:31.548 --> 00:00:33.080
and the cylinder
00:00:33.080 --> 00:00:34.580
in which the gas is in.
00:00:34.580 --> 00:00:37.720
And the universe consists
of both the system
00:00:37.720 --> 00:00:39.723
and the surroundings.
00:00:40.670 --> 00:00:43.890
Next, let's look at the
first law of thermodynamics
00:00:43.890 --> 00:00:45.080
which can be summarized
00:00:45.080 --> 00:00:47.060
by writing delta E is equal
00:00:47.060 --> 00:00:49.100
to Q plus W.
00:00:49.100 --> 00:00:52.470
Delta E is the change
in the internal energy
00:00:52.470 --> 00:00:53.620
of the system.
00:00:53.620 --> 00:00:56.460
And the internal energy refers to the sum
00:00:56.460 --> 00:00:59.510
of all the kinetic and potential energies
00:00:59.510 --> 00:01:01.750
of the components of the system.
00:01:01.750 --> 00:01:05.580
Since we have a monatomic
gas for our system,
00:01:05.580 --> 00:01:07.900
we only have kinetic energy.
00:01:07.900 --> 00:01:10.670
So if you could imagine
adding up the kinetic energy
00:01:10.670 --> 00:01:12.140
for each particle,
00:01:12.140 --> 00:01:14.910
the sum of those kinetic
energies for this example
00:01:14.910 --> 00:01:17.450
would be equal to the internal energy
00:01:17.450 --> 00:01:18.910
of the system.
00:01:18.910 --> 00:01:21.490
Q refers to the heat
00:01:21.490 --> 00:01:24.640
that's transferred from the system.
00:01:24.640 --> 00:01:28.270
So it's either transferred
to or from the system.
00:01:28.270 --> 00:01:31.730
And W refers to the work done on
00:01:31.730 --> 00:01:33.253
or by the system.
00:01:34.440 --> 00:01:36.080
Let's look at the sign conventions
00:01:36.080 --> 00:01:38.300
for the first law of thermodynamics.
00:01:38.300 --> 00:01:40.030
When we think about Q;
00:01:40.030 --> 00:01:43.930
when heat flows into the
system from the surroundings,
00:01:43.930 --> 00:01:47.750
we say that Q is positive.
00:01:47.750 --> 00:01:49.740
When heat flows out of the system
00:01:49.740 --> 00:01:51.520
and into the surroundings,
00:01:51.520 --> 00:01:54.943
we say that Q is negative.
00:01:56.270 --> 00:01:59.530
For work, when work is done on the system
00:01:59.530 --> 00:02:01.080
by the surroundings,
00:02:01.080 --> 00:02:03.610
the work is positive.
00:02:03.610 --> 00:02:05.070
But if work is done
00:02:05.070 --> 00:02:07.420
by the system on the surroundings,
00:02:07.420 --> 00:02:10.400
work is negative.
00:02:10.400 --> 00:02:12.840
It's very useful to think
about internal energy
00:02:12.840 --> 00:02:14.240
like a bank account.
00:02:14.240 --> 00:02:15.900
So if Q is positive
00:02:15.900 --> 00:02:17.520
and work is positive,
00:02:17.520 --> 00:02:20.950
that's like money coming
into your bank account.
00:02:20.950 --> 00:02:22.440
But if Q is negative
00:02:22.440 --> 00:02:23.800
or the work is negative,
00:02:23.800 --> 00:02:26.983
that's like money leaving
your bank account.
00:02:28.040 --> 00:02:30.610
Let's look at an example of
the first law of thermodynamics
00:02:30.610 --> 00:02:32.460
using our sample of helium
00:02:32.460 --> 00:02:33.640
that's in a cylinder
00:02:33.640 --> 00:02:35.720
with a movable piston.
00:02:35.720 --> 00:02:40.150
So let's say that 6,000 joules of energy.
00:02:40.150 --> 00:02:45.150
So 6,000 joules flows from the
surroundings into the system.
00:02:47.290 --> 00:02:49.950
And that heats up our helium particles,
00:02:49.950 --> 00:02:50.980
which then expand
00:02:50.980 --> 00:02:53.800
and push the piston up.
00:02:53.800 --> 00:02:56.580
So the piston gets pushed up,
00:02:56.580 --> 00:03:01.310
which is the system doing
work on the surroundings.
00:03:01.310 --> 00:03:03.660
And let's say that,
00:03:03.660 --> 00:03:08.300
that's 2000 joules of work done
00:03:08.300 --> 00:03:11.550
by the system on the surroundings.
00:03:11.550 --> 00:03:13.230
Using our assigned conventions,
00:03:13.230 --> 00:03:17.210
since heat flowed into the
system from the surroundings,
00:03:17.210 --> 00:03:19.520
that's a positive value for Q.
00:03:19.520 --> 00:03:22.020
And since the work was done
00:03:22.020 --> 00:03:24.380
by the system on the surroundings,
00:03:24.380 --> 00:03:26.650
that's a negative for the work done.
00:03:26.650 --> 00:03:28.200
So we can go ahead and plug in
00:03:28.200 --> 00:03:31.190
to the first law of thermodynamics.
00:03:31.190 --> 00:03:35.080
The heat transferred is
positive 6,000 joules
00:03:35.080 --> 00:03:40.080
and the work done as negative 2000 joules,
00:03:40.480 --> 00:03:42.100
therefore delta E
00:03:42.100 --> 00:03:45.290
or the change in the
internal energy is equal
00:03:45.290 --> 00:03:49.373
to positive 4,000 joules.
00:03:50.220 --> 00:03:53.430
Thinking about internal
energy like our bank account,
00:03:53.430 --> 00:03:56.100
we've gained 4,000 joules.
00:03:56.100 --> 00:03:59.190
So that could be like gaining $4,000.
00:03:59.190 --> 00:04:02.360
Since the system has gained 4,000 joules,
00:04:02.360 --> 00:04:06.690
that must mean the surroundings
has lost 4,000 joules.
00:04:06.690 --> 00:04:08.210
But since energy is conserved,
00:04:08.210 --> 00:04:12.180
the total energy of the
universe remains constant.
00:04:12.180 --> 00:04:14.240
Let's apply the first
law of thermodynamics
00:04:14.240 --> 00:04:16.420
to the combustion of propane
00:04:16.420 --> 00:04:19.360
and an open container
at constant pressure.
00:04:19.360 --> 00:04:20.680
For the combustion of propane,
00:04:20.680 --> 00:04:22.950
the reactants and products
00:04:22.950 --> 00:04:25.150
for the combustion reaction are considered
00:04:25.150 --> 00:04:26.280
to be the system,
00:04:26.280 --> 00:04:29.720
and everything else is the surroundings.
00:04:29.720 --> 00:04:34.400
So this combustion reaction
gives off 2,044 kilojoules
00:04:34.400 --> 00:04:35.380
of energy.
00:04:35.380 --> 00:04:38.160
So that's the heat that's
transferred from the system
00:04:38.160 --> 00:04:39.840
to the surroundings.
00:04:39.840 --> 00:04:43.020
The system also does
two kilojoules of work
00:04:43.020 --> 00:04:44.420
on the surroundings.
00:04:44.420 --> 00:04:47.140
So by convention, we make that negative.
00:04:47.140 --> 00:04:49.610
To find the change in the
internal energy of the system,
00:04:49.610 --> 00:04:51.450
we add Q plus W
00:04:51.450 --> 00:04:56.250
and get negative 2,046 kilojoules.
00:04:57.690 --> 00:04:59.220
Since this reaction was carried out
00:04:59.220 --> 00:05:01.090
under constant external pressure,
00:05:01.090 --> 00:05:03.960
we can write Q sub P here.
00:05:03.960 --> 00:05:07.330
So Q sub P is the heat
00:05:07.330 --> 00:05:10.280
that's transferred at constant pressure,
00:05:10.280 --> 00:05:14.690
and that is equal to the
change in the enthalpy,
00:05:14.690 --> 00:05:18.230
which is symbolized by delta H.
00:05:18.230 --> 00:05:20.550
So the change in enthalpy is the heat
00:05:20.550 --> 00:05:23.600
that's transferred at constant pressure.
00:05:23.600 --> 00:05:25.150
So the change in enthalpy
00:05:25.150 --> 00:05:26.920
for the combustion of propane is equal
00:05:26.920 --> 00:05:31.570
to negative 2,044 kilojoules.
00:05:31.570 --> 00:05:35.280
And notice how the change
in enthalpy is almost
00:05:35.280 --> 00:05:38.800
the same value as the change
in the internal energy.
00:05:38.800 --> 00:05:42.060
So the work done by the
system is a very small amount
00:05:42.060 --> 00:05:42.893
in this case,
00:05:42.893 --> 00:05:44.090
and that's usually the case.
00:05:44.090 --> 00:05:46.710
And since most chemical reactions are done
00:05:46.710 --> 00:05:48.700
under constant pressure,
00:05:48.700 --> 00:05:52.270
chemists care more about
the change in the enthalpy
00:05:52.270 --> 00:05:55.870
than they do about the change
in the internal energy.
00:05:55.870 --> 00:05:57.980
When delta H is negative,
00:05:57.980 --> 00:06:00.530
we call that an exothermic process.
00:06:00.530 --> 00:06:04.733
So the combustion of propane
is an exothermic reaction.
00:06:05.810 --> 00:06:09.390
An endothermic process is
where heat is transferred
00:06:09.390 --> 00:06:11.890
from the surroundings to the systems.
00:06:11.890 --> 00:06:16.310
So the system has gained
heat from the surroundings.
00:06:16.310 --> 00:06:17.520
The change in enthalpy,
00:06:17.520 --> 00:06:21.060
delta H is positive for
an endothermic process.
00:06:21.060 --> 00:06:24.880
An example could be melting an ice cube.
00:06:24.880 --> 00:06:28.230
If heat flows from the
system to the surroundings,
00:06:28.230 --> 00:06:30.890
the system has released
heat to the surroundings,
00:06:30.890 --> 00:06:32.230
and the change in enthalpy,
00:06:32.230 --> 00:06:34.190
delta H is negative.
00:06:34.190 --> 00:06:36.930
And we call this an exothermic process.
00:06:36.930 --> 00:06:38.810
And we already saw an example of that.
00:06:38.810 --> 00:06:43.240
The combustion of propane
is an exothermic reaction.
00:06:43.240 --> 00:06:44.980
So a phase change could be an endo
00:06:44.980 --> 00:06:46.800
or an exothermic process.
00:06:46.800 --> 00:06:49.010
A chemical reaction could also be an endo
00:06:49.010 --> 00:06:50.890
or an exothermic process.
00:06:50.890 --> 00:06:54.370
And even the formation of a
solution could be classified
00:06:54.370 --> 00:06:57.690
as an endo or an exothermic process.
00:06:57.690 --> 00:06:59.740
Let's think about making a solution.
00:06:59.740 --> 00:07:01.440
So let's say that we have a beaker
00:07:01.440 --> 00:07:03.040
and we have it full of water,
00:07:03.040 --> 00:07:04.770
and we take a solid
00:07:04.770 --> 00:07:07.350
and we dissolve the solid in the water
00:07:07.350 --> 00:07:10.240
to form a solution.
00:07:10.240 --> 00:07:12.853
If the dissolution process
is an exothermic process,
00:07:14.470 --> 00:07:17.510
that means the system releases heat
00:07:17.510 --> 00:07:18.640
to the surroundings.
00:07:18.640 --> 00:07:21.270
And since the beaker is
part of the surroundings,
00:07:21.270 --> 00:07:23.630
if we were to put our hand on the beaker
00:07:23.630 --> 00:07:25.250
and the beaker feels hot,
00:07:25.250 --> 00:07:26.740
we know that the disillusion
00:07:26.740 --> 00:07:30.283
of this particular solid
is an exothermic process.
00:07:31.140 --> 00:07:33.850
If we do the same thing
with another solid;
00:07:33.850 --> 00:07:36.740
so we dissolve this solid in water
00:07:36.740 --> 00:07:37.960
to form a solution.
00:07:37.960 --> 00:07:40.320
And we put our hand on the beaker,
00:07:40.320 --> 00:07:42.510
and this time the beaker feels cold.
00:07:42.510 --> 00:07:44.360
The reason the beaker feels cold is
00:07:44.360 --> 00:07:46.830
because energy was transferred
from their surroundings
00:07:46.830 --> 00:07:48.390
to the system.
00:07:48.390 --> 00:07:51.660
And so, the surroundings lost energy.
00:07:51.660 --> 00:07:53.780
And so, therefore we
can say the dissolution
00:07:53.780 --> 00:07:58.683
of this particular solid
was an endothermic process.
|
Representing systems of equations with matrices | https://www.youtube.com/watch?v=V8lIpRHjthk | vtt | https://www.youtube.com/api/timedtext?v=V8lIpRHjthk&ei=6VWUZdLWGqKIp-oP-cSGmAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E71A96F5903E4F4DCFEFBDDB542B1E8828062D17.6386D4E066DAC2A631BF228A4774D82D8008C7B4&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.370 --> 00:00:02.450
- [Instructor] I'm a big fan
of looking at the same problem
00:00:02.450 --> 00:00:05.360
in different ways or different
ways to conceptualize them.
00:00:05.360 --> 00:00:08.210
And so, for example, if I had
a system of three equations
00:00:08.210 --> 00:00:10.290
with three unknowns,
let me just make one up,
00:00:10.290 --> 00:00:15.290
3x - 2y - z = -1,
00:00:15.620 --> 00:00:16.790
that's one equation.
00:00:16.790 --> 00:00:19.090
And in three dimensions,
this would represent a plane.
00:00:19.090 --> 00:00:20.240
And then I have another one,
00:00:20.240 --> 00:00:25.240
2x + 5y + z = 0.
00:00:25.480 --> 00:00:27.500
That would represent another plane.
00:00:27.500 --> 00:00:29.950
Now, if you had two non-parallel planes,
00:00:29.950 --> 00:00:32.850
they would intersect each
other and form a line.
00:00:32.850 --> 00:00:36.100
But then if we have a fourth
plane, so let me write that
00:00:36.100 --> 00:00:41.100
as -4x - y = 8, it's possible,
00:00:41.830 --> 00:00:43.260
not always going to be the case,
00:00:43.260 --> 00:00:45.840
but it's possible that
they will all intersect
00:00:45.840 --> 00:00:49.780
in exactly one x,y,z-coordinate.
00:00:49.780 --> 00:00:52.110
And so, in other videos, we talk about
00:00:52.110 --> 00:00:54.400
solving systems of equations like this,
00:00:54.400 --> 00:00:57.500
with three equations and three unknowns.
00:00:57.500 --> 00:00:59.950
Now, what I want to do in this
video is connect this idea
00:00:59.950 --> 00:01:03.580
to the notion of matrices
and matrix multiplication,
00:01:03.580 --> 00:01:06.330
which we've already
reviewed in other videos.
00:01:06.330 --> 00:01:09.180
So we can think of this exact same problem
00:01:09.180 --> 00:01:10.390
in the following way.
00:01:10.390 --> 00:01:12.290
If we take all of the coefficients
00:01:12.290 --> 00:01:15.400
and we create a three by
three matrix with them,
00:01:15.400 --> 00:01:16.930
So let me do that.
00:01:16.930 --> 00:01:20.020
So for example, let me get
all of the x-coefficients,
00:01:20.020 --> 00:01:22.820
a 3, a 2 and a -4,
00:01:22.820 --> 00:01:27.820
and I'll put it in this first
column here, 3, 2 and -4.
00:01:28.350 --> 00:01:30.156
Let me get all the y-coefficients,
00:01:30.156 --> 00:01:34.832
- 2, 5 and essentially a -1.
00:01:34.832 --> 00:01:37.920
- 2, 5 and a -1.
00:01:37.920 --> 00:01:39.350
And then last but not least,
00:01:39.350 --> 00:01:40.770
all the coefficients on the z's,
00:01:40.770 --> 00:01:44.850
a -1, a +1 and then there's
implicitly a 0z here.
00:01:44.850 --> 00:01:45.970
You can't see it.
00:01:45.970 --> 00:01:50.170
So it would be -1, +1 and then a 0.
00:01:50.170 --> 00:01:52.030
So these are the
coefficients on x in purple,
00:01:52.030 --> 00:01:55.300
on y in yellow and in like a salmon color
00:01:55.300 --> 00:01:57.100
for the z's right over here.
00:01:57.100 --> 00:01:59.410
If we said that that is
going to be multiplied
00:01:59.410 --> 00:02:02.833
by a three-dimensional vector,
00:02:04.320 --> 00:02:08.730
that is, I guess we could
say, unknown, x, y and z,
00:02:08.730 --> 00:02:09.700
that is going to be equal
00:02:09.700 --> 00:02:12.980
to a second three-dimensional
vector, which we do know,
00:02:12.980 --> 00:02:17.090
and that's -1, 0 and 8.
00:02:17.090 --> 00:02:18.740
And I know there's a
lot of things going on
00:02:18.740 --> 00:02:19.730
in your brain right now.
00:02:19.730 --> 00:02:21.570
You're like, Sal, this
looks somewhat magical.
00:02:21.570 --> 00:02:24.680
You just took the coefficients,
put the x,y,z's here,
00:02:24.680 --> 00:02:27.540
put the right-hand sides of
the equal sign, in this case,
00:02:27.540 --> 00:02:29.320
the sides that didn't
have the variables on it,
00:02:29.320 --> 00:02:30.240
put it over here.
00:02:30.240 --> 00:02:32.950
Does this actually make sense?
Does this actually work?
00:02:32.950 --> 00:02:36.010
And to validate that,
let's actually multiply out
00:02:36.010 --> 00:02:39.270
the left-hand side of this
equation right over here.
00:02:39.270 --> 00:02:41.130
So in other videos, we've talked about
00:02:41.130 --> 00:02:44.280
multiplying a three by three matrix
00:02:44.280 --> 00:02:48.110
times a, in this case,
a three by one matrix,
00:02:48.110 --> 00:02:51.060
and this is going to actually
give us a three by one matrix.
00:02:51.060 --> 00:02:52.980
So that's looking good already,
00:02:52.980 --> 00:02:57.200
and the reason why we know
that is these two have to match
00:02:57.200 --> 00:02:59.500
in order for the multiplication
to even be defined.
00:02:59.500 --> 00:03:01.560
And then, the dimensions of the product
00:03:01.560 --> 00:03:03.930
are going to be three by one.
00:03:03.930 --> 00:03:06.310
But let's actually multiply things out.
00:03:06.310 --> 00:03:08.550
Well, we know one way to construct this,
00:03:08.550 --> 00:03:11.300
I'm just gonna focus on
the left-hand side here,
00:03:11.300 --> 00:03:12.620
is to say, all right,
00:03:12.620 --> 00:03:17.380
let's essentially take
this row and this column
00:03:17.380 --> 00:03:19.210
and then take the sum of the product
00:03:19.210 --> 00:03:21.760
of the corresponding terms,
I guess you could say.
00:03:21.760 --> 00:03:25.880
So this is gonna be 3
times x, which is 3x,
00:03:25.880 --> 00:03:27.900
minus 2 times y, -2y,
00:03:29.376 --> 00:03:30.970
minus 1 times z, -1z, like that.
00:03:35.270 --> 00:03:38.750
And then, the next one, I'm going to take
00:03:38.750 --> 00:03:42.580
all of this business and
multiply it by this column.
00:03:42.580 --> 00:03:43.810
So it's gonna be 2 times x,
00:03:43.810 --> 00:03:46.710
and this is just a review
of multiplying matrices,
00:03:46.710 --> 00:03:49.513
plus 5 times y, plus 5y,
00:03:50.410 --> 00:03:53.643
plus 1 times z, plus 1z.
00:03:55.100 --> 00:03:58.560
And then last but not
least, if I take this
00:03:58.560 --> 00:04:00.840
and I do the same thing with that column,
00:04:00.840 --> 00:04:05.840
gonna be -4 times x, -4x, minus 1 times y
00:04:06.300 --> 00:04:09.650
minus, I can just write
-y, and then 0 times z,
00:04:09.650 --> 00:04:11.970
which I could write if
I want to or not write,
00:04:11.970 --> 00:04:12.803
but I could write it.
00:04:12.803 --> 00:04:14.280
So let me just write it
to make things clear.
00:04:14.280 --> 00:04:16.830
And so, the product of what
we have on the left-hand side
00:04:16.830 --> 00:04:18.460
is this right over here.
00:04:18.460 --> 00:04:20.620
And it might look like a three by three,
00:04:20.620 --> 00:04:22.760
but it's actually a three by one here,
00:04:22.760 --> 00:04:25.800
where this would eval..., if
you knew what x, y and z is,
00:04:25.800 --> 00:04:28.400
this is going to evaluate to some number.
00:04:28.400 --> 00:04:32.560
Likewise, this is going to
evaluate to some other number,
00:04:32.560 --> 00:04:34.730
and this is going to
evaluate to another number.
00:04:34.730 --> 00:04:37.180
And we know, from this,
I guess you could say,
00:04:37.180 --> 00:04:40.450
matrix vector or this matrix
equation that we have set up,
00:04:40.450 --> 00:04:43.720
that this, the left-hand
side, this product,
00:04:43.720 --> 00:04:47.630
needs to be equal to what we
have on the right-hand side.
00:04:47.630 --> 00:04:52.470
It needs to be equal to -1, 0 and 8,
00:04:52.470 --> 00:04:54.960
which means, and I think
things might be connecting
00:04:54.960 --> 00:04:58.950
for you now, that this
needs to be equal to that,
00:04:58.950 --> 00:05:03.160
and that this needs to be equal to that,
00:05:03.160 --> 00:05:06.370
and last but not least, -4x - y + 0z
00:05:06.370 --> 00:05:07.600
needs to be equal to eight,
00:05:07.600 --> 00:05:09.750
which is exactly what that original system
00:05:09.750 --> 00:05:11.620
of equations was telling us.
00:05:11.620 --> 00:05:14.040
Now, I know, well, there's
still probably some things
00:05:14.040 --> 00:05:16.020
that are circulating in your mind.
00:05:16.020 --> 00:05:18.860
One question is, well, that's all nice,
00:05:18.860 --> 00:05:21.460
you found a different
way of representing that,
00:05:21.460 --> 00:05:24.800
but how do, does this introduce
a new way of solving this?
00:05:24.800 --> 00:05:26.780
And the answer I'll
give you for now is yes,
00:05:26.780 --> 00:05:29.690
it will lead to a new way of solving this.
00:05:29.690 --> 00:05:31.780
Because if you think about
it, we're taking the product
00:05:31.780 --> 00:05:34.890
of a matrix and a vector
here to get another vector.
00:05:34.890 --> 00:05:36.360
If there's some way to essentially
00:05:36.360 --> 00:05:40.790
unwind this matrix multiplication,
then you might be able
00:05:40.790 --> 00:05:43.590
to do that, apply it to
this vector on the right,
00:05:43.590 --> 00:05:46.850
and then solve for this
unknown vector here.
00:05:46.850 --> 00:05:49.010
And that's the way that
things like a computer,
00:05:49.010 --> 00:05:52.360
a lot of computer algorithms,
actually try to solve problems
00:05:52.360 --> 00:05:56.450
like this, by representing
them as matrices.
00:05:56.450 --> 00:05:57.720
Now, another interesting thing
00:05:57.720 --> 00:05:59.890
just with the representation itself
00:05:59.890 --> 00:06:01.650
is it makes you think about the problem
00:06:01.650 --> 00:06:03.300
a little bit differently.
00:06:03.300 --> 00:06:07.420
You could view this as three
planes in three dimensions
00:06:07.420 --> 00:06:10.210
and what is the x,y,z-coordinates
00:06:10.210 --> 00:06:11.740
where they could intersect,
00:06:11.740 --> 00:06:14.720
or you could view this
three by three matrix here
00:06:14.720 --> 00:06:16.790
as a transformation matrix
00:06:16.790 --> 00:06:19.160
that's applying to, is being applied to
00:06:19.160 --> 00:06:21.740
some unknown three-dimensional vector,
00:06:21.740 --> 00:06:23.480
and under transformation,
00:06:23.480 --> 00:06:25.140
that unknown three-dimensional vector
00:06:25.140 --> 00:06:28.159
is equal to this known
three-dimensional vector,
00:06:28.159 --> 00:06:30.580
- 1, 0 and 8.
00:06:30.580 --> 00:06:32.810
And so the question of
solving this would say,
00:06:32.810 --> 00:06:36.580
all right, can we somehow
perform a reverse transformation,
00:06:36.580 --> 00:06:38.740
an inverse transformation, so to speak,
00:06:38.740 --> 00:06:40.860
on the right-hand side to figure out
00:06:40.860 --> 00:06:43.410
what that unknown vector really is?
00:06:43.410 --> 00:06:44.660
And I'll just leave you there,
00:06:44.660 --> 00:06:48.463
and we'll continue that line
of thought in future videos.
|
Invertible matrices and transformations | https://www.youtube.com/watch?v=S278zOWSsZM | vtt | https://www.youtube.com/api/timedtext?v=S278zOWSsZM&ei=6VWUZY6nG924mLAPnv6O8AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=BBDA54086CD074A4D822115DFF808989896D02AC.93AD462EBAA5FE467A24AB988B2F5551ECA06EDA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:02.680
- We have two by two matrices here
00:00:02.680 --> 00:00:05.630
and in other videos we talk
about how a two by two matrix
00:00:05.630 --> 00:00:10.170
can represent a transformation
of the coordinate plane
00:00:10.170 --> 00:00:11.400
of the two dimensional plane
00:00:11.400 --> 00:00:13.100
where this of course is the x-axis
00:00:13.100 --> 00:00:16.270
and this of course is the y-axis.
00:00:16.270 --> 00:00:18.150
What we're doing in
this video is visualize
00:00:18.150 --> 00:00:20.560
these transformations and
get a visual understanding
00:00:20.560 --> 00:00:24.010
for why it's reasonable
for A to have an inverse
00:00:24.010 --> 00:00:26.000
or for why matrix A is invertible
00:00:26.000 --> 00:00:27.670
and why it's not reasonable
00:00:27.670 --> 00:00:30.280
for B to have an inverse matrix
00:00:30.280 --> 00:00:32.950
or why matrix B is not invertible.
00:00:32.950 --> 00:00:35.060
So just as a reminder transformation
00:00:35.060 --> 00:00:36.800
these transformation matrices
00:00:36.800 --> 00:00:40.020
essentially tell us what to
do with our unit vectors.
00:00:40.020 --> 00:00:43.700
For example, we have
the one zero unit vector
00:00:43.700 --> 00:00:45.840
and the first column of
each of these matrices
00:00:45.840 --> 00:00:49.000
tell us what the one zero unit vector
00:00:49.000 --> 00:00:51.560
the vector that goes one
unit in the extraction
00:00:51.560 --> 00:00:53.120
what it will get transformed
00:00:53.120 --> 00:00:55.470
to under each of these transformations
00:00:55.470 --> 00:00:59.160
and then of course you have
the unit vector in the Y
00:00:59.160 --> 00:01:02.430
direction the zero one unit
vector and the second columns
00:01:02.430 --> 00:01:05.270
here tell us how we would transform that.
00:01:05.270 --> 00:01:09.410
So let's first think about
matrix A, matrix A transforms
00:01:09.410 --> 00:01:12.910
the one zero vector
into the two, one vector
00:01:12.910 --> 00:01:16.600
so the two, one vector is going
to look something like that
00:01:16.600 --> 00:01:18.860
and it transforms the zero one vector
00:01:18.860 --> 00:01:21.740
into the two, three vector
so the two three vector
00:01:21.740 --> 00:01:23.820
is going to look something like this.
00:01:23.820 --> 00:01:27.000
So one way to think about
it instead of our grid
00:01:27.000 --> 00:01:29.020
looking like this grid
that I already had here
00:01:29.020 --> 00:01:31.220
which is just our
standard coordinate axes.
00:01:31.220 --> 00:01:36.220
This is defining a new grid
that would look like this
00:01:36.220 --> 00:01:39.120
and I define this new grid
by looking at our multiples
00:01:39.120 --> 00:01:42.830
of what the one zero vector
has been transformed into
00:01:42.830 --> 00:01:46.360
and we also look at multiples
of what the zero one vector
00:01:46.360 --> 00:01:48.390
has been transformed into.
00:01:48.390 --> 00:01:53.040
So for example, if I were to
take this point right here
00:01:53.040 --> 00:01:56.160
before it is transformed
it has one of each of these
00:01:56.160 --> 00:02:00.570
vectors, well under this
first transformation
00:02:00.570 --> 00:02:03.660
it would be one of each of these vectors.
00:02:03.660 --> 00:02:06.440
So it's going to be one two one vector
00:02:06.440 --> 00:02:11.440
plus one two three vector
so this point will be mapped
00:02:11.780 --> 00:02:15.010
to this point and by that
same logic this point
00:02:15.010 --> 00:02:19.010
right over here which is one
unit more in the extraction
00:02:19.010 --> 00:02:21.490
well now it's going to have one unit more
00:02:21.490 --> 00:02:25.640
in the direction that the X unit vector
00:02:25.640 --> 00:02:28.730
has been transformed into
this point right over here
00:02:28.730 --> 00:02:33.090
by the same logic will be one
unit more in the direction
00:02:33.090 --> 00:02:35.540
that the Y unit vector
has been transformed into
00:02:35.540 --> 00:02:36.640
so it will be there.
00:02:36.640 --> 00:02:39.490
And that this point by the
same logic will be transformed
00:02:39.490 --> 00:02:42.900
into that point and so this
region that I'm showing you
00:02:42.900 --> 00:02:46.453
in white will get
transformed to this region.
00:02:47.610 --> 00:02:50.360
Now there's some obvious
things going on here.
00:02:50.360 --> 00:02:53.100
We have a two dimensional
area that has been transformed
00:02:53.100 --> 00:02:56.090
to another two dimensional
area and in fact, it looks like
00:02:56.090 --> 00:02:59.110
it has been scaled up in
other videos we have talked
00:02:59.110 --> 00:03:02.600
about that this scale factor
is going to be the absolute
00:03:02.600 --> 00:03:05.980
value of the determinant
of A and it's clear
00:03:05.980 --> 00:03:08.010
that frankly, not only is this non-zero
00:03:08.010 --> 00:03:09.470
but it's going to be greater
than what it looks like
00:03:09.470 --> 00:03:13.320
we are scaling up our area
but the very fact that this
00:03:13.320 --> 00:03:16.950
does not equal zero tells
us that we were scaling
00:03:16.950 --> 00:03:20.900
from a two dimensional area to
another two dimensional area.
00:03:20.900 --> 00:03:23.970
And so it's completely
reasonable to be able to go back
00:03:23.970 --> 00:03:27.020
you will, for sure be able
to find a transformation
00:03:27.020 --> 00:03:30.410
that takes you from this
region to that region.
00:03:30.410 --> 00:03:35.410
So that makes us feel good
that A inverse is reasonable.
00:03:37.130 --> 00:03:40.340
Now, as a point of contrast
let's think about matrix B
00:03:40.340 --> 00:03:41.590
right over here.
00:03:41.590 --> 00:03:44.980
Matrix B transforms the
one zero unit vector
00:03:44.980 --> 00:03:46.730
into the two, one unit vector
00:03:46.730 --> 00:03:49.860
so it transforms it into this unit vector
00:03:49.860 --> 00:03:53.060
actually very similarly to how A did it
00:03:53.060 --> 00:03:55.010
but then let's see what it
does to the zero one vector
00:03:55.010 --> 00:03:58.580
transforms this vector
into the four two vector
00:03:58.580 --> 00:04:03.410
four two is this notice
the four two vector
00:04:03.410 --> 00:04:05.560
is just two of the two one vectors
00:04:05.560 --> 00:04:07.210
is going in the same direction
00:04:07.210 --> 00:04:09.800
it just has a different
size or different length
00:04:09.800 --> 00:04:11.580
or a different magnitude.
00:04:11.580 --> 00:04:13.680
So in this situation is taking things
00:04:13.680 --> 00:04:15.460
in two dimensional space
and it's turning them
00:04:15.460 --> 00:04:18.970
into combinations of things
that sit on this same direction.
00:04:18.970 --> 00:04:21.180
So everything in two dimensions
is going to be mapped
00:04:21.180 --> 00:04:24.230
to something along this line here.
00:04:24.230 --> 00:04:26.980
So this region, if I were
to apply transformation B
00:04:26.980 --> 00:04:30.660
it's going to be a region
of this line over here
00:04:30.660 --> 00:04:34.020
anything, if I were to
map it using matrix B
00:04:34.020 --> 00:04:36.900
is going to get mapped onto this line
00:04:36.900 --> 00:04:38.850
so you're going to something with area
00:04:38.850 --> 00:04:42.240
and then you're mapping it
to something that has no area
00:04:42.240 --> 00:04:45.870
so the scaling factor here must be zero.
00:04:45.870 --> 00:04:47.520
So we know since the absolute value
00:04:47.520 --> 00:04:51.810
of the determinant of B is
zero, we could also fairly say
00:04:51.810 --> 00:04:54.330
that the determinant of B is equal to zero
00:04:54.330 --> 00:04:57.600
and the how are you going
to have an inverse matrix?
00:04:57.600 --> 00:04:59.460
How are you going to have
something that can scale
00:04:59.460 --> 00:05:03.150
from zero area to something that has area?
00:05:03.150 --> 00:05:08.150
So we know that B inverse does not exist
00:05:09.440 --> 00:05:12.450
there's nothing that can transform us back
00:05:12.450 --> 00:05:14.330
and so there's a couple of things here
00:05:14.330 --> 00:05:17.660
this reinforces this idea
that if your determinant
00:05:17.660 --> 00:05:20.280
of a transformation matrix is zero
00:05:20.280 --> 00:05:23.950
you're not going to have an
inverse, it's not invertible
00:05:23.950 --> 00:05:26.750
the other thing to recognize
is seeing the patterns
00:05:26.750 --> 00:05:30.350
in the matrix itself here we
saw that the second column
00:05:30.350 --> 00:05:33.320
is just a multiple of the
first column it's twice
00:05:33.320 --> 00:05:37.230
the first column two times two
is four one times two is two
00:05:37.230 --> 00:05:38.820
you can also view it the other way round
00:05:38.820 --> 00:05:43.180
the first row is a
multiple of the second row
00:05:43.180 --> 00:05:45.070
and you can play around
with the math if you wanted
00:05:45.070 --> 00:05:46.990
to generalize it and
see if that's the case
00:05:46.990 --> 00:05:49.460
the determinant will always be zero
00:05:49.460 --> 00:05:52.800
and that's because if you
view them as transformations
00:05:52.800 --> 00:05:56.040
it's going to map to line
and you're gonna lose
00:05:56.040 --> 00:05:59.180
all your area, if you view
it as a representation
00:05:59.180 --> 00:06:01.850
for at least the left-hand
side of a system of equations
00:06:01.850 --> 00:06:04.930
you can think about it as
lines that have the same slope
00:06:04.930 --> 00:06:06.880
but we talk about that in other videos.
|
Invertible matrices and determinants | https://www.youtube.com/watch?v=GuFvSwriy1Q | vtt | https://www.youtube.com/api/timedtext?v=GuFvSwriy1Q&ei=6VWUZeKvG6T6vdIPvKuywAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=770B066537F72151926038DB8F535F78B19C5EAE.5DB83280CD470C76CD2254BD1C43328BB43CE187&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.130 --> 00:00:01.330
- [Instructor] So let's
dig a little bit more
00:00:01.330 --> 00:00:03.420
into matrices and their inverses.
00:00:03.420 --> 00:00:05.940
And in particular, I'm
gonna explore the situations
00:00:05.940 --> 00:00:09.180
in which there might not
be an inverse for a matrix.
00:00:09.180 --> 00:00:12.640
So just as a review, we think
about if we have some matrix,
00:00:12.640 --> 00:00:16.390
A, is there some other matrix
which we could call A inverse
00:00:16.390 --> 00:00:18.570
that when we take the composition of them,
00:00:18.570 --> 00:00:20.890
so if we viewed them
each as transformations,
00:00:20.890 --> 00:00:24.740
we would end up with the
identity transformation.
00:00:24.740 --> 00:00:26.590
Or if we take the product of the two,
00:00:26.590 --> 00:00:28.480
you get the identity matrix.
00:00:28.480 --> 00:00:30.910
And we would also think about it, well,
00:00:30.910 --> 00:00:35.650
if A inverse undoes A, then
A should undo A inverse
00:00:35.650 --> 00:00:38.270
to also get the identity matrix.
00:00:38.270 --> 00:00:42.530
And so another way to
think about it, if I take
00:00:42.530 --> 00:00:46.280
some type of region in
the coordinate plane,
00:00:46.280 --> 00:00:49.130
so this is my x axis, this is my y axis.
00:00:49.130 --> 00:00:52.340
And so let's say my original
region looks something
00:00:52.340 --> 00:00:54.350
like this right over here.
00:00:54.350 --> 00:00:58.950
And I apply the transformation
A, and I get something
00:00:58.950 --> 00:01:01.783
that looks like this, just
making up some things.
00:01:02.680 --> 00:01:05.840
So if I apply the transformation A,
00:01:05.840 --> 00:01:09.260
it takes me from that
region to that region.
00:01:09.260 --> 00:01:12.450
Then we also have a sense
that, okay, A inverse,
00:01:12.450 --> 00:01:15.100
if you transformed this purple thing,
00:01:15.100 --> 00:01:17.610
it should take you back
to where you began.
00:01:17.610 --> 00:01:20.600
Because if you start with
this little blue thing
00:01:20.600 --> 00:01:22.950
and if you have the composition,
well, then that should
00:01:22.950 --> 00:01:25.520
just be transforming it with
the identity transformation,
00:01:25.520 --> 00:01:28.870
so you should just get back to
this little blue thing here.
00:01:28.870 --> 00:01:30.870
Now this might start
triggering some thoughts
00:01:30.870 --> 00:01:34.240
about determinants,
because you might remember
00:01:34.240 --> 00:01:36.710
that the determinant of a matrix tells us
00:01:36.710 --> 00:01:40.270
how much a region's
area will be scaled by.
00:01:40.270 --> 00:01:44.610
In particular, let's say that matrix A
00:01:44.610 --> 00:01:48.490
takes a region that has
an area of, I don't know,
00:01:48.490 --> 00:01:52.350
let's call this area b and let's take,
00:01:52.350 --> 00:01:56.240
let's say it takes that area to 5 times b.
00:01:56.240 --> 00:01:59.140
So the area here is 5b.
00:01:59.140 --> 00:02:02.340
Well, we know that that scaling of 5
00:02:02.340 --> 00:02:05.310
you can determine from the
determinant of matrix A.
00:02:05.310 --> 00:02:07.430
That would tell us that the absolute value
00:02:07.430 --> 00:02:12.430
of the determinant of matrix
A is going to be equal to 5.
00:02:13.460 --> 00:02:16.480
But what does that tell us
about the absolute value
00:02:16.480 --> 00:02:19.233
of the determinant of A inverse then?
00:02:20.160 --> 00:02:25.060
Well, if A is scaling up by
5, it scales areas up by 5,
00:02:25.060 --> 00:02:27.620
then A inverse must be
00:02:27.620 --> 00:02:30.460
scaling areas down by 5.
00:02:30.460 --> 00:02:33.160
So the absolute value of the determinant
00:02:33.160 --> 00:02:36.760
of A inverse should be 1 over 5.
00:02:36.760 --> 00:02:38.490
And so now we have a general property.
00:02:38.490 --> 00:02:40.330
I just happened to use
the number five here,
00:02:40.330 --> 00:02:43.650
but generally speaking, the absolute value
00:02:43.650 --> 00:02:48.160
of the determinant of matrix
A, if it has an inverse,
00:02:48.160 --> 00:02:52.300
should be equal to 1
over the absolute value
00:02:52.300 --> 00:02:55.890
of the determinant of A inverse.
00:02:55.890 --> 00:02:57.930
And we can of course write
that the other way around.
00:02:57.930 --> 00:03:01.620
The absolute value of the
determinant of A inverse
00:03:01.620 --> 00:03:05.700
should be equal to 1 over,
or the reciprocal of,
00:03:05.700 --> 00:03:09.630
the absolute value of
the determinant of A.
00:03:09.630 --> 00:03:11.650
The sum comes straight
out of this property
00:03:11.650 --> 00:03:13.870
that the absolute value of
the determinant tells you
00:03:13.870 --> 00:03:16.290
how much you scale an area by.
00:03:16.290 --> 00:03:19.130
Well knowing that both of these
statements need to be true
00:03:19.130 --> 00:03:21.960
for any matrix A that has an inverse,
00:03:21.960 --> 00:03:24.950
it gives us a clue as to at least one way
00:03:24.950 --> 00:03:28.640
to rule out matrices that
might not have inverses.
00:03:28.640 --> 00:03:31.240
If I were to tell you that the determinant
00:03:31.240 --> 00:03:36.210
of matrix A is zero, will
that have an inverse?
00:03:36.210 --> 00:03:39.250
Well, it can't because if
this quantity right over here
00:03:39.250 --> 00:03:42.510
is zero, or this quantity
right over here is zero,
00:03:42.510 --> 00:03:44.610
that would mean that the
absolute value of the determinant
00:03:44.610 --> 00:03:47.260
of the inverse of the matrix
needs to be one over zero,
00:03:47.260 --> 00:03:49.090
which is undefined.
00:03:49.090 --> 00:03:51.630
And so we have an
interesting conclusion here.
00:03:51.630 --> 00:03:53.980
If the determinant of a
matrix is equal to zero
00:03:53.980 --> 00:03:57.410
there is not going to be an inverse,
00:03:57.410 --> 00:03:59.720
because let's say that there
was some transformation
00:03:59.720 --> 00:04:02.130
that determinant was
zero, instead of something
00:04:02.130 --> 00:04:04.290
that's taking up two-dimensional
area to something else
00:04:04.290 --> 00:04:06.480
that takes two-dimensional
area, it would transform
00:04:06.480 --> 00:04:08.420
something that takes
up two dimensional area
00:04:08.420 --> 00:04:09.950
to something that takes no area.
00:04:09.950 --> 00:04:11.970
So maybe a curve like that,
00:04:11.970 --> 00:04:16.970
that takes up no area
or a line or a point.
00:04:17.120 --> 00:04:19.188
And if you transform to say, a line,
00:04:19.188 --> 00:04:20.730
how do you transform back?
00:04:20.730 --> 00:04:22.560
You'd have to scale up the area infinitely
00:04:22.560 --> 00:04:25.710
in order for it to take up
some two dimensional space.
00:04:25.710 --> 00:04:26.700
So big takeaway.
00:04:26.700 --> 00:04:28.960
We've just said, if the
determinant of a matrix
00:04:28.960 --> 00:04:31.050
is equal to zero, you're not
going to find an inverse.
00:04:31.050 --> 00:04:33.620
And it actually turns out the
case that any other matrix,
00:04:33.620 --> 00:04:36.490
you can find an inverse, but
I'm not going to prove that
00:04:36.490 --> 00:04:38.240
just yet, but hopefully you feel good
00:04:38.240 --> 00:04:40.983
about this principle right over here.
|
Volume density | https://www.youtube.com/watch?v=QoKiCWCsSCo | vtt | https://www.youtube.com/api/timedtext?v=QoKiCWCsSCo&ei=6VWUZajKNYyCp-oPkqaDqAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8D13C72FD0A6919552D77F7F063B41E6A1258757.65CEDE4192ABE78811D41B08A945BBC35617548A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.620 --> 00:00:01.453
- [Instructor] In this video,
00:00:01.453 --> 00:00:04.000
we're gonna talk a
little bit about density
00:00:04.000 --> 00:00:05.980
and we're especially
gonna talk about density
00:00:05.980 --> 00:00:08.510
in the context of volume.
00:00:08.510 --> 00:00:11.910
And one simple way to think about density
00:00:11.910 --> 00:00:15.290
is it's a quantity of something
00:00:15.290 --> 00:00:17.250
and we're going to think
about examples of it
00:00:17.250 --> 00:00:19.320
per unit volume.
00:00:19.320 --> 00:00:21.400
So per volume.
00:00:21.400 --> 00:00:26.320
So for example, let's say
that I have a cubic meter
00:00:26.320 --> 00:00:27.153
right over here,
00:00:27.153 --> 00:00:30.670
actually let me have two
different cubic meters
00:00:30.670 --> 00:00:31.940
just to give you an example.
00:00:31.940 --> 00:00:33.610
So these are both cubic meters
00:00:33.610 --> 00:00:38.610
and let's say in the one on
the left, I have a quantity of
00:00:38.760 --> 00:00:42.850
let's say six of these
dots per cubic meter
00:00:42.850 --> 00:00:44.820
and over here, I only have three
00:00:44.820 --> 00:00:47.160
of these dots per cubic meter.
00:00:47.160 --> 00:00:50.560
Well here, I have a higher
density and in general,
00:00:50.560 --> 00:00:51.980
we're gonna take the quantity
00:00:51.980 --> 00:00:53.900
and divide it by the volume
00:00:53.900 --> 00:00:58.870
and the units are going to be
some quantity per unit volume.
00:00:58.870 --> 00:01:01.410
Now you're typically going
to see mass per unit volume
00:01:01.410 --> 00:01:03.760
but density, especially
in the volume context,
00:01:03.760 --> 00:01:07.100
can refer to any quantity per unit volume.
00:01:07.100 --> 00:01:07.933
Now with that out of the way,
00:01:07.933 --> 00:01:11.110
let's give ourselves a
little bit of an example.
00:01:11.110 --> 00:01:13.390
So here we're told that stone spheres
00:01:13.390 --> 00:01:15.830
thought to be carved by the Diquis people,
00:01:15.830 --> 00:01:17.670
I'm not sure if I'm
pronouncing that correctly,
00:01:17.670 --> 00:01:19.570
more than a thousand years ago
00:01:19.570 --> 00:01:22.230
are a national symbol of Costa Rica.
00:01:22.230 --> 00:01:24.740
One such sphere has a diameter
00:01:24.740 --> 00:01:29.740
of about 1.8 meters and
masses about 8,300 kilograms.
00:01:31.960 --> 00:01:34.690
Based on these measurements,
what is the density
00:01:34.690 --> 00:01:39.690
of this sphere in
kilograms per cubic meter,
00:01:39.700 --> 00:01:43.790
round to the nearest hundred
kilograms per cubic meter.
00:01:43.790 --> 00:01:46.540
So pause this video and see
if you can figure that out.
00:01:48.250 --> 00:01:51.800
So we're gonna want to get
kilograms per cubic meter.
00:01:51.800 --> 00:01:54.820
So we know the total number of kilograms
00:01:54.820 --> 00:01:59.410
in one point in a sphere that
has a diameter of 1.8 meters.
00:01:59.410 --> 00:02:01.470
So that's the total number of kilograms,
00:02:01.470 --> 00:02:03.640
but we don't know the volume just yet.
00:02:03.640 --> 00:02:05.790
So we have a sphere like this.
00:02:05.790 --> 00:02:07.480
This would be a cross section of it.
00:02:07.480 --> 00:02:11.760
Its diameter is 1.8 meters.
00:02:11.760 --> 00:02:14.690
Now you may or may not
already know that the volume
00:02:14.690 --> 00:02:19.690
of a sphere is given by 4/3 PI R cubed.
00:02:22.550 --> 00:02:26.220
And so the radius here is 0.9 meters.
00:02:26.220 --> 00:02:28.780
And so that would be
the R right over here.
00:02:28.780 --> 00:02:33.780
So the volume of one of these
spheres is going to be...
00:02:33.970 --> 00:02:34.803
Let me write it over here.
00:02:34.803 --> 00:02:38.430
The volume is going to be 4/3 PI
00:02:38.430 --> 00:02:43.300
times 0.9 to the third power.
00:02:43.300 --> 00:02:45.130
And we know what the mass is,
00:02:45.130 --> 00:02:48.780
the mass in that volume
is 8,300 kilograms.
00:02:48.780 --> 00:02:51.610
So we would know that the density,
00:02:51.610 --> 00:02:53.960
the density in this situation
00:02:53.960 --> 00:02:56.480
is going to be 8,300 kilograms,
00:02:56.480 --> 00:03:01.480
8,300 kilograms per
this many cubic meters,
00:03:02.180 --> 00:03:07.180
4/3 PI times 0.9 to the
third power cubic meters.
00:03:09.760 --> 00:03:11.640
And we're going to need
a calculator for this
00:03:11.640 --> 00:03:15.640
and we're gonna round to the
nearest hundred kilograms.
00:03:15.640 --> 00:03:20.640
So we have 8,300 divided by,
00:03:21.160 --> 00:03:23.800
let me just open parenthesis here.
00:03:23.800 --> 00:03:28.800
Four divided by three times PI
00:03:31.370 --> 00:03:36.370
times 0.9 to the third power,
00:03:36.700 --> 00:03:40.390
and then I'm going to
close my parentheses,
00:03:40.390 --> 00:03:45.140
is equal to this right over here.
00:03:45.140 --> 00:03:48.760
We want to round to the
nearest hundred kilogram.
00:03:48.760 --> 00:03:53.760
So approximately 2,700
kilograms per cubic meter,
00:03:54.340 --> 00:03:59.340
2,700 or 2,700 kilograms per cubic meter.
00:04:00.930 --> 00:04:02.770
And we are done.
|
Area density | https://www.youtube.com/watch?v=lqXzyybVh6o | vtt | https://www.youtube.com/api/timedtext?v=lqXzyybVh6o&ei=6VWUZdPwG62LhcIPrNSD2AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1BC12435318EA926A8649550209B90E1A5AF11F8.09BA6902443422BB0F820B0768A70161DF206533&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:01.160
- [Narrator] In this video,
00:00:01.160 --> 00:00:05.800
we're going to talk about
density in the context of area.
00:00:05.800 --> 00:00:08.370
And the simplest way of
thinking about it is density
00:00:08.370 --> 00:00:13.370
is going to be some
quantity per unit area.
00:00:13.700 --> 00:00:16.880
So for example, let's say
00:00:16.880 --> 00:00:20.670
that I have a football
field right over here
00:00:20.670 --> 00:00:24.640
and I have another identical
football field right over here.
00:00:24.640 --> 00:00:26.620
Now they have the same area,
00:00:26.620 --> 00:00:31.620
but if I have let's say five
people on this football field
00:00:32.300 --> 00:00:34.150
actually six people on
this football field.
00:00:34.150 --> 00:00:37.300
And I only have three people
on this football field
00:00:37.300 --> 00:00:41.020
the density of people
per average unit area
00:00:41.020 --> 00:00:43.870
or the density of people I
should say per football field
00:00:43.870 --> 00:00:46.230
is going to be higher
in this left example.
00:00:46.230 --> 00:00:49.460
So it's always going to
be quantity per area.
00:00:49.460 --> 00:00:51.760
Now, with that out of the
way, let's do a worked example
00:00:51.760 --> 00:00:55.060
that helps us understand this
idea a little bit better.
00:00:55.060 --> 00:00:57.470
So here we're told the town of Tigersville
00:00:57.470 --> 00:01:02.470
has a population density of
13 cats per square kilometer.
00:01:02.570 --> 00:01:07.090
So they're giving us the density
let me write that 13 cats.
00:01:07.090 --> 00:01:12.090
So the quantity is quantity
and cats per square kilometer.
00:01:12.120 --> 00:01:13.900
That's the density right over there.
00:01:13.900 --> 00:01:18.750
The town is shaped like a
perfect isosceles trapezoid.
00:01:18.750 --> 00:01:20.330
So it looks something
00:01:20.330 --> 00:01:25.150
like this say perfect isosceles trapezoid.
00:01:25.150 --> 00:01:26.820
It's gonna look something like that,
00:01:26.820 --> 00:01:30.700
with two parallel boundaries,
12 kilometers apart.
00:01:30.700 --> 00:01:34.580
So this distance right
over here is 12 kilometers
00:01:34.580 --> 00:01:36.210
one measuring eight kilometers.
00:01:36.210 --> 00:01:38.680
So this side over here is eight kilometers
00:01:38.680 --> 00:01:41.143
the other is 16 that's
a longer one over there.
00:01:42.330 --> 00:01:44.720
How many cats are in Tigersville?
00:01:44.720 --> 00:01:47.750
So they give us the density
here and they give us,
00:01:47.750 --> 00:01:50.290
I think enough information
to figure out the area.
00:01:50.290 --> 00:01:52.750
And they want us to figure
out how many cats we have.
00:01:52.750 --> 00:01:54.310
So what is the quantity?
00:01:54.310 --> 00:01:57.173
So pause this video and see
if you can figure that out.
00:01:58.530 --> 00:01:59.910
Well, just as we said the density
00:01:59.910 --> 00:02:02.830
is equal to quantity divided by area.
00:02:02.830 --> 00:02:06.370
If we multiply both sides
of this equation by area
00:02:06.370 --> 00:02:11.370
you get area times density is
going to be equal to quantity.
00:02:14.400 --> 00:02:16.320
And we know the density.
00:02:16.320 --> 00:02:19.460
It's 13 cats per square
kilometer, and we can figure out
00:02:19.460 --> 00:02:22.090
the area and then just multiply the two.
00:02:22.090 --> 00:02:24.540
So what's the area of
this right over here?
00:02:24.540 --> 00:02:27.710
Well, the area of a
trapezoid is going to be,
00:02:27.710 --> 00:02:30.580
write here area is going
to be 12 kilometers.
00:02:30.580 --> 00:02:32.490
The height of the trapezoid
00:02:32.490 --> 00:02:37.050
times the average of
the two parallel sides
00:02:37.050 --> 00:02:37.883
I guess you could say.
00:02:37.883 --> 00:02:40.896
So the average of those it's
going to be eight kilometers
00:02:40.896 --> 00:02:45.810
plus 16 kilometers over two.
00:02:45.810 --> 00:02:48.810
So this is going to be
equal to 12 kilometers
00:02:48.810 --> 00:02:53.300
times eight plus 16 is
24 divided by two is 12.
00:02:53.300 --> 00:02:55.850
So times 12 kilometers.
00:02:55.850 --> 00:03:00.850
So this gives us 144 square kilometers.
00:03:00.960 --> 00:03:04.620
Now we know we have 13
cats per square kilometer.
00:03:04.620 --> 00:03:06.580
So let me do this year in another color.
00:03:06.580 --> 00:03:11.580
So if I multiply 13 cats
per kilometer squared
00:03:12.930 --> 00:03:17.870
and I multiply that times
this business right over here,
00:03:17.870 --> 00:03:22.150
times 144 square kilometers.
00:03:22.150 --> 00:03:24.690
And you might also notice
that the units cancel out
00:03:24.690 --> 00:03:26.550
the same way that variables might.
00:03:26.550 --> 00:03:28.310
So that cancels out with that.
00:03:28.310 --> 00:03:31.340
You're going to get 13 times 144.
00:03:31.340 --> 00:03:34.570
And the units that you're
left with is just cats.
00:03:34.570 --> 00:03:39.390
So 144 times 13, three times four is 12
00:03:41.200 --> 00:03:44.060
that gives us to 13,
three times a hundred,
00:03:44.060 --> 00:03:46.670
300 plus another hundred is 400.
00:03:46.670 --> 00:03:49.580
Now I'm just gonna multiply
144 essentially by 10
00:03:49.580 --> 00:03:51.920
which is going to be 1440.
00:03:51.920 --> 00:03:54.150
And so if I add up all of that together
00:03:54.150 --> 00:03:55.710
I'm gonna jump down to here.
00:03:55.710 --> 00:03:57.513
I get 1872.
00:03:59.190 --> 00:04:04.190
So this is 1872 cats in
total and we are done.
|
Dividing rational expressions | https://www.youtube.com/watch?v=0cmhBgQNGDI | vtt | https://www.youtube.com/api/timedtext?v=0cmhBgQNGDI&ei=6VWUZYb5Iq70mLAP35KzmAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=CF285F2F1EF9261F9B5255800642A3944F437FC7.B7588C7B623594B9DF6F6D36E2134532AA3713A3&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.230 --> 00:00:01.610
- [Instructor] The goal of this video
00:00:01.610 --> 00:00:03.820
is to take this big, hairy expression,
00:00:03.820 --> 00:00:07.310
where we are essentially
dividing rational expressions
00:00:07.310 --> 00:00:10.470
and see if we can
essentially do the division
00:00:10.470 --> 00:00:12.870
and then write it in reduced terms.
00:00:12.870 --> 00:00:14.550
So if you are so inspired,
00:00:14.550 --> 00:00:16.190
I encourage you to pause the video
00:00:16.190 --> 00:00:19.123
and work on this on your own
before we do this together.
00:00:20.140 --> 00:00:22.050
All right, now let's do this together.
00:00:22.050 --> 00:00:26.630
So this is completely analogous
to dividing fractions.
00:00:26.630 --> 00:00:31.220
So if we were to divide
the fraction six over 25
00:00:32.260 --> 00:00:37.260
by the fraction 15 over nine,
00:00:38.090 --> 00:00:39.900
we know that we can rewrite this
00:00:39.900 --> 00:00:44.900
as six over 25 divided by 15 over nine,
00:00:46.000 --> 00:00:49.150
which we know is the
same thing as six over 25
00:00:49.150 --> 00:00:52.480
times nine over 15.
00:00:52.480 --> 00:00:54.857
And then we can factor
the various numerators
00:00:54.857 --> 00:00:55.930
and the denominators.
00:00:55.930 --> 00:00:57.770
This is two times three.
00:00:57.770 --> 00:00:59.810
This is three times three.
00:00:59.810 --> 00:01:01.910
This is five times five.
00:01:01.910 --> 00:01:04.550
This is five times three.
00:01:04.550 --> 00:01:06.010
Let's see, three in the numerator,
00:01:06.010 --> 00:01:07.830
three in the denominator.
00:01:07.830 --> 00:01:09.760
And actually, that's about
as far as we can get.
00:01:09.760 --> 00:01:12.150
So then we'll have two
times three times three,
00:01:12.150 --> 00:01:14.920
which is going to be 18 in the numerator.
00:01:14.920 --> 00:01:16.100
And then in the denominator,
00:01:16.100 --> 00:01:21.100
we have five times five
times five, which is 125.
00:01:21.180 --> 00:01:23.790
So we're going to do the
exact same thing up here,
00:01:23.790 --> 00:01:25.950
but there's one extra complication.
00:01:25.950 --> 00:01:28.730
We have to keep track of the x values
00:01:28.730 --> 00:01:32.250
that would make this expression
undefined in any way,
00:01:32.250 --> 00:01:34.170
because as we reduce to lowest terms,
00:01:34.170 --> 00:01:35.720
we might lose that information,
00:01:35.720 --> 00:01:37.350
but if we lose that information,
00:01:37.350 --> 00:01:38.970
then we have changed the expression.
00:01:38.970 --> 00:01:40.330
So we have to keep track
00:01:40.330 --> 00:01:43.340
of how we are constraining this domain.
00:01:43.340 --> 00:01:45.300
So first, I can just rewrite this
00:01:45.300 --> 00:01:50.300
as x squared minus three x minus four,
00:01:50.500 --> 00:01:55.483
all of that over negative
three x minus 15.
00:01:57.390 --> 00:02:00.210
And that's getting divided by,
00:02:00.210 --> 00:02:02.750
divided by this business.
00:02:02.750 --> 00:02:07.020
X squared minus 16 over,
00:02:07.020 --> 00:02:12.020
we have x squared minus x minus 30.
00:02:12.760 --> 00:02:14.100
Now, the next thing we can do
00:02:14.100 --> 00:02:17.660
is we can factor the various
numerators and denominators
00:02:17.660 --> 00:02:21.110
and think about which x values
could get us into trouble.
00:02:21.110 --> 00:02:23.600
So x squared minus three x minus four.
00:02:23.600 --> 00:02:25.990
Let's see, negative one.
00:02:25.990 --> 00:02:29.290
Let's see, negative four times plus one
00:02:29.290 --> 00:02:30.270
would be negative four,
00:02:30.270 --> 00:02:31.930
and then these would add
up to negative three.
00:02:31.930 --> 00:02:35.730
So I can rewrite this as x minus four
00:02:35.730 --> 00:02:38.390
times x plus one.
00:02:38.390 --> 00:02:40.240
Rewrite it that way.
00:02:40.240 --> 00:02:43.190
And then I can rewrite
what I have down here,
00:02:43.190 --> 00:02:45.110
I could factor out a negative three.
00:02:45.110 --> 00:02:50.110
So I could write that as
negative three times x plus five.
00:02:50.210 --> 00:02:52.820
And then I could write this one here.
00:02:52.820 --> 00:02:54.440
This is a difference of squares.
00:02:54.440 --> 00:02:59.440
It's going to be x plus
four times x minus four.
00:02:59.490 --> 00:03:02.840
And then last but not
least, this one over here.
00:03:02.840 --> 00:03:06.490
Let's see, if I have a five and a six,
00:03:06.490 --> 00:03:09.090
negative six plus five is negative one,
00:03:09.090 --> 00:03:11.590
negative six times five is negative 30.
00:03:11.590 --> 00:03:13.980
So it's going to be x minus six
00:03:13.980 --> 00:03:16.710
times x plus five.
00:03:16.710 --> 00:03:18.190
Now, before I go any further,
00:03:18.190 --> 00:03:20.100
and the reason why I
factored at that point,
00:03:20.100 --> 00:03:22.130
is now we can think about what x values
00:03:22.130 --> 00:03:23.540
will get us in trouble.
00:03:23.540 --> 00:03:25.100
We know that any x values
00:03:25.100 --> 00:03:28.400
that make any of the
denominators equal to zero,
00:03:28.400 --> 00:03:29.600
that would be undefined.
00:03:29.600 --> 00:03:31.670
So we wanna constrain
our domain in that way.
00:03:31.670 --> 00:03:33.340
So we know, for example,
00:03:33.340 --> 00:03:35.900
that x cannot be equal to negative five.
00:03:35.900 --> 00:03:38.760
That would make this
denominator equal to zero.
00:03:38.760 --> 00:03:40.080
Let me write that here.
00:03:40.080 --> 00:03:43.520
So x cannot be equal to negative five.
00:03:43.520 --> 00:03:47.150
We also know that x
cannot be equal to six.
00:03:47.150 --> 00:03:49.550
X cannot be equal to six.
00:03:49.550 --> 00:03:51.000
And this would also tell us
00:03:51.000 --> 00:03:52.770
that x cannot be equal to negative five.
00:03:52.770 --> 00:03:54.950
So I don't have to rewrite that again.
00:03:54.950 --> 00:03:56.270
But we're not done.
00:03:56.270 --> 00:03:57.850
So we've figured out the x values
00:03:57.850 --> 00:04:00.200
that make these
denominators equal to zero,
00:04:00.200 --> 00:04:02.120
but remember, we're also dividing by
00:04:02.120 --> 00:04:04.530
this entire expression here.
00:04:04.530 --> 00:04:05.490
So anything that would make
00:04:05.490 --> 00:04:08.180
the entire expression equal to
zero would also be a problem,
00:04:08.180 --> 00:04:09.840
'cause you can't divide by zero.
00:04:09.840 --> 00:04:13.460
So anything that would make
this numerator equal to zero,
00:04:13.460 --> 00:04:15.670
which was this numerator right over here,
00:04:15.670 --> 00:04:17.810
would make us also divide by zero.
00:04:17.810 --> 00:04:18.940
So we have to constrain there.
00:04:18.940 --> 00:04:20.780
Not this numerator here, that one's fine.
00:04:20.780 --> 00:04:22.710
That one could be equal to zero.
00:04:22.710 --> 00:04:24.580
You can divide zero by other things.
00:04:24.580 --> 00:04:27.460
So let's see, we could
see that x cannot be equal
00:04:27.460 --> 00:04:29.750
to negative four, and actually,
00:04:29.750 --> 00:04:33.290
x cannot be equal to positive four.
00:04:33.290 --> 00:04:35.560
So now we've fully constrained our domain
00:04:35.560 --> 00:04:37.730
and now we can proceed.
00:04:37.730 --> 00:04:41.280
So let me box this off right over here,
00:04:41.280 --> 00:04:42.130
and then we continue.
00:04:42.130 --> 00:04:43.860
I can rewrite all of this.
00:04:43.860 --> 00:04:48.860
So we're going to have x
minus four times x plus one,
00:04:50.300 --> 00:04:55.300
all of that over negative
three times x plus five,
00:04:56.780 --> 00:04:59.610
and now I'm just going to,
instead of divide by this,
00:04:59.610 --> 00:05:01.760
I'm gonna multiply by the reciprocal.
00:05:01.760 --> 00:05:03.840
So this is going to be times,
00:05:03.840 --> 00:05:05.910
and I'm just gonna take the reciprocal,
00:05:05.910 --> 00:05:10.230
x minus six times x plus five,
00:05:10.230 --> 00:05:11.930
all of that over,
00:05:11.930 --> 00:05:16.930
we have x plus four times x minus four.
00:05:17.520 --> 00:05:20.120
And once again, our domain
is constrained in this way,
00:05:20.120 --> 00:05:22.900
but we see we have an x minus
four in the numerator now,
00:05:22.900 --> 00:05:24.880
x minus four in the denominator,
00:05:24.880 --> 00:05:26.750
x plus five in the denominator,
00:05:26.750 --> 00:05:29.230
x plus five in the numerator.
00:05:29.230 --> 00:05:30.680
And now we can say that this is going
00:05:30.680 --> 00:05:35.680
to be equal to x plus
one times x minus six,
00:05:37.710 --> 00:05:42.710
all of that over negative
three, negative three,
00:05:43.010 --> 00:05:46.730
times x plus four, x plus four.
00:05:46.730 --> 00:05:48.960
So the way it's written
now, we would still,
00:05:48.960 --> 00:05:51.780
it's clear that x cannot
be equal to negative four.
00:05:51.780 --> 00:05:53.250
So this information,
00:05:53.250 --> 00:05:56.000
you can say that it's already
there in this expression
00:05:56.000 --> 00:05:58.620
now that we have reduced
it to lowest terms,
00:05:58.620 --> 00:06:00.830
but this other information
right over here,
00:06:00.830 --> 00:06:02.250
this has been lost.
00:06:02.250 --> 00:06:03.830
So if you want this expression
00:06:03.830 --> 00:06:06.520
to truly be equivalent to
this expression up here,
00:06:06.520 --> 00:06:10.970
you would also have to say
comma x cannot be equal
00:06:10.970 --> 00:06:15.970
to negative five, six, or positive four.
00:06:16.040 --> 00:06:18.910
You could throw the negative
four in there if you like,
00:06:18.910 --> 00:06:22.823
but that one's already in
the expression, so to speak.
|
Multiplying rational expressions | https://www.youtube.com/watch?v=fjJ0C7-N-xU | vtt | https://www.youtube.com/api/timedtext?v=fjJ0C7-N-xU&ei=6VWUZbfXHvzMp-oP8Jaz-Ac&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5AF8A204FA75CE844207B17F8134A6B2521467D7.89EFD447A78825F3A1C777306F9AEB7CCD7FD35D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.200 --> 00:00:01.920
- [Instructor] So what I
have here is an expression
00:00:01.920 --> 00:00:05.240
where I'm multiplying
rational expressions.
00:00:05.240 --> 00:00:08.550
And we want to do this multiplication
00:00:08.550 --> 00:00:10.310
and then reduce to lowest terms.
00:00:10.310 --> 00:00:13.450
So if you feel so inspired,
I encourage you to pause
00:00:13.450 --> 00:00:15.850
this video and see if you
can have a go at that.
00:00:16.690 --> 00:00:19.470
All right, now let's work
through this together.
00:00:19.470 --> 00:00:22.280
So multiplying rational
expressions like this,
00:00:22.280 --> 00:00:25.830
it's very analogous to
multiplying fractions.
00:00:25.830 --> 00:00:30.830
For example, if I were to multiply 6/25
00:00:32.010 --> 00:00:37.010
times 15/9, there's a
few ways you could do it.
00:00:38.300 --> 00:00:40.750
You could just multiply six
times 15 in the numerator,
00:00:40.750 --> 00:00:42.850
and 25 times nine in the denominator.
00:00:42.850 --> 00:00:44.480
But the way that many of us approach it
00:00:44.480 --> 00:00:47.230
so that it's easier to
reduce to lowest terms
00:00:47.230 --> 00:00:49.490
is to factor things, to realize that look,
00:00:49.490 --> 00:00:53.000
six is two times three.
00:00:53.000 --> 00:00:58.000
Nine is three times three,
15 is three times five,
00:00:59.050 --> 00:01:02.440
and 25 is five times five.
00:01:02.440 --> 00:01:04.980
And then you can realize
in your eventual product
00:01:04.980 --> 00:01:05.900
you're going to have a five
00:01:05.900 --> 00:01:07.940
in the numerator, five in the denominator.
00:01:07.940 --> 00:01:10.590
You can, five divided by five is one,
00:01:10.590 --> 00:01:13.040
three divided by three is one,
00:01:13.040 --> 00:01:15.820
and then three divided by three is one.
00:01:15.820 --> 00:01:18.690
And so all you'd be left with is that two
00:01:18.690 --> 00:01:19.670
and then that five.
00:01:19.670 --> 00:01:22.140
So this is going to be equal to 2/5.
00:01:22.140 --> 00:01:23.680
So we'll do the analogous thing
00:01:23.680 --> 00:01:25.420
here with these rational expressions.
00:01:25.420 --> 00:01:26.570
We're going to factor them,
00:01:26.570 --> 00:01:29.150
all of them in the
numerators and denominators.
00:01:29.150 --> 00:01:32.240
And then we'll see if we
can divide the numerator
00:01:32.240 --> 00:01:34.220
and the denominator by the same thing.
00:01:34.220 --> 00:01:35.850
Now, the one thing we have to make sure
00:01:35.850 --> 00:01:39.150
of as we do that is we
keep track of the domain.
00:01:39.150 --> 00:01:41.160
'Cause these rational expressions here,
00:01:41.160 --> 00:01:42.570
they might have x values
00:01:42.570 --> 00:01:45.260
that make their
denominators equal to zero.
00:01:45.260 --> 00:01:49.040
And so even if we reduce to lowest terms,
00:01:49.040 --> 00:01:50.770
and we get rid of those expressions,
00:01:50.770 --> 00:01:53.600
in order for the expressions
to be the same expression,
00:01:53.600 --> 00:01:57.120
we have to constrain the
domain in the same way.
00:01:57.120 --> 00:01:59.110
So let's get started.
00:01:59.110 --> 00:02:01.300
So this is going to be equal to,
00:02:01.300 --> 00:02:02.480
I'll just rewrite everything,
00:02:02.480 --> 00:02:04.140
x squared minus nine.
00:02:04.140 --> 00:02:05.240
How do we factor that?
00:02:05.240 --> 00:02:06.910
Well, that's going to be
a difference of squares.
00:02:06.910 --> 00:02:11.910
We could write that as x plus
three times x minus three.
00:02:12.430 --> 00:02:16.750
And then that is going
to be over this business.
00:02:16.750 --> 00:02:19.670
And let's see, five squared is 25,
00:02:19.670 --> 00:02:22.490
negative five plus negative
five is negative 10.
00:02:22.490 --> 00:02:26.380
So this is going to be x minus five
00:02:27.480 --> 00:02:30.010
times x minus five.
00:02:30.010 --> 00:02:31.850
If what I'm just doing
here with the factoring
00:02:31.850 --> 00:02:33.110
is not making sense,
00:02:33.110 --> 00:02:36.030
I encourage you to review
factoring on Khan Academy.
00:02:36.030 --> 00:02:39.120
And then we multiply
that times, let's see,
00:02:39.120 --> 00:02:41.690
in this numerator here,
I can factor out of four.
00:02:41.690 --> 00:02:45.840
So that's going to be
four times x minus five.
00:02:45.840 --> 00:02:46.770
Which is going to be useful.
00:02:46.770 --> 00:02:49.450
I have an x minus five
there, x minus five there.
00:02:49.450 --> 00:02:51.840
And then that's going to be over.
00:02:51.840 --> 00:02:55.930
Let's see, this expression over here.
00:02:55.930 --> 00:02:58.690
Two plus three is five,
two times three to six.
00:02:58.690 --> 00:03:03.690
So it's going to be x plus
two times x plus three.
00:03:04.250 --> 00:03:07.500
Now before I start
reducing to lowest terms,
00:03:07.500 --> 00:03:09.520
let's think about the domain here.
00:03:09.520 --> 00:03:11.310
And the domain is going to be constrained
00:03:11.310 --> 00:03:14.740
by things that make these
denominators equal to zero.
00:03:14.740 --> 00:03:17.760
So the domain would be all real numbers
00:03:17.760 --> 00:03:20.300
except x cannot equal five.
00:03:20.300 --> 00:03:21.410
Let me write it over here.
00:03:21.410 --> 00:03:25.740
X cannot equal five
because if that happened,
00:03:25.740 --> 00:03:28.260
then this denominator would become zero.
00:03:28.260 --> 00:03:31.583
X cannot be equal to negative two.
00:03:32.480 --> 00:03:34.410
X could not be equal to negative two
00:03:34.410 --> 00:03:36.330
because that would make
the denominator here zero,
00:03:36.330 --> 00:03:38.050
which would make the
denominator here zero.
00:03:38.050 --> 00:03:41.940
And x cannot be equal to negative three.
00:03:41.940 --> 00:03:44.320
So the domain is constrained in this way.
00:03:44.320 --> 00:03:46.050
We have to carry this throughout.
00:03:46.050 --> 00:03:48.000
No matter what we do to the expression,
00:03:48.000 --> 00:03:50.900
this is the constraints on our domain.
00:03:50.900 --> 00:03:55.290
With that out of the way, now
we can reduce to lowest terms.
00:03:55.290 --> 00:03:58.980
So x, we have an x plus
three in the numerator,
00:03:58.980 --> 00:04:00.410
x plus three in the denominator.
00:04:00.410 --> 00:04:02.320
X minus five in the numerator.
00:04:02.320 --> 00:04:04.310
X minus five in the denominator.
00:04:04.310 --> 00:04:07.070
And I think we've gone
about as far as we can.
00:04:07.070 --> 00:04:09.330
And so when we multiply the numerators,
00:04:09.330 --> 00:04:10.570
we are going to get,
00:04:10.570 --> 00:04:14.960
this business is going to
be four times x minus three.
00:04:14.960 --> 00:04:19.430
Four times x minus three,
00:04:19.430 --> 00:04:22.513
over, we have an x minus five here.
00:04:23.510 --> 00:04:25.610
X minus five.
00:04:25.610 --> 00:04:28.523
And then we have an x plus two.
00:04:29.710 --> 00:04:32.410
We have an x plus two.
00:04:32.410 --> 00:04:34.500
And we could leave it
like this if you want.
00:04:34.500 --> 00:04:35.720
In some cases,
00:04:35.720 --> 00:04:39.020
people like to multiply the
things out, but we're done.
00:04:39.020 --> 00:04:41.580
We've just finished multiplying
these rational expressions.
00:04:41.580 --> 00:04:42.650
And we have to remind ourselves
00:04:42.650 --> 00:04:46.100
that x cannot be equal
to any of these things.
00:04:46.100 --> 00:04:48.060
Now, the way that we've simplified it,
00:04:48.060 --> 00:04:50.960
we still have an x minus
five right over here.
00:04:50.960 --> 00:04:53.490
So it might be redundant
to say that x cannot
00:04:53.490 --> 00:04:56.350
be equal to five because
that's still the case
00:04:56.350 --> 00:05:00.200
in our reduced terms expression here.
00:05:00.200 --> 00:05:03.380
And that's true also of
the x cannot be equal
00:05:03.380 --> 00:05:04.540
to negative two.
00:05:04.540 --> 00:05:06.510
We still have an x plus two here.
00:05:06.510 --> 00:05:08.960
So still, even in this
expression it's pretty clear,
00:05:08.960 --> 00:05:11.100
that x cannot be equal to negative two,
00:05:11.100 --> 00:05:12.930
but the x cannot equal negative three
00:05:12.930 --> 00:05:15.890
isn't so obvious when you
just look at this expression.
00:05:15.890 --> 00:05:17.250
But in order for this expression
00:05:17.250 --> 00:05:19.560
to be completely
equivalent to the original,
00:05:19.560 --> 00:05:21.800
it has to have the same domain.
00:05:21.800 --> 00:05:24.400
And so you might want to explicitly say
00:05:24.400 --> 00:05:26.910
that x cannot be equal
to negative three here.
00:05:26.910 --> 00:05:28.630
You could also say the other two,
00:05:28.630 --> 00:05:31.100
but those are, that's still very clear
00:05:31.100 --> 00:05:32.750
when you look at this expression.
|
Inverse matrices and matrix equations | https://www.youtube.com/watch?v=a2S0kuXO3gE | vtt | https://www.youtube.com/api/timedtext?v=a2S0kuXO3gE&ei=6VWUZZObG7-ShcIPue6zgA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=53904F34A80B04F30A073E3675A0B44920BE53FC.AF86E06714F7E85AC96B6A1019C26AB8A1AA6B27&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:02.270
- [Instructor] In a previous
video, we talked about
00:00:02.270 --> 00:00:05.510
how you can represent
a system of equations
00:00:05.510 --> 00:00:08.140
as essentially a matrix equation.
00:00:08.140 --> 00:00:10.460
So for example, here I have two equations
00:00:10.460 --> 00:00:13.490
with two unknowns x, y,
well let's just assume
00:00:13.490 --> 00:00:16.460
that we know what a,
b, p, c, d, and q are,
00:00:16.460 --> 00:00:20.610
and you can represent
this type of system as a
00:00:20.610 --> 00:00:24.040
matrix vector equation like
this, where the coefficients
00:00:24.040 --> 00:00:26.400
on the x's are this first column,
00:00:26.400 --> 00:00:28.850
coefficients on the y's
are the second column.
00:00:28.850 --> 00:00:31.090
And then we see our unknown variables,
00:00:31.090 --> 00:00:34.760
what we would want to solve
for maybe, as this vector here,
00:00:34.760 --> 00:00:37.290
so you could do that as the
unknown two-dimensional vector.
00:00:37.290 --> 00:00:39.900
And then we know when
we either think about it
00:00:39.900 --> 00:00:42.150
as a transformation on this unknown vector
00:00:42.150 --> 00:00:45.450
we get this known vector,
we get the vector pq,
00:00:45.450 --> 00:00:48.110
or you can think about it
as matrix multiplication.
00:00:48.110 --> 00:00:51.220
When you multiply this
vector by this matrix
00:00:51.220 --> 00:00:54.560
you get this pq vector.
00:00:54.560 --> 00:00:56.340
And in other videos we also talked
00:00:56.340 --> 00:00:58.530
about this idea of inverses.
00:00:58.530 --> 00:01:03.100
So for example, if we call
this right over here, matrix A,
00:01:03.100 --> 00:01:06.260
you can imagine that, or what
we're seeing here is matrix A,
00:01:06.260 --> 00:01:10.470
times the vector xy,
00:01:10.470 --> 00:01:12.110
I'll just write it like that,
00:01:12.110 --> 00:01:16.570
is equal to the vector pq.
00:01:16.570 --> 00:01:19.650
I'll just stick to one color
for convenience right now.
00:01:19.650 --> 00:01:23.790
And we talked about this idea
that if you have an inverse
00:01:23.790 --> 00:01:25.480
of a matrix times the matrix
00:01:25.480 --> 00:01:27.670
it's going to give you
the identity matrix.
00:01:27.670 --> 00:01:31.030
So one idea for trying to quote solve,
00:01:31.030 --> 00:01:34.620
this matrix vector equation
is what if we multiplied
00:01:34.620 --> 00:01:38.140
both sides on the left
by the inverse of A?
00:01:38.140 --> 00:01:40.130
So if I had A inverse here
00:01:40.130 --> 00:01:43.770
and if I multiplied by A
inverse here, what would happen?
00:01:43.770 --> 00:01:46.240
Well, assuming A inverse exists,
00:01:46.240 --> 00:01:48.530
and that's actually going to
be the focus of this video,
00:01:48.530 --> 00:01:51.500
if A inverse exists,
then this right over here
00:01:51.500 --> 00:01:55.100
is just going to become
the identity matrix.
00:01:55.100 --> 00:01:57.800
So that's just the matrix
that if I try to transform
00:01:57.800 --> 00:02:00.530
anything or if I multiply
anything by it it's just gonna
00:02:00.530 --> 00:02:02.570
give us that thing that we had before,
00:02:02.570 --> 00:02:04.780
in the two by two scenario,
the identity matrix,
00:02:04.780 --> 00:02:07.940
it looks like that.
00:02:07.940 --> 00:02:10.190
And then on the right-hand
side, we'll be multiplying
00:02:10.190 --> 00:02:12.493
a two by two matrix times the vector pq.
00:02:13.518 --> 00:02:14.760
And so on the left-hand side,
00:02:14.760 --> 00:02:16.820
essentially the identity matrix times xy
00:02:16.820 --> 00:02:21.030
is just going to give us xy,
and on the right hand side
00:02:21.030 --> 00:02:22.780
we would know what that equals to.
00:02:22.780 --> 00:02:25.410
So that would essentially
solve this system
00:02:25.410 --> 00:02:27.940
when it is represented that way.
00:02:27.940 --> 00:02:32.660
But this gives us a clue about
thinking when is it solvable?
00:02:32.660 --> 00:02:35.190
Because when it's solvable,
you're going to have
00:02:35.190 --> 00:02:37.610
a situation where you
do have an inverse here.
00:02:37.610 --> 00:02:39.810
And when it's not
solvable, you're gonna have
00:02:39.810 --> 00:02:41.920
a situation where there
is no inverse here,
00:02:41.920 --> 00:02:46.120
where this matrix A does
not have an inverse.
00:02:46.120 --> 00:02:49.490
So when we go back to what we've
learned in previous algebra
00:02:49.490 --> 00:02:52.080
classes about solving
systems of equations,
00:02:52.080 --> 00:02:54.700
we know there's two scenarios where we get
00:02:54.700 --> 00:02:57.510
either no solutions or an
infinite number of solutions.
00:02:57.510 --> 00:02:59.560
Let me draw a little coordinate axis here.
00:02:59.560 --> 00:03:01.360
We know that the lines
have different slopes.
00:03:01.360 --> 00:03:02.676
So one line looks like this
00:03:02.676 --> 00:03:04.880
and then the other line, it
could look like anything.
00:03:04.880 --> 00:03:06.570
As long as it has a different slope,
00:03:06.570 --> 00:03:09.100
they are going to intersect
at exactly one point.
00:03:09.100 --> 00:03:11.500
Two lines with different
slopes are gonna intersect
00:03:11.500 --> 00:03:13.680
in exactly one point.
00:03:13.680 --> 00:03:16.810
The situation which you
have no solutions is if
00:03:16.810 --> 00:03:19.520
they are the same slope.
00:03:19.520 --> 00:03:23.420
So parallel lines like
this would not intersect.
00:03:23.420 --> 00:03:26.470
Another weird situation that
you get when you solve systems
00:03:26.470 --> 00:03:29.810
is that they have the same
slope, but they're the same line.
00:03:29.810 --> 00:03:31.720
So that would be something like this.
00:03:31.720 --> 00:03:34.420
There would not be a unique
xy, there would actually
00:03:34.420 --> 00:03:37.940
be an infinite xy's that
would satisfy the equation.
00:03:37.940 --> 00:03:40.440
So those are both situations
where we're not finding
00:03:40.440 --> 00:03:43.250
a nice, clean, unique
solution to our system.
00:03:43.250 --> 00:03:45.540
And if we think about the
matrix world, where we're not
00:03:45.540 --> 00:03:48.320
going to find an inverse of
A that when we multiply it
00:03:48.320 --> 00:03:50.830
times pq it gives us
a nice clean solution,
00:03:50.830 --> 00:03:52.180
in either of those scenarios
00:03:52.180 --> 00:03:55.190
where the two equations
have the same slope.
00:03:55.190 --> 00:03:56.820
Now let's think about what do we know
00:03:56.820 --> 00:03:59.820
about abcd when we have the same slope?
00:03:59.820 --> 00:04:01.800
So if we were to try to
put this top equation
00:04:01.800 --> 00:04:04.840
into slope intercept form,
what would that look like?
00:04:04.840 --> 00:04:08.190
Well, let's see we can
subtract ax from both sides.
00:04:08.190 --> 00:04:09.370
So you could have something like this,
00:04:09.370 --> 00:04:13.420
by is equal to p minus ax.
00:04:13.420 --> 00:04:15.100
I just subtract ax from both sides.
00:04:15.100 --> 00:04:17.050
And then if you divide both sides by b,
00:04:17.050 --> 00:04:22.050
you get y is equal to p
over b minus a over bx.
00:04:22.430 --> 00:04:24.980
And so you can see in this first equation
00:04:24.980 --> 00:04:27.700
our slope is negative a over b.
00:04:27.700 --> 00:04:29.410
Now what about the second equation?
00:04:29.410 --> 00:04:31.500
Well, by the same logic,
if you do the same thing,
00:04:31.500 --> 00:04:35.070
you subtract cx from both
sides and then divide by d,
00:04:35.070 --> 00:04:39.240
you're going to get y is equal to q over d
00:04:39.240 --> 00:04:43.780
minus c over dx.
00:04:43.780 --> 00:04:47.430
And so we see the slope
here is negative c over d.
00:04:47.430 --> 00:04:50.260
So these strange scenarios, not strange,
00:04:50.260 --> 00:04:52.270
but these scenarios where
you don't get a nice clean
00:04:52.270 --> 00:04:54.890
unique solution are the
ones where these slopes
00:04:54.890 --> 00:04:56.370
are equivalent to each other.
00:04:56.370 --> 00:04:58.640
So we're talking about
the scenario in which
00:04:58.640 --> 00:05:03.640
negative a over b is equal
to negative c over d.
00:05:04.170 --> 00:05:06.150
Now, to make a little bit
of sense of that, let's say
00:05:06.150 --> 00:05:09.630
we multiply both sides of
this equation by negative bd
00:05:09.630 --> 00:05:11.730
to get rid of these things
out of the denominator.
00:05:11.730 --> 00:05:12.840
So let me do that.
00:05:12.840 --> 00:05:14.140
And I'm multiplying by a negative
00:05:14.140 --> 00:05:18.000
to get rid of the negatives, negative bd.
00:05:18.000 --> 00:05:21.430
So on the left-hand side,
the b cancels with the b,
00:05:21.430 --> 00:05:23.010
negative times a negative is a positive,
00:05:23.010 --> 00:05:26.470
we're gonna get ad, and
on the right-hand side,
00:05:26.470 --> 00:05:30.103
negatives cancel out, d goes
away, and then you have cb.
00:05:32.020 --> 00:05:34.390
Or another way to think about it is,
00:05:34.390 --> 00:05:38.080
ad minus cb is going to be equal to zero.
00:05:38.080 --> 00:05:42.190
When ad minus cb is equal to zero,
00:05:42.190 --> 00:05:47.190
this system of equations does
not have a unique solution.
00:05:47.270 --> 00:05:50.150
Now, things, bells might be
ringing in your head right now,
00:05:50.150 --> 00:05:54.280
because ad, so that's a times d
00:05:54.280 --> 00:05:57.610
minus c times b,
00:05:57.610 --> 00:05:59.780
minus c times b,
00:05:59.780 --> 00:06:02.700
that's the determinant
of this matrix A here.
00:06:02.700 --> 00:06:06.000
So this is going to be
true only in a situation,
00:06:06.000 --> 00:06:09.340
if and only if, the
determinant of our matrix A
00:06:09.340 --> 00:06:10.660
is equal to zero.
00:06:10.660 --> 00:06:12.610
So just like that, we
have a pretty neat clue
00:06:12.610 --> 00:06:15.690
about when you're not going
to see a nice neat solution
00:06:15.690 --> 00:06:17.610
to a systems of equations represented
00:06:17.610 --> 00:06:19.770
as a matrix vector equation like this.
00:06:19.770 --> 00:06:21.240
You're not gonna have a nice, clean
00:06:21.240 --> 00:06:23.400
unique solution when the determinant
00:06:23.400 --> 00:06:27.060
of your matrix A is equal to zero.
00:06:27.060 --> 00:06:29.470
And since you're not going to
have a nice clean solution,
00:06:29.470 --> 00:06:31.530
you must not be able
to find an inverse here
00:06:31.530 --> 00:06:34.030
because if you had an inverse,
you could just multiply it.
00:06:34.030 --> 00:06:37.800
So this is a situation where
this is only going to be true,
00:06:37.800 --> 00:06:39.440
and I haven't proven it rigorously,
00:06:39.440 --> 00:06:42.230
but hopefully it gives you a
little bit of a justification.
00:06:42.230 --> 00:06:46.840
This is a situation where
A inverse doesn't exist.
00:06:46.840 --> 00:06:48.670
So there's a lot that's interesting here.
00:06:48.670 --> 00:06:51.130
In a previous video, we
thought about a matrix A
00:06:51.130 --> 00:06:52.710
and we thought about
it as a transformation
00:06:52.710 --> 00:06:56.320
and how its determinant tells
us how we are scaling areas.
00:06:56.320 --> 00:06:58.630
But if its determinant is
zero, that means you're
00:06:58.630 --> 00:07:00.470
taking things that have
two dimensional area
00:07:00.470 --> 00:07:02.620
and you're scaling them
down to having zero area.
00:07:02.620 --> 00:07:04.520
It'd be very hard to go
the other way around,
00:07:04.520 --> 00:07:07.890
which is what A inverse
transformation matrix would do.
00:07:07.890 --> 00:07:11.070
Here, we're getting the same
result, not viewing matrix A
00:07:11.070 --> 00:07:14.640
as a transformation, but
viewing it as a representation
00:07:14.640 --> 00:07:17.920
of a system of linear equations like this.
00:07:17.920 --> 00:07:20.090
But once again, we got the same idea
00:07:20.090 --> 00:07:22.610
that the determinant
of A is equal to zero.
00:07:22.610 --> 00:07:24.910
You're not going to get a
nice clean solution here.
00:07:24.910 --> 00:07:27.743
And so the inverse does not exist.
|
Composing 3x3 matrices | https://www.youtube.com/watch?v=2O18RbWmrYA | vtt | https://www.youtube.com/api/timedtext?v=2O18RbWmrYA&ei=6VWUZZrpI92fxN8P4-eBiAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=389D6A6120A01ED3D0B2DB92A2BE364E015ECA42.A493326489418803D4BD84D54ED3A84642173869&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.160 --> 00:00:02.700
- [Instructor] So we have two,
three by three matrices here,
00:00:02.700 --> 00:00:04.700
matrix A and matrix B.
00:00:04.700 --> 00:00:05.870
And we can of course,
00:00:05.870 --> 00:00:08.940
view each of them as a transformation
00:00:08.940 --> 00:00:11.200
in three dimensional space.
00:00:11.200 --> 00:00:12.710
Now, what we're going to
think about in this video
00:00:12.710 --> 00:00:15.630
is the composition of A of Bs.
00:00:15.630 --> 00:00:17.730
So you can think of this
as the transformation
00:00:17.730 --> 00:00:21.720
where you apply B first, and
then you apply A after that.
00:00:21.720 --> 00:00:23.210
And then we can represent that
00:00:23.210 --> 00:00:25.280
by another three by three matrix,
00:00:25.280 --> 00:00:26.810
which is partially completed here.
00:00:26.810 --> 00:00:29.000
We have the first and
the third column here.
00:00:29.000 --> 00:00:30.450
And so my question to you is
00:00:30.450 --> 00:00:33.790
what is this middle column
where I have these three blanks?
00:00:33.790 --> 00:00:36.740
Pause the video and try
to work through that.
00:00:36.740 --> 00:00:39.770
All right, now let's work
through this together.
00:00:39.770 --> 00:00:43.160
So one way to think about
how to construct A of B
00:00:43.160 --> 00:00:44.420
is that what you're doing is
00:00:44.420 --> 00:00:46.950
you're taking each of the columns of B
00:00:46.950 --> 00:00:47.783
and you're thinking
00:00:47.783 --> 00:00:50.450
about what would they be
under the transformation A.
00:00:50.450 --> 00:00:53.430
So if you were to apply
the transformation A,
00:00:53.430 --> 00:00:56.130
to this column, right over here,
00:00:56.130 --> 00:00:58.360
you would get this column.
00:00:58.360 --> 00:01:02.130
If you apply the transformation
A to this column,
00:01:02.130 --> 00:01:03.330
right over here,
00:01:03.330 --> 00:01:05.170
you would get this column.
00:01:05.170 --> 00:01:06.410
So what we really need to do
00:01:06.410 --> 00:01:10.110
is apply the transformation
A to this column,
00:01:10.110 --> 00:01:12.050
to the middle column, right over here.
00:01:12.050 --> 00:01:13.240
And just as a reminder,
00:01:13.240 --> 00:01:15.100
how this transformation works.
00:01:15.100 --> 00:01:17.230
A vector zero to three,
00:01:17.230 --> 00:01:22.230
you can think of it as zero
of the one zero, zero vector,
00:01:26.010 --> 00:01:28.420
the unit vector in the X direction.
00:01:28.420 --> 00:01:33.420
Plus two of the zero, one, zero vector
00:01:33.830 --> 00:01:38.830
plus three of the zero, zero one vector.
00:01:40.350 --> 00:01:41.730
Now, when you're applying transformation,
00:01:41.730 --> 00:01:44.460
instead of using these unit vectors,
00:01:44.460 --> 00:01:47.760
you use the image of them
under this transformation.
00:01:47.760 --> 00:01:49.340
And now in this situation,
00:01:49.340 --> 00:01:51.600
instead of one zero, zero vector,
00:01:51.600 --> 00:01:54.200
we are going to be using this thing,
00:01:54.200 --> 00:01:56.030
instead of a zero one zero,
00:01:56.030 --> 00:01:58.950
we're going to be using this thing.
00:01:58.950 --> 00:02:00.860
Instead of a zero, zero one,
00:02:00.860 --> 00:02:03.990
we are going to be using this thing.
00:02:03.990 --> 00:02:05.900
So this middle column,
00:02:05.900 --> 00:02:07.520
when it's transformed by this vector
00:02:07.520 --> 00:02:11.660
is going to be zero, instead
of the one zero, zero one,
00:02:11.660 --> 00:02:15.610
it's going to be zero
of the negative three,
00:02:15.610 --> 00:02:18.370
negative three, three vector.
00:02:18.370 --> 00:02:23.370
And then we have plus
two, plus two of the zero.
00:02:25.380 --> 00:02:27.130
Let me do that in that purple color
00:02:27.130 --> 00:02:32.130
of the zero, negative two, three vector.
00:02:33.520 --> 00:02:34.760
And then last but not least,
00:02:34.760 --> 00:02:38.650
you're going to have
three of the plus three
00:02:38.650 --> 00:02:40.420
of then I'll do that in yellow,
00:02:40.420 --> 00:02:45.160
the zero negative for one vector.
00:02:45.160 --> 00:02:47.540
Now we just do the math.
00:02:47.540 --> 00:02:49.420
So when you play zero times, all of this,
00:02:49.420 --> 00:02:51.410
you're just gonna have a
zero, zero, zero vector.
00:02:51.410 --> 00:02:53.000
So we can, those all go away.
00:02:53.000 --> 00:02:55.780
And then you are left with, let's see,
00:02:55.780 --> 00:02:59.040
this one is going to be
two times zero is zero.
00:02:59.040 --> 00:03:00.960
Two times negative two is negative four,
00:03:00.960 --> 00:03:02.890
two times three is six.
00:03:02.890 --> 00:03:07.700
You're gonna have that,
plus three times zero
00:03:07.700 --> 00:03:11.010
is zero, three times
negative four is negative 12,
00:03:11.010 --> 00:03:12.870
three times one is three.
00:03:12.870 --> 00:03:14.650
I could have written
this a little bit neater,
00:03:14.650 --> 00:03:16.220
but hopefully you get the idea.
00:03:16.220 --> 00:03:18.100
And then when we add those two things,
00:03:18.100 --> 00:03:21.760
zero plus zero, is zero.
00:03:21.760 --> 00:03:26.260
Negative four plus
negative 12 is negative 16,
00:03:26.260 --> 00:03:31.210
six plus three is nine, and we're done.
00:03:31.210 --> 00:03:36.053
We have just completed
the composition of A of B.
|
Inverse matrix introduction | https://www.youtube.com/watch?v=sT9IgHjjhiY | vtt | https://www.youtube.com/api/timedtext?v=sT9IgHjjhiY&ei=6VWUZbikIJC8hcIPxa21CA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=916F055F3BDBC0CA0A3C9719B077E70E7FD2722F.5BAACFCFCA692C029368F91F584AECA50BFBEB6C&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.060 --> 00:00:02.730
- [Instructor] We know that
when we're just multiplying
00:00:02.730 --> 00:00:05.780
regular numbers we have
the notion of a reciprocal.
00:00:05.780 --> 00:00:08.640
For example, if I were to take
two and I were to multiply it
00:00:08.640 --> 00:00:12.270
by its reciprocal, it
would be equal to one.
00:00:12.270 --> 00:00:13.640
Or if I were to just take a
00:00:13.640 --> 00:00:16.020
and a is not equal to zero
and I were to multiply it
00:00:16.020 --> 00:00:19.800
by its reciprocal for any
a, that is not equal to zero
00:00:19.800 --> 00:00:21.950
this will also be equal to one.
00:00:21.950 --> 00:00:25.700
And this is a number that
if I multiply times anything
00:00:25.700 --> 00:00:29.040
I am just going to get
that original number.
00:00:29.040 --> 00:00:31.220
So that's interesting, put
in the back of our minds
00:00:31.220 --> 00:00:33.290
you learned this many, many years ago.
00:00:33.290 --> 00:00:34.500
Now we also have something
00:00:34.500 --> 00:00:37.040
that comes out of our
knowledge of functions.
00:00:37.040 --> 00:00:39.900
We know that if there's some function
00:00:39.900 --> 00:00:44.030
let's call it f(x) that
goes from some set,
00:00:44.030 --> 00:00:45.790
we call that our domain
00:00:45.790 --> 00:00:49.290
to some other set we call that our range,
00:00:49.290 --> 00:00:51.070
that in many cases, not all cases
00:00:51.070 --> 00:00:55.117
so this is the function f
that goes from x to f(x).
00:00:56.060 --> 00:00:59.500
That in many cases,
but not always the case
00:00:59.500 --> 00:01:02.200
there's another function
that can take us back.
00:01:02.200 --> 00:01:06.270
And we call that other
function, the inverse of f.
00:01:06.270 --> 00:01:11.080
So that if you apply
the inverse of f to f(x)
00:01:11.080 --> 00:01:13.130
you're going to get
back to where you were.
00:01:13.130 --> 00:01:15.240
You're going to get back to x.
00:01:15.240 --> 00:01:17.180
And we also know that it
goes the other way around.
00:01:17.180 --> 00:01:21.173
For example, if you did
f of f inverse of x,
00:01:24.260 --> 00:01:26.800
that too will get us back to x.
00:01:26.800 --> 00:01:28.230
So the natural question is
00:01:28.230 --> 00:01:31.240
is there an analog for
an inverse of a function,
00:01:31.240 --> 00:01:33.410
or for reciprocal when we're multiplying
00:01:33.410 --> 00:01:36.333
when we think about matrices.
00:01:37.450 --> 00:01:40.090
So let's play with a few ideas.
00:01:40.090 --> 00:01:43.310
So let's imagine a matrix
as a transformation,
00:01:43.310 --> 00:01:45.330
which we have already talked about it.
00:01:45.330 --> 00:01:47.560
When we think about
matrices as transformations
00:01:47.560 --> 00:01:49.020
they really are functions.
00:01:49.020 --> 00:01:51.190
There are functions that
are taking one point
00:01:51.190 --> 00:01:52.600
in a certain dimensional space
00:01:52.600 --> 00:01:55.590
let's say in the coordinate
plane, to another point
00:01:55.590 --> 00:01:58.250
it transforms a vector to another vector.
00:01:58.250 --> 00:02:01.920
For example, let's imagine
something that does
00:02:01.920 --> 00:02:06.160
a clockwise 90 degree rotation.
00:02:06.160 --> 00:02:08.990
And we know how to construct
that transformation matrix
00:02:08.990 --> 00:02:11.130
which really is a function.
00:02:11.130 --> 00:02:14.070
What it does is, in our
transformation matrix
00:02:14.070 --> 00:02:19.070
we want to say, what do we do
with the one zero unit vector?
00:02:20.760 --> 00:02:25.700
And what also do we do with
the zero one unit vector
00:02:25.700 --> 00:02:27.700
when you do that transformation?
00:02:27.700 --> 00:02:32.330
Well, if you're doing a
90 degree clockwise turn,
00:02:32.330 --> 00:02:34.530
then the one zero unit vector
00:02:34.530 --> 00:02:37.520
is going to go right over here.
00:02:37.520 --> 00:02:39.000
And so that's going to be turned
00:02:39.000 --> 00:02:42.280
into the zero negative one vector.
00:02:42.280 --> 00:02:43.990
So I'll write that right there.
00:02:43.990 --> 00:02:46.980
And then the zero one
vector is going to be turned
00:02:46.980 --> 00:02:49.400
into the one zero vector.
00:02:49.400 --> 00:02:50.233
So let me write it down.
00:02:50.233 --> 00:02:53.000
This is 90 degrees clockwise
00:02:54.010 --> 00:02:54.900
and then we can think about
00:02:54.900 --> 00:02:57.340
what 90 degree counter-clockwise
00:03:01.290 --> 00:03:02.760
would look like
00:03:02.760 --> 00:03:04.010
you're going counterclockwise
00:03:04.010 --> 00:03:06.940
your original one zero
vector right over here
00:03:06.940 --> 00:03:07.950
is going to go over here.
00:03:07.950 --> 00:03:10.940
It's going to become the zero one vector.
00:03:10.940 --> 00:03:13.400
So we will write that right over here.
00:03:13.400 --> 00:03:18.400
And then the zero one vector
will then become this vector
00:03:18.410 --> 00:03:20.840
if you're doing a 90 degree
counterclockwise rotation
00:03:20.840 --> 00:03:24.400
it's going to become the
negative one zero vector
00:03:24.400 --> 00:03:26.400
negative one, zero vector.
00:03:26.400 --> 00:03:29.150
So in theory these two transformations
00:03:29.150 --> 00:03:30.830
should undo each other.
00:03:30.830 --> 00:03:31.990
If I do a transformation
00:03:31.990 --> 00:03:33.910
that first gets 90 degrees clockwise,
00:03:33.910 --> 00:03:35.170
and then I apply a transformation
00:03:35.170 --> 00:03:36.930
that's 90 degrees counter-clockwise
00:03:36.930 --> 00:03:39.630
I should get back to where we began.
00:03:39.630 --> 00:03:40.630
Now let's see what happens
00:03:40.630 --> 00:03:43.600
when we compose these two transformations
00:03:43.600 --> 00:03:44.810
and we know how to do that.
00:03:44.810 --> 00:03:45.660
We've already talked about it.
00:03:45.660 --> 00:03:49.510
We essentially multiply
these two matrices.
00:03:49.510 --> 00:03:53.040
If you were to multiply
zero, negative one,
00:03:53.040 --> 00:03:58.040
one, zero times zero,
negative one, one, zero.
00:03:58.950 --> 00:03:59.793
What do we get?
00:04:00.850 --> 00:04:03.930
Well, let's see these, this top left
00:04:03.930 --> 00:04:05.550
this is composing two, two
00:04:05.550 --> 00:04:08.570
by two matrices is equivalent
to multiplying them
00:04:08.570 --> 00:04:09.910
we've seen that in other videos.
00:04:09.910 --> 00:04:13.590
And so first we will look
at this row and this column
00:04:13.590 --> 00:04:17.640
and that's going to be zero
times zero plus one times one.
00:04:17.640 --> 00:04:19.050
So that is going to be one.
00:04:19.050 --> 00:04:22.370
They're going to look at
this row and this column.
00:04:22.370 --> 00:04:24.500
So zero times negative one
00:04:24.500 --> 00:04:27.350
plus one times zero is
just going to be zero.
00:04:27.350 --> 00:04:29.850
And then we're going to multiply
00:04:29.850 --> 00:04:31.610
this row times each of those columns.
00:04:31.610 --> 00:04:34.530
So negative one times zero is zero
00:04:34.530 --> 00:04:37.220
plus zero times one is zero
00:04:37.220 --> 00:04:40.710
and then negative one
times negative one is one
00:04:40.710 --> 00:04:43.040
plus zero times zero is one.
00:04:43.040 --> 00:04:46.970
And look what happened when
we took the composition of
00:04:46.970 --> 00:04:50.170
these two matrices that
should undo each other
00:04:50.170 --> 00:04:51.200
we see that it does.
00:04:51.200 --> 00:04:53.900
It turns into the identity transformation
00:04:53.900 --> 00:04:55.180
or the identity matrix.
00:04:55.180 --> 00:04:57.890
We know that this matrix right
over here as a transformation
00:04:57.890 --> 00:05:01.370
it's just going to map
everything onto themselves.
00:05:01.370 --> 00:05:03.850
Now, this is really
interesting because if we view
00:05:03.850 --> 00:05:06.900
these two by two transformation
matrices as functions,
00:05:06.900 --> 00:05:09.870
we've just shown that if we call this
00:05:09.870 --> 00:05:13.930
say our first function then
can call this it's inverse.
00:05:13.930 --> 00:05:16.460
And actually we use that same language
00:05:16.460 --> 00:05:18.410
when we talk about matrices.
00:05:18.410 --> 00:05:21.330
If we call this as being equal to A
00:05:21.330 --> 00:05:24.730
we would call this as
being equal to A inverse.
00:05:24.730 --> 00:05:27.400
So if I were to take matrix A
00:05:27.400 --> 00:05:30.630
and I were to multiply
that times its inverse
00:05:30.630 --> 00:05:35.120
I should get the identity
matrix, which is right over here.
00:05:35.120 --> 00:05:36.730
And here I'm speaking in generalities
00:05:36.730 --> 00:05:38.820
I'm not even just talking
about the two by two case.
00:05:38.820 --> 00:05:40.160
That should be the three by three case
00:05:40.160 --> 00:05:42.800
the four by four case so on and so forth.
00:05:42.800 --> 00:05:45.610
And we also know, that I could
have defined this bottom one
00:05:45.610 --> 00:05:48.180
as A and the top one as A inverse.
00:05:48.180 --> 00:05:50.370
And so the other way
should be true as well.
00:05:50.370 --> 00:05:54.180
A inverse times A should
also be equivalent
00:05:54.180 --> 00:05:55.420
to the identity matrix.
00:05:55.420 --> 00:05:58.080
And so that's completely
analogous to what we saw
00:05:58.080 --> 00:05:59.600
in these function examples
00:05:59.600 --> 00:06:01.210
between a function and its inverse
00:06:01.210 --> 00:06:02.820
because the other day, as we said
00:06:02.820 --> 00:06:05.020
an end by end matrix can be viewed
00:06:05.020 --> 00:06:09.490
as a transformation can
be viewed as a function.
00:06:09.490 --> 00:06:11.740
And we also see that it
has analogs to just how
00:06:11.740 --> 00:06:13.320
we think about multiplication.
00:06:13.320 --> 00:06:15.300
'Cause here we could
do this multiplication
00:06:15.300 --> 00:06:18.040
as a composition of transformations
00:06:18.040 --> 00:06:21.230
but we also can just view
this as matrix multiplication.
00:06:21.230 --> 00:06:22.510
And so if we take a matrix
00:06:22.510 --> 00:06:24.760
and we multiply it by its inverse,
00:06:24.760 --> 00:06:26.360
that's analogous to taking a number
00:06:26.360 --> 00:06:28.220
and multiplying by its reciprocal
00:06:28.220 --> 00:06:30.030
and we get the equivalent of
00:06:30.030 --> 00:06:31.900
what in the number
world would just be one,
00:06:31.900 --> 00:06:34.320
but in the matrix world
is the identity matrix.
00:06:34.320 --> 00:06:36.670
'Cause the identity matrix
has this nice property
00:06:36.670 --> 00:06:39.960
that if I were to take the identity matrix
00:06:39.960 --> 00:06:42.690
and I were to multiply at times any matrix
00:06:42.690 --> 00:06:44.810
you're gonna get the original matrix again
00:06:44.810 --> 00:06:48.080
which is what we saw at least
within the analog that we saw
00:06:48.080 --> 00:06:49.953
in the regular number world.
|
Help Khan Academy Double Down On Our Efforts | https://www.youtube.com/watch?v=1vMVqhh_wi4 | vtt | https://www.youtube.com/api/timedtext?v=1vMVqhh_wi4&ei=6VWUZb-gHtm1vdIPrYeQEA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=BF044753C208F1CCDEEBF39F4F0925F30132D0D5.76EAE93BA9449B918B2D6636AA0281A8E3BD0B35&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.350 --> 00:00:02.910
- Hi everyone, Sal Khan
here from Khan Academy
00:00:02.910 --> 00:00:04.330
and I just wanted to remind you
00:00:04.330 --> 00:00:06.550
that if you're in the position to do so,
00:00:06.550 --> 00:00:08.900
to think about making a
donation to Khan Academy.
00:00:08.900 --> 00:00:10.800
We are a not for profit organization
00:00:10.800 --> 00:00:12.810
and we can only exist through donations
00:00:12.810 --> 00:00:14.710
from folks like yourself.
00:00:14.710 --> 00:00:16.289
And now, as we are approaching
00:00:16.289 --> 00:00:20.320
the one year anniversary of
schools in the United States
00:00:20.320 --> 00:00:21.960
and actually schools in much of the world
00:00:21.960 --> 00:00:25.120
having to shut down physically
because of the pandemic,
00:00:25.120 --> 00:00:27.850
it's even more that we
double down our efforts.
00:00:27.850 --> 00:00:30.080
Obviously, during the school closures,
00:00:30.080 --> 00:00:33.800
many, many, many folks leaned
even more on Khan Academy.
00:00:33.800 --> 00:00:35.500
It was the place where they went
00:00:35.500 --> 00:00:38.120
to make sure that they kept
pace with their classes
00:00:38.120 --> 00:00:39.600
or if they weren't
getting distance learning
00:00:39.600 --> 00:00:41.520
that they were able to get their learning.
00:00:41.520 --> 00:00:42.670
But now, as we're starting to see
00:00:42.670 --> 00:00:43.980
the light at the end of the tunnel,
00:00:43.980 --> 00:00:45.720
I've talked about this very publicly,
00:00:45.720 --> 00:00:49.070
we really have to view this
as a disaster recovery effort
00:00:49.070 --> 00:00:52.290
because so many students,
most students arguably,
00:00:52.290 --> 00:00:54.470
have accumulated all
sorts of learning loss
00:00:54.470 --> 00:00:55.800
over this past year.
00:00:55.800 --> 00:00:58.140
Some students have fallen
off the radar completely.
00:00:58.140 --> 00:01:01.240
And so, as we go into the
end of this school year
00:01:01.240 --> 00:01:03.280
and actually the next several years,
00:01:03.280 --> 00:01:06.770
we need to make sure that there
is free accessible resources
00:01:06.770 --> 00:01:08.560
for students, for parents,
00:01:08.560 --> 00:01:10.248
and for teachers and school districts
00:01:10.248 --> 00:01:12.850
to make sure they can personalize
00:01:12.850 --> 00:01:14.090
to the needs of students.
00:01:14.090 --> 00:01:15.760
And as you can imagine, that's exactly
00:01:15.760 --> 00:01:17.800
what Khan Academy is focused on.
00:01:17.800 --> 00:01:20.760
We had over 12 billion learning minutes
00:01:20.760 --> 00:01:23.840
on Khan Academy in
2020, and we expect that
00:01:23.840 --> 00:01:25.860
that will only accelerate
in the years ahead.
00:01:25.860 --> 00:01:27.440
That's 12 billion minutes
00:01:27.440 --> 00:01:29.129
of learners around the world
00:01:29.129 --> 00:01:32.350
really being able to
dig in into their gaps,
00:01:32.350 --> 00:01:34.200
make up for any unfinished learning,
00:01:34.200 --> 00:01:37.090
and then learn at grade level or beyond.
00:01:37.090 --> 00:01:38.580
So if you're in a position to do so,
00:01:38.580 --> 00:01:40.970
the social return on investment,
00:01:40.970 --> 00:01:42.910
the social benefit to cost ratio
00:01:42.910 --> 00:01:45.590
for Khan Academy is off the charts.
00:01:45.590 --> 00:01:48.528
And so hopefully, we'll
make both your heart
00:01:48.528 --> 00:01:50.960
and your head feel good about the impact
00:01:50.960 --> 00:01:52.500
that you will have on millions
00:01:52.500 --> 00:01:53.960
and millions of learners today
00:01:53.960 --> 00:01:56.353
and billions of learners in the future.
|
Proof: Matrix determinant gives area of image of unit square under mapping | https://www.youtube.com/watch?v=_OiMiQGKvvc | vtt | https://www.youtube.com/api/timedtext?v=_OiMiQGKvvc&ei=6VWUZbiSHpSgp-oPo4uywAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B3BE1F0E13494EE48EFDAD67B9D64BFBE916CBC7.8356DA8C5AEDD17A6A3E73E716C2D8DFAE3AB482&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.480 --> 00:00:02.370
- [Instructor] The goal of
this video is to feel good
00:00:02.370 --> 00:00:04.920
about the connection
that we've talked about
00:00:04.920 --> 00:00:07.200
between the absolute
value of the determinant
00:00:07.200 --> 00:00:08.780
of a two by two matrix
00:00:08.780 --> 00:00:12.720
and the area of the
parallelogram that's defined
00:00:12.720 --> 00:00:15.790
by the two column vectors of that matrix.
00:00:15.790 --> 00:00:18.160
So for example, I have this column vector
00:00:18.160 --> 00:00:21.720
right over here ac, so
that's this blue vector.
00:00:21.720 --> 00:00:23.070
So this distance right over here,
00:00:23.070 --> 00:00:25.230
it goes a in the x direction.
00:00:25.230 --> 00:00:27.900
So this distance right over here is a,
00:00:27.900 --> 00:00:30.070
and then it goes c in the y direction.
00:00:30.070 --> 00:00:33.930
So this distance right
over here is equal to c.
00:00:33.930 --> 00:00:38.930
And so this distance up
here is also equal to a,
00:00:39.040 --> 00:00:42.880
and this is also equal to c.
00:00:42.880 --> 00:00:44.550
So we have this vector
00:00:44.550 --> 00:00:46.910
and then we have the bd vector,
00:00:46.910 --> 00:00:49.640
and bd vector, so in the x direction
00:00:49.640 --> 00:00:53.050
it goes a distance of b right over there.
00:00:53.050 --> 00:00:55.830
Or if we draw it over here,
it goes a distance of b.
00:00:55.830 --> 00:00:57.030
And in the vertical direction,
00:00:57.030 --> 00:00:59.540
again it goes a distance of d.
00:00:59.540 --> 00:01:01.500
So this right over here is d
00:01:01.500 --> 00:01:04.540
and this distance right over here is d.
00:01:04.540 --> 00:01:07.930
And we can see that the
parallelogram created or defined
00:01:07.930 --> 00:01:12.930
by those two vectors, it's
area is right over there.
00:01:13.500 --> 00:01:17.440
Now let's see if we can
connect that to the determinant
00:01:17.440 --> 00:01:20.160
or the absolute value of the
determinant of this matrix.
00:01:20.160 --> 00:01:23.040
And we're just going to assume
for the sake of simplicity
00:01:23.040 --> 00:01:26.080
that a, b, c and d are positive values,
00:01:26.080 --> 00:01:29.060
although we can in the
future do this same thing
00:01:29.060 --> 00:01:30.470
where we had some other combination
00:01:30.470 --> 00:01:32.250
where some of them are not positive,
00:01:32.250 --> 00:01:33.395
but this will hopefully give you a clue
00:01:33.395 --> 00:01:35.505
of how we can prove it.
00:01:35.505 --> 00:01:40.505
Now, how can we figure out the
area of this parallelogram?
00:01:40.700 --> 00:01:43.260
Well, one technique would be find the area
00:01:43.260 --> 00:01:47.530
of this larger rectangle right over here,
00:01:47.530 --> 00:01:48.900
and then from that,
00:01:48.900 --> 00:01:52.740
subtract out the parts that
are not in the parallelogram.
00:01:52.740 --> 00:01:54.350
And so let's do that.
00:01:54.350 --> 00:01:57.163
So what's the area of
this larger rectangle?
00:01:58.010 --> 00:02:00.010
Let's see the dimensions here are,
00:02:00.010 --> 00:02:04.020
this length from here to here is a,
00:02:04.020 --> 00:02:07.210
and then from here to here is b.
00:02:07.210 --> 00:02:09.380
So this is a plus b on this side.
00:02:09.380 --> 00:02:11.320
And on this side up here,
00:02:11.320 --> 00:02:15.020
this part is d and then this
part is c right over here.
00:02:15.020 --> 00:02:16.120
So it's d plus c.
00:02:16.120 --> 00:02:17.910
So the area of the whole thing
00:02:17.910 --> 00:02:22.910
is going to be a plus b, times d plus c,
00:02:23.600 --> 00:02:25.350
which is equal to, we just do
00:02:25.350 --> 00:02:27.070
the distributive property a few times.
00:02:27.070 --> 00:02:32.070
It's going to be ad
plus ac plus bd plus bc.
00:02:35.530 --> 00:02:37.760
Now, from that we're going
to wanna subtract out all
00:02:37.760 --> 00:02:40.430
of these other parts that
are not in the parallelogram.
00:02:40.430 --> 00:02:41.570
So let's do that.
00:02:41.570 --> 00:02:44.310
So you have this triangle right over here
00:02:44.310 --> 00:02:48.160
whose area would be ac over
two, a times c over two,
00:02:48.160 --> 00:02:50.920
but you also have this one,
which has the same area.
00:02:50.920 --> 00:02:52.680
So if we subtract both of them out
00:02:52.680 --> 00:02:54.950
we'd wanna subtract out a total of ac.
00:02:54.950 --> 00:02:56.800
Each of those are ac over two.
00:02:56.800 --> 00:03:00.200
So to count both of them
let's subtract out an ac.
00:03:00.200 --> 00:03:03.470
And then of course we could
do these two triangles.
00:03:03.470 --> 00:03:06.850
And the area of each of these
triangles is bd over two,
00:03:06.850 --> 00:03:08.670
b times d over two,
00:03:08.670 --> 00:03:11.100
but add them together,
their combined area is bd.
00:03:11.100 --> 00:03:12.953
So let's subtract that out, minus bd.
00:03:13.900 --> 00:03:18.210
And now, what is the area
of this right over here?
00:03:18.210 --> 00:03:22.910
Well, that is b times
c, so minus b times c,
00:03:22.910 --> 00:03:25.650
actually and that's also the
area of this right over here.
00:03:25.650 --> 00:03:27.030
So we have another b times c,
00:03:27.030 --> 00:03:29.980
so minus 2bc.
00:03:29.980 --> 00:03:31.780
So let's see what's going on.
00:03:31.780 --> 00:03:35.740
So if we subtract these
out, that takes out that,
00:03:35.740 --> 00:03:40.110
that takes out that, and
if you take bc minus 2bc
00:03:40.110 --> 00:03:42.650
we're gonna be left
with just a negative bc.
00:03:42.650 --> 00:03:44.280
So all of this is going to be equal
00:03:44.280 --> 00:03:46.900
to ad, what we have there.
00:03:46.900 --> 00:03:50.860
Bc minus 2bc is just
gonna be a negativebc.
00:03:50.860 --> 00:03:53.843
Well, this is going to be the determinant
00:03:53.843 --> 00:03:58.843
of our matrix, a times d minus b times c.
00:03:59.550 --> 00:04:02.280
So this isn't a proof that
for any a, b, c, or d,
00:04:02.280 --> 00:04:04.430
the absolute value of
the determinant is equal
00:04:04.430 --> 00:04:06.500
to this area, but it
shows you the case where
00:04:06.500 --> 00:04:07.830
you have a positive determinant
00:04:07.830 --> 00:04:09.830
and all of these values are positive.
00:04:09.830 --> 00:04:11.620
So hopefully that feels
somewhat satisfying.
00:04:11.620 --> 00:04:13.720
And you can try, if you
like to prove the cases
00:04:13.720 --> 00:04:15.470
if you don't have a positive determinant
00:04:15.470 --> 00:04:18.003
or if some combination
of these are negative.
|
Finding area of figure after transformation using determinant | https://www.youtube.com/watch?v=aVuCoUxt3vc | vtt | https://www.youtube.com/api/timedtext?v=aVuCoUxt3vc&ei=6VWUZa-RIc6cp-oPt42ayAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9EF6168447B3087E2AECE7272182092083633DEA.DE399A76643B64296702B5AAF7E9565DDAF342AD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.170 --> 00:00:03.220
- [Tutor] We're told to consider
this matrix transformation
00:00:03.220 --> 00:00:04.710
or this is a matrix that you can view,
00:00:04.710 --> 00:00:06.190
represents a transformation
00:00:06.190 --> 00:00:07.810
on the entire coordinate plane.
00:00:07.810 --> 00:00:10.740
And then they tell us that the
transformation is performed
00:00:10.740 --> 00:00:12.310
on the following rectangle.
00:00:12.310 --> 00:00:15.470
So this is the rectangle
before the transformation
00:00:15.470 --> 00:00:17.390
and they say, what is the area
00:00:17.390 --> 00:00:21.530
of the image of the rectangle
under this transformation?
00:00:21.530 --> 00:00:25.210
So the image of the rectangle
is what the rectangle becomes
00:00:25.210 --> 00:00:26.460
after the transformation.
00:00:26.460 --> 00:00:28.240
So pause this video and
see if you can answer that
00:00:28.240 --> 00:00:30.090
before we work through it on our own.
00:00:31.490 --> 00:00:34.260
All right, so the main
thing to realize is,
00:00:34.260 --> 00:00:36.640
if we have a matrix transformation
00:00:36.640 --> 00:00:38.990
or a transformation matrix like this
00:00:38.990 --> 00:00:42.810
if we take the absolute
value of its determinant,
00:00:42.810 --> 00:00:47.810
that value tells us how much
that transformation scales up
00:00:49.350 --> 00:00:51.200
areas of figures.
00:00:51.200 --> 00:00:52.160
So let's just do that,
00:00:52.160 --> 00:00:55.320
let's evaluate the absolute
value of the determinant here.
00:00:55.320 --> 00:00:57.960
So the absolute value of the determinant
00:00:57.960 --> 00:01:00.880
would be the absolute value of 5 times 8,
00:01:00.880 --> 00:01:05.880
5 times 8 minus 9 times 4, 9 times 4.
00:01:07.290 --> 00:01:09.240
Remember for a 2 by 2 matrix,
00:01:09.240 --> 00:01:12.380
the determinant is just this times this
00:01:12.380 --> 00:01:15.310
minus this times that.
00:01:15.310 --> 00:01:20.310
And so that's going to be the
absolute value of 40 minus 36
00:01:20.860 --> 00:01:23.090
which is just the absolute value of 4
00:01:23.090 --> 00:01:25.620
which is just going to be equal to 4.
00:01:25.620 --> 00:01:28.280
So this tells us that this transformation
00:01:28.280 --> 00:01:32.400
will scale up area by a factor of 4.
00:01:32.400 --> 00:01:35.120
So what's the area before
the transformation?
00:01:35.120 --> 00:01:37.660
Well, we can see that this is, let's see,
00:01:37.660 --> 00:01:42.660
it's 5 units tall and it is 7 units wide.
00:01:43.700 --> 00:01:48.320
So this has an area of 35 square
units, pre transformation.
00:01:48.320 --> 00:01:50.650
So post transformation,
we just multiply it
00:01:50.650 --> 00:01:53.520
by the absolute value of
the determinant to get,
00:01:53.520 --> 00:01:57.710
let's see, 4 times 30 is 120
00:01:57.710 --> 00:01:59.990
plus 4 times 5 is another 20.
00:01:59.990 --> 00:02:01.210
So this is going to get us
00:02:01.210 --> 00:02:05.693
to 140 square units and we're done.
|
Interpreting determinants in terms of area | https://www.youtube.com/watch?v=ER_96Mx-KEE | vtt | https://www.youtube.com/api/timedtext?v=ER_96Mx-KEE&ei=6VWUZZHyH86evdIPqvmj8AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1955E2FCD982A3710E983F7952B19514A2B49337.1AD47168182B611CCA1747B603D27D21169D1B72&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.390 --> 00:00:02.810
- [Instructor] So I have
a two by two matrix here
00:00:02.810 --> 00:00:06.480
and we could view it as
having two column vectors.
00:00:06.480 --> 00:00:09.980
So the first column can
define this vector three, one,
00:00:09.980 --> 00:00:11.620
which I've depicted in blue here.
00:00:11.620 --> 00:00:14.792
And then that second
column, you can view it
00:00:14.792 --> 00:00:16.930
as telling us that we have
another vector, one, two,
00:00:16.930 --> 00:00:19.780
which I have depicted in this pink color.
00:00:19.780 --> 00:00:22.494
Now, an interesting
interpretation of the determinant
00:00:22.494 --> 00:00:24.970
of this two by two matrix is that
00:00:24.970 --> 00:00:26.980
the absolute value of the determinant
00:00:26.980 --> 00:00:29.272
is the area of the parallelogram defined
00:00:29.272 --> 00:00:31.220
by these two vectors.
00:00:31.220 --> 00:00:33.100
What I mean by the parallelogram defined
00:00:33.100 --> 00:00:34.660
by these two vectors?
00:00:34.660 --> 00:00:37.590
Well, imagine taking this
bottom vector and shifting it
00:00:37.590 --> 00:00:40.546
so it's tail is at the
head of this pink vector.
00:00:40.546 --> 00:00:44.650
So it would look like this, hand draw it.
00:00:44.650 --> 00:00:46.460
Looks something like that.
00:00:46.460 --> 00:00:48.690
And then if you were to
take this pink vector
00:00:48.690 --> 00:00:51.540
and copy it and shift
it up into the right.
00:00:51.540 --> 00:00:54.432
So its tail is at the head
of the original blue vector.
00:00:54.432 --> 00:00:56.930
It's going to look something like that.
00:00:56.930 --> 00:00:59.040
And so you can see, you
can use that technique
00:00:59.040 --> 00:01:02.160
to take any two vectors
in the coordinate plane.
00:01:02.160 --> 00:01:04.660
And they will define a parallelogram.
00:01:04.660 --> 00:01:06.120
And it turns out that the area
00:01:06.120 --> 00:01:08.230
of this parallelogram is going to be equal
00:01:08.230 --> 00:01:10.830
to the absolute value of the determinant
00:01:10.830 --> 00:01:12.080
of this matrix here.
00:01:12.080 --> 00:01:13.510
So what's that going to be?
00:01:13.510 --> 00:01:15.420
Well, we know of figure
out the determinant.
00:01:15.420 --> 00:01:18.250
It is three times two, which is six.
00:01:18.250 --> 00:01:23.070
Minus one times one, which is
one, which is equal to five.
00:01:23.070 --> 00:01:26.000
And of course the absolute
value of five is five.
00:01:26.000 --> 00:01:28.240
Now that's pretty cool in and of itself.
00:01:28.240 --> 00:01:31.450
We figured out one
interpretation of a determinant
00:01:31.450 --> 00:01:33.180
which will be useful as we build up
00:01:33.180 --> 00:01:35.320
our understanding of matrices.
00:01:35.320 --> 00:01:37.781
But another interpretation
is to say, all right,
00:01:37.781 --> 00:01:41.310
what if A is a transformation matrix,
00:01:41.310 --> 00:01:42.890
and I'm just rewriting it.
00:01:42.890 --> 00:01:45.420
So we know what a
transformation matrix does.
00:01:45.420 --> 00:01:49.350
It tells us what to do with
the unit vectors, so to speak.
00:01:49.350 --> 00:01:52.800
So for example, I have
this vector right over here
00:01:52.800 --> 00:01:56.100
which is the vector one, zero.
00:01:56.100 --> 00:01:58.780
We know that a transformation
matrix says, all right
00:01:58.780 --> 00:02:00.230
take that one, zero vector
00:02:00.230 --> 00:02:03.220
and turn it into the three, one vector.
00:02:03.220 --> 00:02:06.166
So turn that into that right over there.
00:02:06.166 --> 00:02:10.260
And we know we have the
other, or another unit vector.
00:02:10.260 --> 00:02:13.040
Let's call this, this right over here
00:02:13.040 --> 00:02:16.310
is the zero, one vector.
00:02:16.310 --> 00:02:19.540
Goes zero in the X direction,
one in the Y direction.
00:02:19.540 --> 00:02:21.210
And the transformation matrix says,
00:02:21.210 --> 00:02:24.333
hey, turn that into the one, two vector.
00:02:25.520 --> 00:02:26.600
But then you can think about it,
00:02:26.600 --> 00:02:30.940
it's also not just transforming
the individual vectors.
00:02:30.940 --> 00:02:35.150
It's also scaling up the
area defined by the vectors.
00:02:35.150 --> 00:02:37.610
So the area defined by these two original,
00:02:37.610 --> 00:02:40.650
we could say unit vectors,
we can see it's one by one.
00:02:40.650 --> 00:02:42.670
It's that area right over there.
00:02:42.670 --> 00:02:44.580
So this transformation is taking us
00:02:44.580 --> 00:02:47.350
from an area of one to an area, five.
00:02:47.350 --> 00:02:49.840
It's scaling it up by a factor of five.
00:02:49.840 --> 00:02:51.470
Now that's reasonably interesting
00:02:51.470 --> 00:02:54.110
just for this one unit square.
00:02:54.110 --> 00:02:56.120
But because of that
it'll actually scale up
00:02:56.120 --> 00:02:58.690
the area of any figure.
00:02:58.690 --> 00:03:00.000
Let's say had a figure like this.
00:03:00.000 --> 00:03:04.480
So this type of oval circle
thing, it has some area.
00:03:04.480 --> 00:03:06.515
If you apply this transformation matrix
00:03:06.515 --> 00:03:09.050
it will look something like this.
00:03:09.050 --> 00:03:10.590
I'm just approximating it.
00:03:10.590 --> 00:03:13.160
It would look something like that.
00:03:13.160 --> 00:03:15.720
So this will tell us that this bigger blob
00:03:15.720 --> 00:03:19.030
has five times the area
of this original blue blob
00:03:19.030 --> 00:03:21.790
because the bigger blob is the image.
00:03:21.790 --> 00:03:24.470
Once we've transformed the smaller blob
00:03:24.470 --> 00:03:27.700
by this transformation matrix.
00:03:27.700 --> 00:03:28.810
So if I were to tell you
00:03:28.810 --> 00:03:33.413
that the area of this smaller
circle is let's say 0.6
00:03:35.700 --> 00:03:37.970
but then we were to
apply the transformation.
00:03:37.970 --> 00:03:39.370
And someone were to ask you,
00:03:40.321 --> 00:03:41.154
what is the area of this bigger blob?
00:03:41.154 --> 00:03:43.720
Which is the image of the smaller circle
00:03:43.720 --> 00:03:45.410
after the transformation?
00:03:45.410 --> 00:03:48.770
Well, you take 0.6, multiply
it by the absolute value
00:03:48.770 --> 00:03:51.210
of the determinant of the
transformation matrix.
00:03:51.210 --> 00:03:52.470
You'd multiply it by five.
00:03:52.470 --> 00:03:57.470
So 0.6 times five would
be three square units.
00:03:57.920 --> 00:04:00.060
And a hint at the reason
why this works is,
00:04:00.060 --> 00:04:02.000
is that any region on the coordinate plane
00:04:02.000 --> 00:04:05.821
can be represented as a series of squares.
00:04:05.821 --> 00:04:08.210
And then if you apply the transformation
00:04:08.210 --> 00:04:10.060
you're really just transforming each
00:04:10.060 --> 00:04:11.940
of those individual squares.
00:04:11.940 --> 00:04:15.750
So the scaling up of the area
would be the same scale you do
00:04:15.750 --> 00:04:18.133
to any one of those smaller squares.
|
Intro to determinant notation and computation | https://www.youtube.com/watch?v=ZAkmBOCiNqU | vtt | https://www.youtube.com/api/timedtext?v=ZAkmBOCiNqU&ei=6VWUZZT5Htmop-oPl76EkAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D1CD767078FC14A1DCF2E58FAACF01B0582E78D2.DC7F18BC81A2EA427ED178522811703FB241823E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.420 --> 00:00:01.670
- [Instructor] In this
video, we're gonna talk
00:00:01.670 --> 00:00:05.800
about something called
determinants of matrices.
00:00:05.800 --> 00:00:08.110
So I'll start just
telling you the notation
00:00:08.110 --> 00:00:09.400
and how do you compute it.
00:00:09.400 --> 00:00:12.940
And then we'll think about
ways that you can interpret it.
00:00:12.940 --> 00:00:17.140
So let's give ourselves
a two by two matrix here.
00:00:17.140 --> 00:00:20.060
So, and actually, I'll
give it in general terms.
00:00:20.060 --> 00:00:24.430
So let's say that this
top-left term here is A,
00:00:24.430 --> 00:00:28.550
and then this one here is B the top-right.
00:00:28.550 --> 00:00:30.830
The bottom-left is C,
00:00:30.830 --> 00:00:34.150
and then let's call this bottom-right D.
00:00:34.150 --> 00:00:36.040
And I'm gonna do that
in a different color.
00:00:36.040 --> 00:00:38.010
So this is D right over here.
00:00:38.010 --> 00:00:39.890
the determinant of this matrix.
00:00:39.890 --> 00:00:41.930
And actually, let me
just call this matrix.
00:00:41.930 --> 00:00:44.610
Let's say that this is matrix A.
00:00:44.610 --> 00:00:47.510
So there's a bunch of ways
to call the determinant,
00:00:47.510 --> 00:00:49.420
or have the notation for the determinant.
00:00:49.420 --> 00:00:50.860
We could write it like this.
00:00:50.860 --> 00:00:51.970
We could have these little,
00:00:51.970 --> 00:00:54.060
it looks like absolute value signs,
00:00:54.060 --> 00:00:55.350
but it really means determinant
00:00:55.350 --> 00:00:57.380
when you apply it to a matrix.
00:00:57.380 --> 00:01:00.700
So the determinant of matrix A.
00:01:00.700 --> 00:01:02.310
You can write it that way.
00:01:02.310 --> 00:01:06.990
You could write it this way,
the determinant of matrix A.
00:01:08.320 --> 00:01:09.830
You could write it that way.
00:01:09.830 --> 00:01:11.060
Or you could write it this way,
00:01:11.060 --> 00:01:13.250
where you put these lines that look
00:01:13.250 --> 00:01:15.750
like big absolute value
signs instead of the brackets
00:01:15.750 --> 00:01:17.670
when you describe the numbers.
00:01:17.670 --> 00:01:19.280
So you could also write it this way.
00:01:19.280 --> 00:01:20.810
And I haven't explained
what determinant is
00:01:20.810 --> 00:01:21.890
or even how to compute it yet.
00:01:21.890 --> 00:01:23.640
I'm just talking about the notation
00:01:23.640 --> 00:01:28.140
of how you even talk about
the determinant of a matrix.
00:01:28.140 --> 00:01:29.470
So you can also write it this way,
00:01:29.470 --> 00:01:31.260
just rewrite the whole matrix
00:01:31.260 --> 00:01:34.950
with those vertical bars next to it.
00:01:34.950 --> 00:01:36.890
This is defined as,
00:01:36.890 --> 00:01:39.350
and we'll see how it's
useful in the future,
00:01:39.350 --> 00:01:42.330
the top-left time's the bottom-right.
00:01:42.330 --> 00:01:46.240
So A times D minus
00:01:49.050 --> 00:01:51.583
the top-right times the bottom-left.
00:01:52.698 --> 00:01:53.531
BC.
00:01:55.910 --> 00:01:57.370
So another way to think about it,
00:01:57.370 --> 00:02:02.370
it is just these two, the
product of these two minus,
00:02:03.210 --> 00:02:05.160
so that's those two right over there,
00:02:05.160 --> 00:02:10.160
minus the product of
these two right over here.
00:02:10.300 --> 00:02:13.230
So let's just first, before
we start to interpret this,
00:02:13.230 --> 00:02:16.440
get a little practice, just
computing a determinant.
00:02:16.440 --> 00:02:18.540
So let me give you a matrix.
00:02:18.540 --> 00:02:21.750
So let's say I have the matrix one,
00:02:21.750 --> 00:02:26.240
negative two, three, and five.
00:02:26.240 --> 00:02:29.200
Pause this video and
see if you can compute
00:02:29.200 --> 00:02:30.900
the determinant of this matrix.
00:02:30.900 --> 00:02:33.030
Let's call this matrix B.
00:02:33.030 --> 00:02:36.650
I want you to figure out
the determinant of matrix B.
00:02:36.650 --> 00:02:38.350
What is this going to be equal to?
00:02:39.680 --> 00:02:41.520
All right, now let's do this together.
00:02:41.520 --> 00:02:44.950
So you're going to have the
product of these two numbers.
00:02:44.950 --> 00:02:48.810
So we have one times five
00:02:48.810 --> 00:02:49.810
minus
00:02:50.680 --> 00:02:54.410
the product of these two numbers,
00:02:54.410 --> 00:02:58.810
which is three times negative two.
00:02:58.810 --> 00:03:01.170
And that of course, is going to be equal
00:03:01.170 --> 00:03:03.620
to one times five is five,
00:03:03.620 --> 00:03:06.510
three times negative two is negative six.
00:03:06.510 --> 00:03:10.350
But we're subtracting a negative six.
00:03:10.350 --> 00:03:15.190
Five minus negative six is the
same thing as five plus six
00:03:15.190 --> 00:03:18.680
which is going to be equal to 11.
00:03:18.680 --> 00:03:20.880
Now that we know how to
compute a determinant,
00:03:20.880 --> 00:03:21.920
in a future video,
00:03:21.920 --> 00:03:24.120
I will give you an
interesting interpretation
00:03:24.120 --> 00:03:25.423
of the determinant.
|
Empowering Young Women - Susan Wojcicki on Homeroom with Sal | https://www.youtube.com/watch?v=8fnlfi0hCO8 | vtt | https://www.youtube.com/api/timedtext?v=8fnlfi0hCO8&ei=6VWUZafbIKi7vdIP2LqA8Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2C1B8B931882A86A84B97EEA4CE791A2E0AE15A0.661344F7735F0E62420F0C427CE79ED0B9A7093B&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.330 --> 00:00:02.780
- Hi, everyone. Sal Khan
here from Khan Academy.
00:00:02.780 --> 00:00:05.100
Welcome to the Homeroom,
00:00:05.100 --> 00:00:07.170
I guess we say live stream and podcast.
00:00:07.170 --> 00:00:09.740
Although we are pre-recording
today's session.
00:00:09.740 --> 00:00:12.280
First of all, Happy
International Women's Day.
00:00:12.280 --> 00:00:13.760
And we have a very exciting guest today
00:00:13.760 --> 00:00:17.080
to talk about her life and
the internet and YouTube,
00:00:17.080 --> 00:00:20.010
Susan Wojcicki, who is the CEO of YouTube,
00:00:20.010 --> 00:00:22.030
a small website that
you might have heard of
00:00:22.030 --> 00:00:23.567
that has to deal with videos.
00:00:23.567 --> 00:00:25.470
But before we jump into that conversation
00:00:25.470 --> 00:00:27.860
where we talk about all of those things
00:00:27.860 --> 00:00:29.230
I will give my standard reminders.
00:00:29.230 --> 00:00:30.910
First of all, a reminder that Khan Academy
00:00:30.910 --> 00:00:32.660
is a not-for-profit organization,
00:00:32.660 --> 00:00:34.970
and we can only exist through
philanthropic donations
00:00:34.970 --> 00:00:36.000
from folks like yourself.
00:00:36.000 --> 00:00:37.590
So if you're in a position to do so,
00:00:37.590 --> 00:00:40.740
please go to khanacademy.org/donate.
00:00:40.740 --> 00:00:42.320
I also wanna give a special shout out
00:00:42.320 --> 00:00:45.440
to several organizations that stepped up,
00:00:45.440 --> 00:00:47.160
especially during the pandemic,
00:00:47.160 --> 00:00:49.420
when they realized that
Khan Academy's traffic
00:00:49.420 --> 00:00:50.810
was three times normal,
00:00:50.810 --> 00:00:52.220
and we were running at a deficit,
00:00:52.220 --> 00:00:53.960
and we wanted to accelerate
a whole bunch of things
00:00:53.960 --> 00:00:55.260
to support more folks.
00:00:55.260 --> 00:00:58.910
So special thanks to Bank of
America, AT&T, Google.org,
00:00:58.910 --> 00:01:01.190
Novartis, Fastly and General Motors
00:01:01.190 --> 00:01:03.170
for stepping up and
helping us fill that gap.
00:01:03.170 --> 00:01:05.020
But we still need more support,
00:01:05.020 --> 00:01:07.060
especially as we go into 2021.
00:01:07.060 --> 00:01:09.170
So anything you can do
is much appreciated.
00:01:09.170 --> 00:01:10.530
And then the last announcement,
00:01:10.530 --> 00:01:13.460
there was a version of
this of this live stream
00:01:13.460 --> 00:01:15.100
that you can get in podcast form,
00:01:15.100 --> 00:01:16.660
wherever you get your podcasts.
00:01:16.660 --> 00:01:19.630
Homeroom with Sal the Podcast.
00:01:19.630 --> 00:01:23.710
So with that, I am excited
to introduce Susan Wojcicki.
00:01:23.710 --> 00:01:25.830
Susan, good to see you.
00:01:25.830 --> 00:01:27.810
- Thank you for having me, Sal.
00:01:27.810 --> 00:01:28.903
It's good to be here.
00:01:30.120 --> 00:01:31.050
- Great to have you here.
00:01:31.050 --> 00:01:33.900
And you know, we've known
each other for a while.
00:01:33.900 --> 00:01:36.700
You know, I've been known to
do a few things on YouTube.
00:01:38.420 --> 00:01:40.430
- We've known each other
for many, many years.
00:01:40.430 --> 00:01:42.800
I can't even remember when we first met.
00:01:42.800 --> 00:01:44.760
It's been so long.
00:01:44.760 --> 00:01:46.440
- Oh, it's probably on
the order of 10 years,
00:01:46.440 --> 00:01:47.790
and I know your mother.
00:01:47.790 --> 00:01:51.260
We don't live too far
away from each other.
00:01:51.260 --> 00:01:53.350
Well, there's so much I
wanna talk to you about.
00:01:53.350 --> 00:01:56.060
I think most people know about YouTube,
00:01:56.060 --> 00:01:58.640
but I think it's always
interesting to hear about
00:01:59.690 --> 00:02:03.040
the organization from
the CEO's point of view,
00:02:03.040 --> 00:02:05.520
especially what do you hope it becomes.
00:02:05.520 --> 00:02:08.720
So what's your best sense
of the mission of YouTube,
00:02:08.720 --> 00:02:10.880
or what do you think it
can become over the next,
00:02:10.880 --> 00:02:12.063
let's say, 10 years?
00:02:12.910 --> 00:02:14.820
- Yeah. Well, so we have a mission.
00:02:14.820 --> 00:02:16.300
So I'll tell you what the mission is,
00:02:16.300 --> 00:02:20.970
which is to give everyone a
voice and show them the world.
00:02:20.970 --> 00:02:24.080
And so if you look at the first part,
00:02:24.080 --> 00:02:25.410
to give everyone a voice,
00:02:25.410 --> 00:02:28.290
how do we enable anyone who
wants to share something
00:02:28.290 --> 00:02:29.123
with the world,
00:02:29.123 --> 00:02:30.810
how to enable them to do that?
00:02:30.810 --> 00:02:35.360
So, I think YouTube has
really made a lot of...
00:02:35.360 --> 00:02:37.270
We've been revolutionary
in many ways, right?
00:02:37.270 --> 00:02:40.500
We have millions of channels and creators,
00:02:40.500 --> 00:02:41.930
but we still have a lot of work to do
00:02:41.930 --> 00:02:44.650
to continue to enable
people all over the world
00:02:44.650 --> 00:02:46.900
to create video and make it easier,
00:02:46.900 --> 00:02:49.200
and continue to grow that,
00:02:49.200 --> 00:02:50.240
but show them the world.
00:02:50.240 --> 00:02:52.410
I think that's actually
where we're really aligned
00:02:52.410 --> 00:02:53.560
in terms of our mission,
00:02:53.560 --> 00:02:56.600
so that people everywhere
can come to YouTube
00:02:56.600 --> 00:02:57.910
and learn anything they want,
00:02:57.910 --> 00:03:00.940
or experience any kind
of music, entertainment,
00:03:00.940 --> 00:03:02.650
look up any kind of information.
00:03:02.650 --> 00:03:05.810
And so I've also said that
YouTube, in some ways,
00:03:05.810 --> 00:03:09.623
is like a public video library,
00:03:10.610 --> 00:03:13.340
and we keep growing and growing
00:03:13.340 --> 00:03:15.080
in terms of offering new topics
00:03:15.080 --> 00:03:17.200
and we have books from like books,
00:03:17.200 --> 00:03:19.970
like videos from new people.
00:03:19.970 --> 00:03:23.320
And our goal is just to
continue to be a resource
00:03:23.320 --> 00:03:25.980
for people around the world to learn.
00:03:25.980 --> 00:03:27.610
And I've been really inspired by that.
00:03:27.610 --> 00:03:29.470
I sometimes see in different
parts of the world,
00:03:29.470 --> 00:03:30.303
wherever I go,
00:03:30.303 --> 00:03:32.050
people tell me what
they learned on YouTube.
00:03:32.050 --> 00:03:34.973
So that's something we
wanna continue to grow.
00:03:36.270 --> 00:03:37.730
- I think that's the surprising thing.
00:03:37.730 --> 00:03:38.970
You know, when YouTube was just starting
00:03:38.970 --> 00:03:39.803
to get off the ground
00:03:39.803 --> 00:03:41.710
and people started to associate it with,
00:03:41.710 --> 00:03:43.120
you know, just entertainment,
00:03:43.120 --> 00:03:44.830
but very quickly humanity
00:03:44.830 --> 00:03:47.230
realized that kind of
knowledge could be shared.
00:03:47.230 --> 00:03:52.230
And I actually think YouTube
will go down in world history
00:03:52.340 --> 00:03:54.240
as a moment in human history,
00:03:54.240 --> 00:03:55.820
where for, you know,
00:03:55.820 --> 00:03:57.610
humans are separate themselves
00:03:57.610 --> 00:03:59.820
from the rest of the animal
kingdom by having culture
00:03:59.820 --> 00:04:01.340
and having shared knowledge,
00:04:01.340 --> 00:04:03.080
which for many tens of thousands of years
00:04:03.080 --> 00:04:04.950
happened through an oral tradition,
00:04:04.950 --> 00:04:07.690
then we invented a writing,
00:04:07.690 --> 00:04:09.350
and then that allowed it to persist,
00:04:09.350 --> 00:04:12.720
and not kind of lose information
as that information spread,
00:04:12.720 --> 00:04:14.950
but writing loses a
little bit of the oral.
00:04:14.950 --> 00:04:17.830
And now with on-demand video and YouTube
00:04:18.790 --> 00:04:20.640
and mass distribution of it,
00:04:20.640 --> 00:04:22.220
you kind of have all of the above,
00:04:22.220 --> 00:04:24.490
that any one person can express their oral
00:04:24.490 --> 00:04:26.970
or their video or the visual
tradition and their knowledge,
00:04:26.970 --> 00:04:28.280
and then it's literally available
00:04:28.280 --> 00:04:30.270
to every human being on the planet.
00:04:30.270 --> 00:04:31.750
Do you all ever view yourself that way,
00:04:31.750 --> 00:04:33.360
as like the globe's,
00:04:33.360 --> 00:04:35.080
I guess you did say it's the library,
00:04:35.080 --> 00:04:36.540
it's the brain,
00:04:36.540 --> 00:04:39.793
the knowledge of humanity
is literally on YouTube.
00:04:40.970 --> 00:04:42.280
- I definitely see the impact,
00:04:42.280 --> 00:04:44.360
because people everywhere
tell me what they learn,
00:04:44.360 --> 00:04:47.200
and especially now, during the pandemic,
00:04:47.200 --> 00:04:48.233
we played a really key role.
00:04:48.233 --> 00:04:50.510
A lot of people had to do
things for the first time,
00:04:50.510 --> 00:04:53.340
like fix something in their
house, give a haircut,
00:04:53.340 --> 00:04:54.460
learn a new skill.
00:04:54.460 --> 00:04:56.240
And the fact that YouTube could do that
00:04:56.240 --> 00:04:58.500
and could be there in
that moment of crisis
00:04:58.500 --> 00:05:00.580
was really, really valuable.
00:05:00.580 --> 00:05:01.727
So I definitely understand that,
00:05:01.727 --> 00:05:03.790
and our goal is to continue to grow that
00:05:03.790 --> 00:05:05.130
and support those use cases,
00:05:05.130 --> 00:05:07.093
so everybody can have that resource.
00:05:08.260 --> 00:05:09.240
- Absolutely, and obviously,
00:05:09.240 --> 00:05:10.800
most people who are watching this,
00:05:10.800 --> 00:05:13.290
many of them who are
watching it on YouTube,
00:05:13.290 --> 00:05:16.240
know that, you know, I showed
up on people's radar...
00:05:16.240 --> 00:05:17.710
You know, Khan Academy
has a lot of things.
00:05:17.710 --> 00:05:19.120
We have videos and exercises,
00:05:19.120 --> 00:05:21.460
but it's the YouTube
that really helped people
00:05:21.460 --> 00:05:22.780
know what we're all about,
00:05:22.780 --> 00:05:24.190
and was an easy way to discover.
00:05:24.190 --> 00:05:25.050
You mentioned haircuts.
00:05:25.050 --> 00:05:26.780
My wife watched a couple
of YouTube videos,
00:05:26.780 --> 00:05:28.520
and, you know, I think it's...
00:05:28.520 --> 00:05:29.610
You know, my hair has issues,
00:05:29.610 --> 00:05:31.930
but it's one of the better
haircuts that I've gotten.
00:05:31.930 --> 00:05:32.840
And I've fixed a toilet.
00:05:32.840 --> 00:05:34.230
I fixed the toilet twice
00:05:34.230 --> 00:05:36.100
over the last nine months
00:05:36.100 --> 00:05:37.490
based on YouTube videos.
00:05:37.490 --> 00:05:39.100
And I think they're working.
00:05:39.100 --> 00:05:41.490
So that's absolutely true.
00:05:41.490 --> 00:05:44.070
You know, on the other
side of that though,
00:05:44.070 --> 00:05:45.400
there's a lot of conversation
00:05:45.400 --> 00:05:48.300
about misinformation and
the spreading of, you know,
00:05:48.300 --> 00:05:50.520
how people get into their own silos.
00:05:50.520 --> 00:05:52.180
How do y'all think about that on YouTube?
00:05:52.180 --> 00:05:54.350
How do y'all try to make sense of people
00:05:54.350 --> 00:05:56.910
who are spreading misinformation,
00:05:56.910 --> 00:05:59.330
or, you know, people just
gravitating to things
00:05:59.330 --> 00:06:01.980
that already confirm whatever
biases they might have?
00:06:03.340 --> 00:06:06.120
- So great question and
really important question.
00:06:06.120 --> 00:06:08.630
And we've put a huge amount of effort
00:06:08.630 --> 00:06:10.780
to figure out the right
solutions for that.
00:06:10.780 --> 00:06:13.360
And so basically we
talk about all this work
00:06:13.360 --> 00:06:15.100
around responsibility.
00:06:15.100 --> 00:06:18.790
And so we have what we call
the four Rs of responsibility.
00:06:18.790 --> 00:06:22.080
And the first one is about content
00:06:22.080 --> 00:06:23.360
that we would remove
00:06:23.360 --> 00:06:25.950
if it is content that we think could lead
00:06:25.950 --> 00:06:27.120
to real-world harm.
00:06:27.120 --> 00:06:29.700
So like, let's just talk about COVID,
00:06:29.700 --> 00:06:31.760
just to put this in perspective.
00:06:31.760 --> 00:06:35.180
So there were different
conspiracies that came out,
00:06:35.180 --> 00:06:39.790
like one of them was that
COVID came from 5G cell towers,
00:06:39.790 --> 00:06:44.373
and it goes against all consensus,
00:06:45.620 --> 00:06:46.453
from medical consensus.
00:06:46.453 --> 00:06:48.267
And so that was something
where we would say,
00:06:48.267 --> 00:06:49.590
"That's clearly not true."
00:06:49.590 --> 00:06:50.423
We need to remove it,
00:06:50.423 --> 00:06:53.230
because people were
destroying cell towers,
00:06:53.230 --> 00:06:55.380
and we also don't want people to go out
00:06:55.380 --> 00:06:56.560
and then do risky behavior.
00:06:56.560 --> 00:06:58.530
So we are able to work
with medical professionals
00:06:58.530 --> 00:06:59.480
to find content
00:07:02.768 --> 00:07:04.240
that was clearly violative.
00:07:04.240 --> 00:07:07.610
And again, we work with the
medical professionals on that.
00:07:07.610 --> 00:07:09.650
But then we also raised up information,
00:07:09.650 --> 00:07:14.303
so information that we
knew that was accurate.
00:07:16.040 --> 00:07:17.300
So like how to wash your hands.
00:07:17.300 --> 00:07:18.450
I never thought we'd serve so many
00:07:18.450 --> 00:07:20.770
how to wash your hand videos.
00:07:20.770 --> 00:07:22.930
We worked with 85 different
00:07:22.930 --> 00:07:24.580
health professional organizations
00:07:24.580 --> 00:07:26.760
from around the world,
00:07:26.760 --> 00:07:30.560
and we made sure that all of
that information was delivered.
00:07:30.560 --> 00:07:31.620
So whether you did a search,
00:07:31.620 --> 00:07:32.570
whether you watched the video,
00:07:32.570 --> 00:07:35.560
you could link and you could
see authoritative information.
00:07:35.560 --> 00:07:38.230
And then there's some content
that's just borderline,
00:07:38.230 --> 00:07:42.550
like it might be something that
isn't really a big problem,
00:07:42.550 --> 00:07:43.540
but it's low quality.
00:07:43.540 --> 00:07:44.460
And that's just something
00:07:44.460 --> 00:07:46.890
that we are less likely
to recommend to our users,
00:07:46.890 --> 00:07:49.390
because we wanna give them
high quality information.
00:07:49.390 --> 00:07:51.210
We don't want them to
come and see something
00:07:51.210 --> 00:07:54.020
that says like, "Aliens
landed in your backyard."
00:07:54.020 --> 00:07:55.820
That's very unlikely.
00:07:55.820 --> 00:07:58.860
And so, again, we don't
want to go too far,
00:07:58.860 --> 00:08:00.870
and say, hey, we're
restricting free speech,
00:08:00.870 --> 00:08:03.190
because that's very important too,
00:08:03.190 --> 00:08:07.380
that we can enable a broad set
of opinions and perspectives.
00:08:07.380 --> 00:08:12.380
So we also are reducing
information that is low quality
00:08:13.560 --> 00:08:16.820
in terms of how we handle
that in our recommendations.
00:08:16.820 --> 00:08:18.640
- No, that last point, I
always like to clarify,
00:08:18.640 --> 00:08:20.570
whenever people say that, you know,
00:08:20.570 --> 00:08:21.700
this is reducing free speech,
00:08:21.700 --> 00:08:22.900
I was like, "You know, free speech
00:08:22.900 --> 00:08:24.650
is the right to say things that,
00:08:24.650 --> 00:08:27.110
first of all, you know, somehow
do not undermine government
00:08:27.110 --> 00:08:28.790
or would hurt people,
00:08:28.790 --> 00:08:29.960
but you have the right to say it,
00:08:29.960 --> 00:08:31.340
but you don't have the right to for it
00:08:31.340 --> 00:08:34.840
to be amplified by other media companies."
00:08:34.840 --> 00:08:36.390
If you go back 100 years ago,
00:08:36.390 --> 00:08:37.810
I could say whatever I want,
00:08:37.810 --> 00:08:40.190
I could complain about government,
00:08:40.190 --> 00:08:41.930
or come up with conspiracy theories,
00:08:41.930 --> 00:08:43.380
but it doesn't mean
that the New York Times
00:08:43.380 --> 00:08:45.300
have to publish whatever I had to say.
00:08:45.300 --> 00:08:46.810
And there's an analogy now
00:08:46.810 --> 00:08:48.670
that it does not have to be validated,
00:08:48.670 --> 00:08:51.880
or you don't have the
right to be amplified.
00:08:51.880 --> 00:08:54.050
So I think it's an interesting nuance.
00:08:54.050 --> 00:08:56.170
Yes, you can't be arrested for coming up
00:08:56.170 --> 00:08:57.140
with a conspiracy theory,
00:08:57.140 --> 00:08:59.690
but you can't just spread it willy nilly,
00:08:59.690 --> 00:09:01.720
and say, "That's my right.
00:09:01.720 --> 00:09:03.930
You know, I would love to dig a little bit
00:09:03.930 --> 00:09:08.090
into your journey to
becoming CEO of YouTube.
00:09:08.090 --> 00:09:10.430
We have a lot of young
people who watch this.
00:09:10.430 --> 00:09:12.060
It's International Women's Day.
00:09:12.060 --> 00:09:13.330
I think there's a lot of young women
00:09:13.330 --> 00:09:16.490
who look up to you as a
real leader in industry
00:09:16.490 --> 00:09:17.690
across the board.
00:09:17.690 --> 00:09:19.930
When you were young, what were you like,
00:09:19.930 --> 00:09:22.430
and is this what you thought
you were going to do?
00:09:23.530 --> 00:09:25.240
- No, I had no idea
00:09:25.240 --> 00:09:26.870
this is what I was gonna do.
00:09:26.870 --> 00:09:29.840
And maybe I'm showing
my age by saying this,
00:09:29.840 --> 00:09:32.050
but we didn't have the
internet when I was young,
00:09:32.050 --> 00:09:34.930
so I couldn't have even imagined that.
00:09:34.930 --> 00:09:39.620
And I mean, I think as a young kid,
00:09:39.620 --> 00:09:40.743
what was I like?
00:09:41.670 --> 00:09:44.770
First of all, I was really
into doing arts and crafts.
00:09:44.770 --> 00:09:46.840
I was really into being creative
00:09:46.840 --> 00:09:47.673
and making things,
00:09:47.673 --> 00:09:51.140
like I would make paper and pot holders.
00:09:51.140 --> 00:09:53.600
My first business was making spice ropes
00:09:53.600 --> 00:09:54.840
and selling them to my neighbor.
00:09:54.840 --> 00:09:57.490
So I just like to make stuff.
- What's a spice rope?
00:09:58.740 --> 00:10:03.510
- I would braid yarn and then
tie cinnamon sticks to it
00:10:03.510 --> 00:10:07.230
and take colored fabric
and put spices in there.
00:10:07.230 --> 00:10:10.040
And I just would make stuff.
00:10:10.040 --> 00:10:15.040
And for me, I had this realization
00:10:16.698 --> 00:10:19.830
that technology was about creation.
00:10:19.830 --> 00:10:23.053
It was about making things
and creating things.
00:10:25.120 --> 00:10:26.710
A lot of people didn't seem to see that,
00:10:26.710 --> 00:10:28.370
especially not then,
00:10:28.370 --> 00:10:29.450
but I totally got it.
00:10:29.450 --> 00:10:32.230
I was like, "Wow, I can make all kinds
00:10:32.230 --> 00:10:33.810
of really interesting software,
00:10:33.810 --> 00:10:37.890
and it can be distributed,
00:10:37.890 --> 00:10:40.280
and so, so many people can see it
00:10:40.280 --> 00:10:43.126
and they can use it and
I can interact with them.
00:10:43.126 --> 00:10:46.063
And once I got that idea,
00:10:47.130 --> 00:10:49.940
I just said like, "Oh,
I have to be in tech.
00:10:49.940 --> 00:10:52.850
This is the best field for me
00:10:52.850 --> 00:10:53.970
based on all my interests
00:10:53.970 --> 00:10:56.270
with the creativity and making things,
00:10:56.270 --> 00:10:58.700
and seeing how I could
have an impact that way."
00:10:58.700 --> 00:11:00.640
I didn't know where it was gonna lead,
00:11:00.640 --> 00:11:03.290
but as long as I was
making things, I was happy,
00:11:03.290 --> 00:11:06.273
and that's what got me started in tech.
00:11:07.190 --> 00:11:08.170
- No, very similar to me.
00:11:08.170 --> 00:11:09.700
It's all about this notion of creation,
00:11:09.700 --> 00:11:12.990
and that you can create things
that have incredible scale,
00:11:12.990 --> 00:11:15.140
incredible impact.
00:11:15.140 --> 00:11:16.990
And once you went into tech,
00:11:16.990 --> 00:11:18.430
what did you think you
were gonna actually...
00:11:18.430 --> 00:11:19.550
How did you get started?
00:11:19.550 --> 00:11:23.273
Did you take a traditional
software engineering route?
00:11:24.490 --> 00:11:27.877
Connect the dots between
this interest in creation
00:11:27.877 --> 00:11:29.163
and where you are now.
00:11:30.230 --> 00:11:32.090
- Well, I took a computer science class
00:11:32.090 --> 00:11:33.320
my senior year in college.
00:11:33.320 --> 00:11:36.120
I took the computer science
for computer science majors,
00:11:37.970 --> 00:11:40.650
At the time I thought, "Oh, it's too late.
00:11:40.650 --> 00:11:42.207
Oh, I'm too old."
00:11:43.447 --> 00:11:45.030
Like, I was a humanities major,
00:11:45.030 --> 00:11:47.760
so I was like, "I must be
too old to change careers,"
00:11:47.760 --> 00:11:48.593
'cause I was--
00:11:48.593 --> 00:11:49.900
- I find it funny when a 20-year-old
00:11:49.900 --> 00:11:51.587
says they're too old, 21.
00:11:51.587 --> 00:11:52.480
- I thought I was too old,
00:11:52.480 --> 00:11:56.060
as 20 or 21-year-old, to start
learning computer science,
00:11:56.060 --> 00:11:57.790
'cause I had friends and they were majors,
00:11:57.790 --> 00:11:59.070
and they had taken it for three years,
00:11:59.070 --> 00:12:01.300
and we were all about to graduate.
00:12:01.300 --> 00:12:05.900
But I realized that I
wanted to do something
00:12:05.900 --> 00:12:06.733
in computer science.
00:12:06.733 --> 00:12:10.800
And so that was my first role,
00:12:10.800 --> 00:12:11.840
or that was my first, you know,
00:12:11.840 --> 00:12:13.700
that's when I was academically engaged
00:12:13.700 --> 00:12:14.690
with computer science,
00:12:14.690 --> 00:12:17.880
and then I grew up in the Palo Alto area.
00:12:17.880 --> 00:12:20.130
So I think that probably
had something to do with it.
00:12:20.130 --> 00:12:23.100
And I came back after college,
00:12:23.100 --> 00:12:28.100
and I wound up working at this
educational software startup.
00:12:28.290 --> 00:12:31.010
So here I am, Sal,
00:12:31.010 --> 00:12:33.403
I don't know, many, many years later,
00:12:34.666 --> 00:12:37.570
working with you around education.
00:12:37.570 --> 00:12:40.300
So I had that interest then.
00:12:40.300 --> 00:12:42.260
I still have that interest now,
00:12:42.260 --> 00:12:44.130
but I was just a project manager
00:12:44.130 --> 00:12:48.550
for making software for
kids around education,
00:12:48.550 --> 00:12:50.400
and I loved it.
00:12:50.400 --> 00:12:52.539
It was creation.
00:12:52.539 --> 00:12:54.530
Kids would write about
how they use the software,
00:12:54.530 --> 00:12:57.630
how they learn something
and the impact it had.
00:12:57.630 --> 00:13:00.000
And so I just said like,
"This is what I'm gonna do.
00:13:00.000 --> 00:13:01.807
I'm so committed to this."
00:13:04.222 --> 00:13:06.590
I can keep going. You wanna know more?
00:13:06.590 --> 00:13:09.460
- No, I do. I actually never
knew about this chapter.
00:13:09.460 --> 00:13:10.570
I mean, I'm especially curious
00:13:10.570 --> 00:13:13.110
about what do you think it
was that you told yourself
00:13:13.110 --> 00:13:14.500
or the skills that you brought
00:13:14.500 --> 00:13:17.280
to the table that allowed
you to really thrive
00:13:17.280 --> 00:13:18.330
in this world,
00:13:18.330 --> 00:13:22.010
and obviously, you know, keep
rising through the ranks?
00:13:22.010 --> 00:13:24.740
You know, you joined Google
at a very early stage,
00:13:24.740 --> 00:13:26.793
and then now as CEO of YouTube,
00:13:27.710 --> 00:13:28.940
you know, I know it's a
hard question to answer,
00:13:28.940 --> 00:13:30.140
'cause you're a humble person,
00:13:30.140 --> 00:13:33.370
but be not so humble for a few seconds.
00:13:33.370 --> 00:13:34.330
- Sure.
00:13:34.330 --> 00:13:36.120
If I look back at my career,
00:13:36.120 --> 00:13:39.710
there were a few key things
that really helped me.
00:13:39.710 --> 00:13:43.053
One of them was, first of all,
00:13:45.624 --> 00:13:47.100
I was just looking to do
something interesting.
00:13:47.100 --> 00:13:47.933
I was just thinking,
00:13:47.933 --> 00:13:51.567
"How can I use my skills
to help create something
00:13:51.567 --> 00:13:53.277
that will be used by people,
00:13:53.277 --> 00:13:54.330
and that will be useful
00:13:54.330 --> 00:13:55.790
and make the world a better place?
00:13:55.790 --> 00:13:57.540
And when I joined Google,
00:13:57.540 --> 00:14:00.260
I was in place 16 of Google.
00:14:00.260 --> 00:14:01.640
When I joined Google,
00:14:01.640 --> 00:14:03.350
nobody thought that Google
00:14:03.350 --> 00:14:05.260
was that interesting of a company,
00:14:05.260 --> 00:14:07.970
but I saw that it was enabling people
00:14:07.970 --> 00:14:09.870
to find information in new ways.
00:14:09.870 --> 00:14:13.610
And so being able to just
focus on what was important,
00:14:13.610 --> 00:14:15.330
what I saw was adding value,
00:14:15.330 --> 00:14:17.340
whether or not other people agreed or not,
00:14:17.340 --> 00:14:19.970
was part of what helped me.
00:14:19.970 --> 00:14:21.500
I think it was the same thing for YouTube.
00:14:21.500 --> 00:14:23.470
When I first started working on YouTube,
00:14:23.470 --> 00:14:26.230
nobody thought it was that big a deal.
00:14:26.230 --> 00:14:29.710
They thought it was a small little company
00:14:29.710 --> 00:14:31.660
with like a lot of cats on skateboards.
00:14:31.660 --> 00:14:33.070
It wasn't really going anywhere,
00:14:33.070 --> 00:14:35.120
but I saw that people could use it
00:14:35.120 --> 00:14:37.760
for creating and sharing ideas,
00:14:37.760 --> 00:14:38.760
and information,
00:14:38.760 --> 00:14:43.250
and new musicians and
artists and creators.
00:14:43.250 --> 00:14:46.930
So seeing ideas early
and believing in them
00:14:46.930 --> 00:14:48.670
has definitely helped me.
00:14:48.670 --> 00:14:52.270
But then I would say there's a part two,
00:14:52.270 --> 00:14:56.060
which was maybe less inspiration
and more perspiration,
00:14:56.060 --> 00:14:58.350
which is just sticking with it,
00:14:58.350 --> 00:15:01.270
and working hard and not giving up,
00:15:01.270 --> 00:15:03.200
and getting through all the hard times,
00:15:03.200 --> 00:15:06.420
and just sticking with it,
00:15:06.420 --> 00:15:10.120
keep working on it, keep
waking up every day,
00:15:10.120 --> 00:15:13.320
thinking about how you can
make the company better,
00:15:13.320 --> 00:15:15.160
and add value,
00:15:15.160 --> 00:15:17.790
and get through the tough times.
00:15:17.790 --> 00:15:21.660
So I'd say that those
are the two key parts,
00:15:21.660 --> 00:15:23.510
the inspiration and the perspiration.
00:15:24.370 --> 00:15:25.410
- It makes a lot of sense.
00:15:25.410 --> 00:15:26.740
And I have so many questions for you,
00:15:26.740 --> 00:15:28.010
but I know we have a lot of questions
00:15:28.010 --> 00:15:30.890
that have come in
appropriately for you on video.
00:15:30.890 --> 00:15:33.110
So the first question
we have is from Izzy,
00:15:33.110 --> 00:15:34.813
if we could watch that video.
00:15:34.813 --> 00:15:36.687
- I was wondering what you wanted to do
00:15:36.687 --> 00:15:37.520
when you were my age.
00:15:37.520 --> 00:15:40.193
And did you ever think you'd
be the CEO of a huge company?
00:15:43.400 --> 00:15:45.270
- No, I never thought I'd would be the CEO
00:15:45.270 --> 00:15:46.290
of a huge company.
00:15:46.290 --> 00:15:49.680
And when I was your age,
00:15:49.680 --> 00:15:51.950
I probably wanted to...
00:15:51.950 --> 00:15:53.800
I was just interested in
a lot of different things.
00:15:53.800 --> 00:15:56.950
I didn't really know what
the future held for me,
00:15:56.950 --> 00:15:58.980
but I was interested in arts and crafts.
00:15:58.980 --> 00:16:00.510
I was interested in science.
00:16:00.510 --> 00:16:03.840
I was interested in entrepreneurship.
00:16:03.840 --> 00:16:05.470
I would just start things.
00:16:05.470 --> 00:16:07.430
And like I said, I would make things
00:16:07.430 --> 00:16:09.300
and sell it to my neighbors.
00:16:09.300 --> 00:16:14.050
And all of those turned out in
the end to be useful skills.
00:16:14.050 --> 00:16:17.190
So I just encourage all of
you to explore the world,
00:16:17.190 --> 00:16:18.860
find what you love,
00:16:18.860 --> 00:16:23.570
find the areas that you
wanna keep working on,
00:16:23.570 --> 00:16:26.390
and that ultimately will
lead you to somewhere,
00:16:26.390 --> 00:16:28.300
because to choose a career,
00:16:28.300 --> 00:16:29.610
to choose a profession,
00:16:29.610 --> 00:16:32.550
it has to be something
that is meaningful for you.
00:16:32.550 --> 00:16:34.770
It'll be much easier and
you'll do a better job
00:16:34.770 --> 00:16:35.900
if it's meaningful to you.
00:16:35.900 --> 00:16:39.060
So choose something that
you enjoy doing every day,
00:16:39.060 --> 00:16:42.620
and that you see benefits the world,
00:16:42.620 --> 00:16:45.603
and that, ultimately,
you derive meaning from.
00:16:47.660 --> 00:16:48.493
- Completely agree.
00:16:48.493 --> 00:16:50.853
And the next question
we have is from Lily.
00:16:51.690 --> 00:16:53.090
- For young women who are looking
00:16:53.090 --> 00:16:56.820
into being in management
positions or positions of power,
00:16:56.820 --> 00:16:58.090
what advice do you have for them
00:16:58.090 --> 00:17:00.510
in trying to get past
those gender stereotypes
00:17:00.510 --> 00:17:01.410
of being too pushy
00:17:01.410 --> 00:17:03.660
or too bossy when try
to achieve their goals?
00:17:05.780 --> 00:17:09.740
- So there are definitely
a lot of challenges.
00:17:09.740 --> 00:17:13.750
And some of the ways
that I have overcome them
00:17:13.750 --> 00:17:16.860
is by, first of all, working really hard,
00:17:16.860 --> 00:17:19.060
which I'm sure all of you do.
00:17:19.060 --> 00:17:24.060
And also I'd say, with
some of the stereotypes,
00:17:24.090 --> 00:17:27.340
or people maybe who are
maybe not as supportive,
00:17:27.340 --> 00:17:30.040
I've tried to ignore the people
00:17:30.040 --> 00:17:31.410
who might be less supportive
00:17:31.410 --> 00:17:33.660
and make friends with the people who are.
00:17:33.660 --> 00:17:35.360
And so I've found it really valuable
00:17:35.360 --> 00:17:36.770
over the course of my career
00:17:36.770 --> 00:17:38.850
to figure out who my allies are,
00:17:38.850 --> 00:17:40.160
to work closely with them,
00:17:40.160 --> 00:17:42.343
develop close relationships with them,
00:17:43.890 --> 00:17:47.380
and just continue doing
the work that you're doing.
00:17:47.380 --> 00:17:50.090
And I do think we're at a time
00:17:50.090 --> 00:17:53.180
where companies are working really hard
00:17:53.180 --> 00:17:55.530
to have diverse workforces,
00:17:55.530 --> 00:17:57.340
because we recognize that diversity
00:17:57.340 --> 00:17:58.710
makes a stronger company,
00:17:58.710 --> 00:18:00.440
it makes a better product,
00:18:00.440 --> 00:18:03.920
and I encourage all of you
to pursue your passions,
00:18:03.920 --> 00:18:05.960
and just to continue to work hard,
00:18:05.960 --> 00:18:09.200
and don't give up and find your allies.
00:18:09.200 --> 00:18:12.773
And if you find someone
who's not supportive,
00:18:15.616 --> 00:18:17.290
just do your best to, you know,
00:18:17.290 --> 00:18:19.110
keep working through that.
00:18:19.110 --> 00:18:23.290
And certainly, while there
are different stereotypes,
00:18:23.290 --> 00:18:24.830
the stereotypes are always changing,
00:18:24.830 --> 00:18:28.280
and I really hope by the time
that a lot of you grow up,
00:18:28.280 --> 00:18:30.170
that some of the stereotypes you mentioned
00:18:30.170 --> 00:18:32.973
are not anything that you
have to face in the future.
00:18:34.200 --> 00:18:35.400
- And just following up on that,
00:18:35.400 --> 00:18:38.280
you know, for those who don't know, Susan,
00:18:38.280 --> 00:18:40.910
you and your siblings and your
mother are kind of famous.
00:18:40.910 --> 00:18:42.750
You know, as sisters,
00:18:42.750 --> 00:18:45.670
all of you have been wildly successful.
00:18:45.670 --> 00:18:47.060
You know, you have a
sister who's a physician,
00:18:47.060 --> 00:18:50.500
you have a sister who is a CEO of 23andMe.
00:18:50.500 --> 00:18:54.878
Your mother is world
famous as an educator,
00:18:54.878 --> 00:18:57.930
a journalism teacher,
et cetera, et cetera.
00:18:57.930 --> 00:19:00.410
Is there something that
your mother gave you
00:19:00.410 --> 00:19:02.660
or you had between your
yourselves as sisters
00:19:02.660 --> 00:19:03.830
that you could share,
00:19:03.830 --> 00:19:06.320
with kind of sisters around the world,
00:19:06.320 --> 00:19:07.470
that really helped you?
00:19:08.460 --> 00:19:11.900
- I wish I could say
it was just one thing,
00:19:11.900 --> 00:19:16.900
but I do think the one thing
my mom gave to all of us
00:19:17.250 --> 00:19:22.233
was certainly the focus on persistence,
00:19:23.550 --> 00:19:27.220
believing in yourself and
not getting embarrassed.
00:19:27.220 --> 00:19:31.120
So my mom was always the first person
00:19:31.120 --> 00:19:34.840
to ask a hard question in an audience.
00:19:34.840 --> 00:19:39.840
Like, she used to always
be the one who would say...
00:19:40.420 --> 00:19:42.110
She felt like if she had been wrong,
00:19:42.110 --> 00:19:43.920
she needed to speak up about it.
00:19:43.920 --> 00:19:46.340
And sometimes as a kid, that
was really embarrassing,
00:19:46.340 --> 00:19:47.630
but I learned over time,
00:19:47.630 --> 00:19:49.140
it's really important to use your voice.
00:19:49.140 --> 00:19:51.580
It's really important
to say what you believe
00:19:51.580 --> 00:19:54.160
and to speak up for yourself.
00:19:54.160 --> 00:19:57.800
And I do think that those
skills have helped all of us,
00:19:57.800 --> 00:19:59.070
because if you believe in yourself,
00:19:59.070 --> 00:20:00.200
you speak up for yourself,
00:20:00.200 --> 00:20:01.290
but you're working hard
00:20:01.290 --> 00:20:03.520
and doing a great job
of what you're doing,
00:20:03.520 --> 00:20:05.600
you're gonna find a way to be successful.
00:20:05.600 --> 00:20:08.350
And I think that we
learned a lot of skills
00:20:08.350 --> 00:20:10.450
from my mom and my dad,
00:20:10.450 --> 00:20:11.400
who's the professor,
00:20:11.400 --> 00:20:15.053
and who was consistently hardworking,
00:20:18.191 --> 00:20:21.820
and we learned that those
are all things that it takes.
00:20:21.820 --> 00:20:24.750
And if you keep it up and work hard,
00:20:24.750 --> 00:20:29.750
you'll end up with something
that is compelling for you.
00:20:31.310 --> 00:20:35.293
- Yeah, well, we have another
question here from Imari.
00:20:35.293 --> 00:20:37.660
- What are some activities or actions
00:20:37.660 --> 00:20:40.300
that you recommend for
young women entering college
00:20:40.300 --> 00:20:42.280
to prepare them for career success?
00:20:45.280 --> 00:20:47.080
- So for career success,
00:20:47.080 --> 00:20:48.590
for people who are entering college
00:20:48.590 --> 00:20:50.120
or entering the workforce,
00:20:50.120 --> 00:20:52.770
I would really encourage
you to think about
00:20:52.770 --> 00:20:53.980
what is meaningful for you,
00:20:53.980 --> 00:20:58.240
because it's very hard to do
a job that you don't like.
00:20:58.240 --> 00:21:02.300
You have to find something
that really speaks to you.
00:21:02.300 --> 00:21:04.550
And I see that among my own kids,
00:21:04.550 --> 00:21:06.550
and all the kids that I work with,
00:21:06.550 --> 00:21:08.630
that people come from
very different places.
00:21:08.630 --> 00:21:11.610
And there are very different
passions that people have.
00:21:11.610 --> 00:21:15.360
And so to the extent that
you can look inside yourself,
00:21:15.360 --> 00:21:17.810
and think about what would
be really meaningful for you,
00:21:17.810 --> 00:21:20.640
and find a way to explore that,
00:21:20.640 --> 00:21:24.700
and that if your work
speaks to you in a deep way,
00:21:24.700 --> 00:21:26.940
and you take meaning from it,
00:21:26.940 --> 00:21:29.410
it will help you get
through the hard times.
00:21:29.410 --> 00:21:33.480
It will help you stick with
it and make a difference.
00:21:33.480 --> 00:21:36.060
So I encourage you just
to really think about
00:21:36.060 --> 00:21:37.010
what your passions are,
00:21:37.010 --> 00:21:39.570
and you have to be practical
too, realistically,
00:21:39.570 --> 00:21:42.370
I think that's something I
learned from my mom also,
00:21:42.370 --> 00:21:44.140
like, I would have probably said, oh.
00:21:44.140 --> 00:21:45.140
If you had asked me as a kid,
00:21:45.140 --> 00:21:47.540
I've always said, "Oh, I just
want to be like an artist,
00:21:47.540 --> 00:21:49.300
and draw pictures,
00:21:49.300 --> 00:21:50.850
and, you know, make candles,"
00:21:50.850 --> 00:21:53.560
and as compelling as all of that is,
00:21:53.560 --> 00:21:54.617
she also encouraged me like,
00:21:54.617 --> 00:21:56.030
"Yes, you need to be
able to make a living.
00:21:56.030 --> 00:21:57.170
You have to be able to do something
00:21:57.170 --> 00:21:58.190
where you can support yourself."
00:21:58.190 --> 00:22:02.590
So marrying the two of
what your passion is,
00:22:02.590 --> 00:22:04.530
but where there's market and demand
00:22:04.530 --> 00:22:06.580
for the things that you're interested in,
00:22:07.630 --> 00:22:11.100
those are good places for you
to look at future careers.
00:22:11.100 --> 00:22:12.490
And also encourage
people to look at things
00:22:12.490 --> 00:22:13.323
that are growing.
00:22:13.323 --> 00:22:15.630
Like, in many ways, I
benefited from being in tech,
00:22:15.630 --> 00:22:16.930
which was a growing industry,
00:22:16.930 --> 00:22:18.590
so there were always new jobs.
00:22:18.590 --> 00:22:20.740
There was always something new to explore.
00:22:20.740 --> 00:22:22.900
And so to the extent that
you can choose an area
00:22:22.900 --> 00:22:23.860
that is expanding,
00:22:23.860 --> 00:22:25.588
that's the whole area is growing,
00:22:25.588 --> 00:22:26.640
it's gonna be easier to get more jobs.
00:22:26.640 --> 00:22:28.410
It's going to be easier to get promoted.
00:22:28.410 --> 00:22:30.680
So that's another thing to consider
00:22:30.680 --> 00:22:33.270
as you factor your future career in
00:22:33.270 --> 00:22:35.393
and what areas you're gonna go into.
00:22:37.000 --> 00:22:37.880
- No, I love that advice.
00:22:37.880 --> 00:22:39.430
I always tell folks,
00:22:39.430 --> 00:22:40.690
actually, on one part of your brain,
00:22:40.690 --> 00:22:42.000
you should be hyper pragmatic.
00:22:42.000 --> 00:22:43.420
look at the industries that are growing,
00:22:43.420 --> 00:22:44.810
that compensate well,
00:22:44.810 --> 00:22:46.110
and that, you know, are bearable,
00:22:46.110 --> 00:22:48.160
you can enjoy working in that,
00:22:48.160 --> 00:22:49.200
but as you do that,
00:22:49.200 --> 00:22:51.780
carve out some space to
also be hyper idealistic
00:22:51.780 --> 00:22:52.990
and have your passions.
00:22:52.990 --> 00:22:54.240
And we're in a unique time.
00:22:54.240 --> 00:22:55.600
I mean, YouTube shows us this,
00:22:55.600 --> 00:22:57.880
my narrative shows this,
your narrative shows this,
00:22:57.880 --> 00:23:00.430
that those things will
intersect in surprising ways.
00:23:00.430 --> 00:23:02.190
There's ways to publish your passions.
00:23:02.190 --> 00:23:03.310
There's other people in the world
00:23:03.310 --> 00:23:04.700
that will also have those passions,
00:23:04.700 --> 00:23:07.490
and it can turn into a
career in and of itself.
00:23:07.490 --> 00:23:09.963
There's another question here from Ruby.
00:23:11.110 --> 00:23:12.610
- You must have faced a lot of obstacles
00:23:12.610 --> 00:23:13.780
getting to where you are today,
00:23:13.780 --> 00:23:15.900
and I'm wondering if you
ever felt like giving up.
00:23:15.900 --> 00:23:18.743
If so, how were you able to
overcome that? Thank you.
00:23:20.290 --> 00:23:22.070
- [Sal] Oh, great question.
00:23:22.070 --> 00:23:23.150
- Yeah, great question.
00:23:23.150 --> 00:23:24.830
I definitely have had hard days,
00:23:24.830 --> 00:23:27.480
and there've been moments where
I have felt like giving up,
00:23:27.480 --> 00:23:31.703
but I've often realized that if I give up,
00:23:33.940 --> 00:23:37.300
well, then I don't get to
keep doing what I love doing.
00:23:37.300 --> 00:23:39.610
And if I give up,
00:23:39.610 --> 00:23:42.560
because someone was difficult,
00:23:42.560 --> 00:23:45.000
well, then they win and
they get what they want,
00:23:45.000 --> 00:23:48.900
and I don't get to continue to
make my points of view heard.
00:23:48.900 --> 00:23:52.320
So I usually,
00:23:52.320 --> 00:23:54.030
when I have a bad day,
00:23:54.030 --> 00:23:56.710
I just call it a night
and I go to bed early,
00:23:56.710 --> 00:23:58.160
and I wake up,
00:23:58.160 --> 00:24:02.810
and most days, like, I
feel ready to do it again,
00:24:02.810 --> 00:24:05.660
and ready to revisit the situation.
00:24:05.660 --> 00:24:09.600
And I find a way to smooth
over whatever was really hard.
00:24:09.600 --> 00:24:14.600
And I encourage you just
to find something you love
00:24:14.610 --> 00:24:15.593
and stick with it.
00:24:17.480 --> 00:24:18.860
- Yeah, and I always remind folks,
00:24:18.860 --> 00:24:19.970
you know, there's no movie
00:24:19.970 --> 00:24:22.730
where the protagonist does not
have to deal with adversity.
00:24:22.730 --> 00:24:24.360
So whenever those adverse moments happen,
00:24:24.360 --> 00:24:26.100
say, "Well, this is
just part of my movie."
00:24:26.100 --> 00:24:27.870
And the movie would not be interesting
00:24:27.870 --> 00:24:28.970
without these moments.
00:24:28.970 --> 00:24:30.290
And you're absolutely right.
00:24:30.290 --> 00:24:33.000
The things that you think
are existential crises,
00:24:33.000 --> 00:24:34.600
you know, within reason,
00:24:34.600 --> 00:24:35.507
a week later, you're like,
00:24:35.507 --> 00:24:37.060
"I just have to power through it."
00:24:37.060 --> 00:24:39.710
There's ways that it can
sometimes get better,
00:24:39.710 --> 00:24:42.430
and you just have to
sometimes realize that it,
00:24:42.430 --> 00:24:44.880
you know, staying in the
game is half the battle.
00:24:45.900 --> 00:24:48.030
- Yeah, and I've had many times things
00:24:48.030 --> 00:24:49.080
didn't go the way I wanted,
00:24:49.080 --> 00:24:51.480
and many times things failed,
00:24:51.480 --> 00:24:53.730
and many times I made mistakes,
00:24:53.730 --> 00:24:54.960
and then I had to come back,
00:24:54.960 --> 00:24:57.323
and say, "Oh, I learned from that."
00:25:01.070 --> 00:25:02.090
That's how life is,
00:25:02.090 --> 00:25:06.160
and what makes you stronger
is overcoming that,
00:25:06.160 --> 00:25:08.000
and internalizing that,
00:25:08.000 --> 00:25:10.810
and saying, "Well, what
did I learn from that?
00:25:10.810 --> 00:25:13.610
And how can I change how
my life is going forward?"
00:25:13.610 --> 00:25:16.960
And if you are continuously learning,
00:25:16.960 --> 00:25:20.250
if you are having as many experiences,
00:25:20.250 --> 00:25:22.220
and then benefiting from them,
00:25:22.220 --> 00:25:24.730
and figuring out how you
can do everything better,
00:25:24.730 --> 00:25:27.790
then that all adds up.
00:25:27.790 --> 00:25:30.600
And there are a lot of
times where we're at work
00:25:30.600 --> 00:25:32.110
and people come to me
with different ideas,
00:25:32.110 --> 00:25:33.160
and be like,
00:25:33.160 --> 00:25:36.100
I'll say, "I know about doing that,
00:25:36.100 --> 00:25:38.030
'cause I did it and it didn't work."
00:25:38.030 --> 00:25:39.220
I can tell you why,
00:25:39.220 --> 00:25:41.380
'cause there are a lot of things I've done
00:25:41.380 --> 00:25:42.430
that have not worked.
00:25:43.960 --> 00:25:45.800
But I learned from it and
I'm not doing them again.
00:25:45.800 --> 00:25:47.340
And I'm actually telling other people too,
00:25:47.340 --> 00:25:49.010
like, don't do that.
00:25:49.010 --> 00:25:50.440
Sometimes I'll even say,
"Hey, you know what?
00:25:50.440 --> 00:25:51.670
You can try it, the world's different,
00:25:51.670 --> 00:25:53.550
like, maybe things have changed."
00:25:53.550 --> 00:25:58.500
And so I'm also open to how
something could be different now
00:25:58.500 --> 00:25:59.530
than it was in the past.
00:25:59.530 --> 00:26:00.363
But I tell them, like,
00:26:00.363 --> 00:26:01.800
"This is why it didn't work for me,
00:26:01.800 --> 00:26:03.990
you should take that into consideration
00:26:03.990 --> 00:26:05.740
as you consider your future plans."
00:26:07.113 --> 00:26:07.946
- You know, related to that,
00:26:07.946 --> 00:26:09.260
when people look at
you, when I look at you,
00:26:09.260 --> 00:26:10.860
you're like, oh, Susan Wojcicki,
00:26:10.860 --> 00:26:12.510
you know, titan of tech,
00:26:12.510 --> 00:26:13.680
has it all figured out,
00:26:13.680 --> 00:26:14.623
she's made it.
00:26:16.451 --> 00:26:19.600
What are the things that you feel
00:26:19.600 --> 00:26:21.860
that you feel sometimes unsure about
00:26:21.860 --> 00:26:22.743
or that you stress about?
00:26:22.743 --> 00:26:24.030
Because I think that's something that,
00:26:24.030 --> 00:26:24.870
you know, it's very easy...
00:26:24.870 --> 00:26:26.954
We all know the things we stress about,
00:26:26.954 --> 00:26:28.390
but when we look at the
Susan Wojcickis of the world,
00:26:28.390 --> 00:26:30.010
like they have it figured out.
00:26:30.010 --> 00:26:33.133
So, you know, show us that
you're like the rest of us.
00:26:34.310 --> 00:26:36.130
- Well, there are definitely...
00:26:36.130 --> 00:26:39.070
A lot of times I'm doing
things I've never done before,
00:26:39.070 --> 00:26:40.870
just because tech is in a new place
00:26:40.870 --> 00:26:42.430
that it's never been before,
00:26:42.430 --> 00:26:45.020
and we're having to figure out a lot
00:26:45.020 --> 00:26:48.090
of challenging situations
based on the size
00:26:48.090 --> 00:26:50.930
or where we are and how we can do better.
00:26:50.930 --> 00:26:55.730
And I mean, there's so
many different examples.
00:26:55.730 --> 00:26:59.060
And I mean, maybe I can just
think of like all the times
00:26:59.060 --> 00:27:01.943
that my kids have told
me how we've screwed up.
00:27:04.066 --> 00:27:06.583
And, I actually just think that,
00:27:07.910 --> 00:27:09.353
when you screw up,
00:27:11.510 --> 00:27:13.070
you should just say that,
00:27:13.070 --> 00:27:14.530
and just be honest about it.
00:27:14.530 --> 00:27:18.180
And so, you know,
00:27:18.180 --> 00:27:21.780
I look at like our Rewind video
that we did two years ago.
00:27:21.780 --> 00:27:24.913
It was the most disliked
video on the internet.
00:27:26.944 --> 00:27:28.310
- What was that?
00:27:28.310 --> 00:27:30.700
Maybe I was in under a rock someplace,
00:27:30.700 --> 00:27:32.040
but the most disliked...
00:27:32.040 --> 00:27:33.459
What is this video?
- You were under a rock.
00:27:33.459 --> 00:27:34.420
Every kid on this video,
00:27:34.420 --> 00:27:35.600
they know what I'm talking about.
00:27:35.600 --> 00:27:37.490
They know about this video,
00:27:37.490 --> 00:27:40.280
that other videos on
YouTube had taken years
00:27:40.280 --> 00:27:42.430
to have this many dislikes.
00:27:42.430 --> 00:27:45.220
And then our video, in a matter of weeks,
00:27:45.220 --> 00:27:48.020
sorry, in matter of a week, of days,
00:27:48.020 --> 00:27:50.080
it became the most disliked
video on the internet.
00:27:50.080 --> 00:27:54.240
And so I just was like,
"Yeah, the video was cringey.
00:27:54.240 --> 00:27:56.040
My kids were like, "It was cringey."
00:27:57.047 --> 00:27:58.740
I was like, "Okay, it was a cringey video.
00:27:58.740 --> 00:27:59.573
So what?
00:27:59.573 --> 00:28:00.840
We made the worst video,
00:28:00.840 --> 00:28:02.950
like the most disliked video, fine.
00:28:02.950 --> 00:28:06.477
Like, we'll make something
different next year."
00:28:06.477 --> 00:28:09.270
And so sometimes you just
got to go with, yeah,
00:28:09.270 --> 00:28:10.240
we made a mistake.
00:28:10.240 --> 00:28:11.190
Things didn't go well.
00:28:11.190 --> 00:28:12.140
So I can tell you, like,
00:28:12.140 --> 00:28:14.300
at that moment, it was not...
00:28:15.340 --> 00:28:19.600
people at YouTube were not
feeling good that the video
00:28:19.600 --> 00:28:22.943
was becoming the most disliked
video on the internet.
00:28:24.160 --> 00:28:25.330
But you learn from it.
00:28:25.330 --> 00:28:29.670
And, I think having some
humor about it too sometimes,
00:28:29.670 --> 00:28:31.690
is, you know, when you can,
00:28:31.690 --> 00:28:33.850
when it's something like that,
00:28:33.850 --> 00:28:36.487
where you can just say,
00:28:36.487 --> 00:28:38.977
"Let's just laugh and move on."
00:28:40.410 --> 00:28:41.243
- No, and I have to say,
00:28:41.243 --> 00:28:44.610
it takes an incredible
security to bring up, you know,
00:28:44.610 --> 00:28:45.620
if you asked me to bring it,
00:28:45.620 --> 00:28:46.453
and I have them,
00:28:46.453 --> 00:28:49.423
my major failures over the last
year, three years, 10 years,
00:28:50.520 --> 00:28:51.437
there's a part of my brain says,
00:28:51.437 --> 00:28:52.280
"Sal, don't bring it up.
00:28:52.280 --> 00:28:53.190
Then people are gonna know,
00:28:53.190 --> 00:28:55.210
you know, all your weaknesses."
00:28:55.210 --> 00:28:57.390
It takes a lot to bring that up,
00:28:57.390 --> 00:28:58.820
but really appreciate that.
00:28:58.820 --> 00:29:00.773
We have another question from Imani.
00:29:01.810 --> 00:29:02.790
- I was just curious,
00:29:02.790 --> 00:29:04.940
what strong women have inspired
00:29:04.940 --> 00:29:08.110
or influenced you to
become the powerful leader
00:29:08.110 --> 00:29:09.123
that you are today?
00:29:11.930 --> 00:29:14.060
- Who has inspired me?
00:29:14.060 --> 00:29:16.440
Well, many people along the way.
00:29:16.440 --> 00:29:19.860
My mom definitely inspired me.
00:29:19.860 --> 00:29:21.490
And as a kid,
00:29:21.490 --> 00:29:25.180
I was always really
impressed with Marie Curie.
00:29:25.180 --> 00:29:28.210
And she was my icon as a kid.
00:29:28.210 --> 00:29:31.940
She is someone who holds two Nobel Prizes.
00:29:31.940 --> 00:29:33.970
And I don't think there
are a lot of other people
00:29:33.970 --> 00:29:36.230
who have achieved that
in different fields.
00:29:36.230 --> 00:29:38.530
And her daughter also has a Nobel Prize,
00:29:38.530 --> 00:29:40.210
which I always thought
was really impressive.
00:29:40.210 --> 00:29:43.733
So she was one of my icons.
00:29:45.400 --> 00:29:47.370
But I would also say
that a lot of the people
00:29:47.370 --> 00:29:48.920
who mentored me
00:29:48.920 --> 00:29:52.053
and helped me get to where I am,
00:29:53.330 --> 00:29:54.310
they were not always women.
00:29:54.310 --> 00:29:55.680
In fact, most of the time they were men,
00:29:55.680 --> 00:29:57.260
because most of the people
00:29:57.260 --> 00:30:02.260
in positions above me at Google,
00:30:02.270 --> 00:30:03.900
in tech, were men.
00:30:03.900 --> 00:30:08.900
And there were a lot of super
supportive mentors that I had.
00:30:08.960 --> 00:30:11.670
And I always remind people, like,
00:30:11.670 --> 00:30:14.220
whether they're a mentee or a mentor,
00:30:14.220 --> 00:30:16.380
that anyone,
00:30:16.380 --> 00:30:17.940
like, anyone regardless
of their backgrounds,
00:30:17.940 --> 00:30:18.900
you can mentor someone.
00:30:18.900 --> 00:30:20.500
They don't have to look
like you or be like,
00:30:20.500 --> 00:30:24.430
you can just find someone who is talented
00:30:24.430 --> 00:30:25.800
that you wanna mentor,
00:30:25.800 --> 00:30:28.490
and, again, your mentors
00:30:28.490 --> 00:30:31.990
can be different from the
backgrounds you came from,
00:30:31.990 --> 00:30:34.120
and they can be really helpful to you.
00:30:34.120 --> 00:30:35.940
So I'm very thankful
00:30:35.940 --> 00:30:38.360
for all the people who
mentored me along the way,
00:30:38.360 --> 00:30:41.780
even though they came from
different backgrounds than I did,
00:30:41.780 --> 00:30:42.613
and they definitely helped me,
00:30:42.613 --> 00:30:44.310
and I definitely learned from them.
00:30:45.910 --> 00:30:47.220
- Absolutely.
00:30:47.220 --> 00:30:49.010
And you know, I know we're running low.
00:30:49.010 --> 00:30:50.153
I could talk to you for hours.
00:30:50.153 --> 00:30:51.210
There's so many questions I have
00:30:51.210 --> 00:30:53.000
about your life, about YouTube.
00:30:53.000 --> 00:30:54.920
I know we touched on
the subject of learning.
00:30:54.920 --> 00:30:57.000
Obviously Khan Academy is
very focused on learning,
00:30:57.000 --> 00:30:59.590
and YouTube has been a
big part of that journey,
00:30:59.590 --> 00:31:01.470
when I was making content for my cousins,
00:31:01.470 --> 00:31:02.720
and still do.
00:31:02.720 --> 00:31:05.360
I made three videos that I
uploaded onto YouTube yesterday,
00:31:05.360 --> 00:31:07.100
so I'm still very active there.
00:31:07.100 --> 00:31:10.080
What's your dream,
00:31:10.080 --> 00:31:13.090
if you fast forward five, 10 20 years,
00:31:13.090 --> 00:31:14.980
for, you know,
00:31:14.980 --> 00:31:16.910
I don't know if you
think in terms of legacy,
00:31:16.910 --> 00:31:18.160
but, you know, the impact
00:31:18.160 --> 00:31:19.960
that you wanna have through YouTube?
00:31:21.780 --> 00:31:24.300
- So we definitely think about YouTube
00:31:24.300 --> 00:31:26.570
and how we can continue to grow it.
00:31:26.570 --> 00:31:30.250
And I'm always just amazed
of all the new topics
00:31:30.250 --> 00:31:33.770
and new ways that we can enable voices
00:31:33.770 --> 00:31:36.110
around the world to come
and to share their story.
00:31:36.110 --> 00:31:38.040
And so part of our goal
00:31:38.040 --> 00:31:40.750
is to enable the next
generation of storytellers
00:31:40.750 --> 00:31:45.240
and to help them be able to do
that and to make a business.
00:31:45.240 --> 00:31:47.330
And the flip side of that
00:31:47.330 --> 00:31:50.690
is that we can have
incredibly compelling content
00:31:50.690 --> 00:31:54.160
for people around the world, on any topic.
00:31:54.160 --> 00:31:57.490
And so if you look at YouTube,
00:31:57.490 --> 00:31:59.820
I see that we bring many value.
00:31:59.820 --> 00:32:01.330
And of course, like, you know,
00:32:01.330 --> 00:32:06.330
enabling all the fun
videos and music videos,
00:32:06.590 --> 00:32:10.220
but we're also dealing with a
lot of really important topics
00:32:10.220 --> 00:32:12.383
that just were not talked about before,
00:32:13.300 --> 00:32:16.580
whether that involves
mental health issues,
00:32:16.580 --> 00:32:19.450
or hearing from people
of different backgrounds
00:32:19.450 --> 00:32:23.210
that never were represented
on media traditionally,
00:32:23.210 --> 00:32:24.930
like, those are really compelling
00:32:24.930 --> 00:32:26.663
and important points of view.
00:32:27.629 --> 00:32:28.600
- You know, one last question,
00:32:28.600 --> 00:32:30.530
it feels like there's two competing winds.
00:32:30.530 --> 00:32:35.300
There is one wind where there's
more tools and resources,
00:32:35.300 --> 00:32:37.170
YouTube, Khan Academy, you know,
00:32:37.170 --> 00:32:39.210
all the other things that Google provides,
00:32:39.210 --> 00:32:41.730
that are enabling the
individual to publish,
00:32:41.730 --> 00:32:42.760
to express themselves,
00:32:42.760 --> 00:32:45.200
to discover points of view, to learn.
00:32:45.200 --> 00:32:46.840
It really does feel like
we're an inflection point,
00:32:46.840 --> 00:32:50.000
a renaissance, so to
speak, in human society.
00:32:50.000 --> 00:32:51.600
On the other side,
00:32:51.600 --> 00:32:54.000
there are reasons why
people can get cynical.
00:32:54.000 --> 00:32:55.760
It feels like we are more polarized
00:32:55.760 --> 00:32:57.550
as a country or as a world.
00:32:57.550 --> 00:33:00.550
It feels like, you know,
inequity is growing.
00:33:00.550 --> 00:33:03.180
It feels like people aren't
listening to each other anymore.
00:33:03.180 --> 00:33:05.370
You know, the climate's in trouble.
00:33:05.370 --> 00:33:07.670
If there's a young person watching...
00:33:07.670 --> 00:33:09.370
And there's a pandemic,
00:33:09.370 --> 00:33:12.300
and people are feeling
isolated and lonely.
00:33:12.300 --> 00:33:14.820
What message can you give to someone
00:33:14.820 --> 00:33:18.230
who's kind of trying to
navigate these two currents?
00:33:18.230 --> 00:33:21.320
- YouTube does enable people
00:33:21.320 --> 00:33:23.190
to connect with each other as humans.
00:33:23.190 --> 00:33:24.670
And there's something very human
00:33:24.670 --> 00:33:27.960
about the fact that people
are, a lot of times,
00:33:27.960 --> 00:33:30.680
going to YouTube and
talking about how they feel,
00:33:30.680 --> 00:33:33.880
what their deepest challenges were,
00:33:33.880 --> 00:33:35.690
about diseases they have,
00:33:35.690 --> 00:33:38.070
and there's something really cathartic
00:33:38.070 --> 00:33:40.730
about people going and
sharing the challenges
00:33:40.730 --> 00:33:41.563
that they have.
00:33:41.563 --> 00:33:44.970
And we've seen other people
really be able to relate
00:33:44.970 --> 00:33:45.980
and benefit from that.
00:33:45.980 --> 00:33:48.460
So I do see a human connection
00:33:48.460 --> 00:33:50.290
that's incredibly powerful on YouTube
00:33:50.290 --> 00:33:52.890
for us to understand each
other more as humans.
00:33:52.890 --> 00:33:57.390
And I've also seen that
there's an incredible amount
00:33:57.390 --> 00:33:58.430
of good that comes,
00:33:58.430 --> 00:34:03.430
whether it's something
like the 20 million trees
00:34:05.830 --> 00:34:10.560
that are being planted
and organized on YouTube,
00:34:10.560 --> 00:34:14.470
or fundraisers to support
people during hard times.
00:34:14.470 --> 00:34:18.150
And so I do see that YouTube
00:34:18.150 --> 00:34:21.490
can be used for all of
kinds of good outcomes.
00:34:21.490 --> 00:34:24.670
And I encourage you to use
00:34:24.670 --> 00:34:27.040
like YouTube and all social platforms,
00:34:27.040 --> 00:34:28.670
if there's a cause you believe in,
00:34:28.670 --> 00:34:30.080
you can make a difference,
00:34:30.080 --> 00:34:31.300
you can make a video,
00:34:31.300 --> 00:34:33.050
you can organize groups,
00:34:33.050 --> 00:34:35.800
and I encourage you to speak your voice,
00:34:35.800 --> 00:34:39.560
and now's the best time
ever to be able to do that.
00:34:39.560 --> 00:34:42.870
So I encourage you to do what's important
00:34:42.870 --> 00:34:44.613
for you and to speak up.
00:34:46.329 --> 00:34:49.420
- No, thank you so much
for that. I'm inspired.
00:34:49.420 --> 00:34:51.728
I'm gonna go use social media
00:34:51.728 --> 00:34:53.850
to try to change the world.
00:34:53.850 --> 00:34:55.060
Well, Susan, thank you so much.
00:34:55.060 --> 00:34:56.530
I know you're incredibly busy.
00:34:56.530 --> 00:34:58.540
And thank you for making
the time out for all of us,
00:34:58.540 --> 00:34:59.830
and all of the students who are watching,
00:34:59.830 --> 00:35:01.300
and their questions.
00:35:01.300 --> 00:35:05.980
And, you know, I'm excited
to be part of your journey,
00:35:05.980 --> 00:35:09.250
which you are empowering Khan
Academy on so many levels,
00:35:09.250 --> 00:35:12.410
and see where we can take the world.
00:35:12.410 --> 00:35:13.640
- Well, thank you.
00:35:13.640 --> 00:35:16.630
And I'm glad we have been
part of your journey too.
00:35:16.630 --> 00:35:18.170
- Well, thanks everyone for joining.
00:35:18.170 --> 00:35:19.370
As you could tell,
00:35:19.370 --> 00:35:20.900
you know, these conversations,
00:35:20.900 --> 00:35:22.430
when you have a guest like Susan,
00:35:22.430 --> 00:35:23.770
I could talk for hours,
00:35:23.770 --> 00:35:25.280
so much to learn from,
00:35:25.280 --> 00:35:27.130
and I find her to be incredibly inspiring.
00:35:27.130 --> 00:35:29.300
And you know, I've known
Susan and her family
00:35:29.300 --> 00:35:31.460
for many years now.
00:35:31.460 --> 00:35:34.230
And you know, every time I chat,
00:35:34.230 --> 00:35:35.550
I never cease to be impressed
00:35:35.550 --> 00:35:37.610
by what, actually, her and her sisters
00:35:37.610 --> 00:35:40.750
and her mother are accomplishing
on a regular basis.
00:35:40.750 --> 00:35:42.543
So I thank you all for joining.
00:35:43.593 --> 00:35:44.980
We're actually going to have...
00:35:44.980 --> 00:35:46.540
Our next show is March 10th.
00:35:46.540 --> 00:35:48.050
The guest is Mark Sternberg.
00:35:48.050 --> 00:35:49.510
It'll actually be hosted
00:35:49.510 --> 00:35:54.510
by Khan Academy's Chief Learning
Officer, Kristen DiCerbo.
00:35:54.530 --> 00:35:55.810
And they're going to be talking...
00:35:55.810 --> 00:35:59.230
This is Mark Sternberg from
the Walton Family Foundation,
00:35:59.230 --> 00:36:00.840
and we'll talk about philanthropy
00:36:00.840 --> 00:36:02.870
and learning and impact on education.
00:36:02.870 --> 00:36:06.070
So I look forward to
seeing all of y'all there.
00:36:06.070 --> 00:36:08.053
Have a good weekend.
00:36:09.157 --> 00:36:11.740
(bright music)
|
Composite functions to model extraterrestrial skydiving | https://www.youtube.com/watch?v=UMTeKCLvv9E | vtt | https://www.youtube.com/api/timedtext?v=UMTeKCLvv9E&ei=6VWUZYK9I7a4mLAPkeKb8AU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E2B50C5A9B7B4EBF462DF4C13B92194B3078CDEC.B0A424A08439F7D85760FB2C0003EB36E5DCD8A0&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.140 --> 00:00:02.240
- [Instructor] We're told
that Flox is a skydiver
00:00:02.240 --> 00:00:04.450
on the planet Lernon.
00:00:04.450 --> 00:00:09.170
The function. A of w is
equal to 0.2 times W squared,
00:00:09.170 --> 00:00:12.270
gives the area, A, in square meters
00:00:12.270 --> 00:00:17.270
under Flox's parachute when
it has a width of W meters.
00:00:17.570 --> 00:00:18.890
That makes sense.
00:00:18.890 --> 00:00:21.460
The function V of A is
equal to the square root
00:00:21.460 --> 00:00:26.440
of 980 over A gives Flox's maximum speed
00:00:26.440 --> 00:00:29.700
in meters per second when she skydives
00:00:29.700 --> 00:00:34.300
with an area of A square
meters under her parachute.
00:00:34.300 --> 00:00:35.340
All right.
00:00:35.340 --> 00:00:38.940
Write an expression to model
Flox's terminal velocity
00:00:38.940 --> 00:00:42.950
when her parachute is W meters wide,
00:00:42.950 --> 00:00:45.790
and then they want us to
evaluate the terminal velocity
00:00:45.790 --> 00:00:47.670
when her parachute is 14 meters wide.
00:00:47.670 --> 00:00:49.890
Well, let's just focus
on the first part first.
00:00:49.890 --> 00:00:52.624
Pause the video and see if
you can have a go at that.
00:00:52.624 --> 00:00:53.530
All right.
00:00:53.530 --> 00:00:55.490
Now let's just think about
what they're asking us.
00:00:55.490 --> 00:00:59.030
They want us to model terminal velocity
00:00:59.030 --> 00:01:02.700
when her parachute is W meters wide.
00:01:02.700 --> 00:01:04.890
So really what they want us to do
00:01:04.890 --> 00:01:07.810
is come up with a terminal velocity.
00:01:07.810 --> 00:01:12.770
Let's call that V, that
is a function of W,
00:01:12.770 --> 00:01:16.760
that is a function of the
width of her parachute.
00:01:16.760 --> 00:01:20.190
Well, we have a function here
that gives terminal velocity
00:01:20.190 --> 00:01:23.430
as a function of the
area of her parachute,
00:01:23.430 --> 00:01:25.740
but lucky for us, we have another function
00:01:25.740 --> 00:01:30.160
that gives us area as a function of width.
00:01:30.160 --> 00:01:32.450
And so we could say this is
going to be the same thing
00:01:32.450 --> 00:01:36.070
as V of this function, right over here.
00:01:36.070 --> 00:01:40.960
I'll do it in another color, A of w.
00:01:40.960 --> 00:01:44.200
And so that is going to be equal to,
00:01:44.200 --> 00:01:46.510
let me keep the colors consistent.
00:01:46.510 --> 00:01:49.870
Well, everywhere, where I
see an A in this expression,
00:01:49.870 --> 00:01:54.260
I would replace it with A of
W, which is 0.2 W squared.
00:01:54.260 --> 00:01:56.330
So it's going to be
equal to the square root
00:01:56.330 --> 00:02:01.330
of 980 over instead of
A, I am going to write,
00:02:01.990 --> 00:02:05.880
instead of this, I am going
to write 0.2 W squared,
00:02:05.880 --> 00:02:09.140
because that is A as a function of W.
00:02:09.140 --> 00:02:13.310
0.2 W squared.
00:02:13.310 --> 00:02:16.270
So this right over here,
this is an expression
00:02:16.270 --> 00:02:19.920
that models Flox's terminal velocity, V,
00:02:19.920 --> 00:02:24.010
as a function of the
width of her parachute.
00:02:24.010 --> 00:02:27.060
So that's what we have right over there.
00:02:27.060 --> 00:02:28.380
And then the next part, they say,
00:02:28.380 --> 00:02:30.480
what is Flox's terminal
velocity when her parachute
00:02:30.480 --> 00:02:32.670
is 14 meters wide?
00:02:32.670 --> 00:02:35.500
Well, then we just have
to say, okay, W is 14.
00:02:35.500 --> 00:02:37.410
Let's just evaluate this expression.
00:02:37.410 --> 00:02:40.733
So we'll get the square root of 980
00:02:43.480 --> 00:02:48.480
over 0.2 times 14 squared.
00:02:49.350 --> 00:02:52.720
Well, 14 squared is 196
00:02:54.810 --> 00:02:57.800
and this would be equal to the square root
00:02:57.800 --> 00:03:00.799
of, see, 980 divided by 196,
00:03:00.799 --> 00:03:04.340
I believe is exactly five.
00:03:04.340 --> 00:03:06.603
So this would be five divided by 0.2.
00:03:07.510 --> 00:03:10.420
And so, five divided by
essentially one fifth
00:03:10.420 --> 00:03:11.850
is the same thing as five times five.
00:03:11.850 --> 00:03:14.580
So this would be the square root of 25,
00:03:14.580 --> 00:03:16.700
which is equal to five.
00:03:16.700 --> 00:03:19.310
And the terminal velocity, since we gave
00:03:19.310 --> 00:03:22.450
the width in meters,
this is going to give us
00:03:22.450 --> 00:03:24.210
the maximum speed in meters per second.
00:03:24.210 --> 00:03:27.683
So five meters per second, and we're done.
|
Reading inverse values from a graph | https://www.youtube.com/watch?v=nEWYKpTCX-U | vtt | https://www.youtube.com/api/timedtext?v=nEWYKpTCX-U&ei=6VWUZbjDIPS2mLAP_LOFqAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=42F21B55025630045FC861231821EB5261B19843.AD925BE27D1F0BEDCB792853FC55299D546F60C6&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.450 --> 00:00:01.960
- [Instructor] We're told
the following graph shows
00:00:01.960 --> 00:00:04.400
y is equal to f of x, all right.
00:00:04.400 --> 00:00:05.767
And then the first question they say is,
00:00:05.767 --> 00:00:09.450
"What appears to be the
value of f inverse of two?"
00:00:09.450 --> 00:00:12.100
Pause the video and see if
you can have a go at that.
00:00:12.970 --> 00:00:14.760
All right, now let's work
through this together.
00:00:14.760 --> 00:00:15.670
So it's important to realize
00:00:15.670 --> 00:00:18.390
they're not asking us what f of two is.
00:00:18.390 --> 00:00:20.700
They're asking us f inverse of two.
00:00:20.700 --> 00:00:23.880
f of two we would say,
"Okay, when x is equal to two
00:00:23.880 --> 00:00:25.460
that's the input into our function."
00:00:25.460 --> 00:00:28.260
And then the graph tells us that f of two
00:00:28.260 --> 00:00:31.280
it looks like it might be
a little bit more than 2.5.
00:00:31.280 --> 00:00:33.320
Maybe it's approximately 2.6.
00:00:34.250 --> 00:00:35.430
But that's not what they're asking us.
00:00:35.430 --> 00:00:38.970
They're asking us f inverse of two.
00:00:38.970 --> 00:00:41.730
And just as a reminder of
what an inverse function is,
00:00:41.730 --> 00:00:43.940
if we have some input, x,
00:00:43.940 --> 00:00:46.040
and we input into our function, f,
00:00:46.040 --> 00:00:49.420
that is going to output f of x.
00:00:49.420 --> 00:00:51.580
Now, if we were to input f of x
00:00:51.580 --> 00:00:56.270
into the inverse function
for f, then the output here,
00:00:56.270 --> 00:00:59.940
which is going to be f inverse of f of x
00:00:59.940 --> 00:01:02.660
is going to get us back
to this original x,
00:01:02.660 --> 00:01:04.970
is going to be equal to x.
00:01:04.970 --> 00:01:07.690
So we are really, in this scenario,
00:01:07.690 --> 00:01:12.690
dealing with this part of this
chain of inputs and outputs.
00:01:12.930 --> 00:01:16.700
We're saying we want to figure
out what f inverse of two is.
00:01:16.700 --> 00:01:19.570
So this part, right over here
is going to be equal to two.
00:01:19.570 --> 00:01:23.230
So we're saying when f
of x is equal to two,
00:01:23.230 --> 00:01:25.800
what is the corresponding x?
00:01:25.800 --> 00:01:30.350
So when f of x is equal to two,
what is the corresponding X?
00:01:30.350 --> 00:01:31.650
We get four.
00:01:31.650 --> 00:01:32.640
So let's write that down.
00:01:32.640 --> 00:01:36.230
f inverse of two is equal to four.
00:01:36.230 --> 00:01:37.740
So when x is equal to four,
00:01:37.740 --> 00:01:40.240
you input that f of four is equal to two
00:01:40.240 --> 00:01:44.190
or f inverse of two is equal to four.
00:01:44.190 --> 00:01:45.217
Now the next part they say,
00:01:45.217 --> 00:01:49.440
"Sketch the graph of y is
equal to f inverse of x."
00:01:49.440 --> 00:01:50.870
So an important thing to realize
00:01:50.870 --> 00:01:55.180
is if we're saying that
b is equal to f of a
00:01:55.180 --> 00:02:00.180
which implies that the point
a,b is on the graph of f,
00:02:00.510 --> 00:02:02.380
then we're dealing with f inverse.
00:02:02.380 --> 00:02:06.680
We would know that a would
be equal to f inverse of b.
00:02:06.680 --> 00:02:08.660
You can think about swapping these two,
00:02:08.660 --> 00:02:10.090
the a and the b's here,
00:02:10.090 --> 00:02:14.740
which means that b,a
would be on f inverse.
00:02:14.740 --> 00:02:17.646
So any coordinate point that's
on our original graph f,
00:02:17.646 --> 00:02:19.670
if you swap the x and the y,
00:02:19.670 --> 00:02:22.020
that's going to be on our f inverse.
00:02:22.020 --> 00:02:23.930
So let's just pick some points.
00:02:23.930 --> 00:02:25.500
And once again, they're
just saying sketch,
00:02:25.500 --> 00:02:27.300
so it doesn't have to be perfect.
00:02:27.300 --> 00:02:29.610
So if we look at this
point right over here,
00:02:29.610 --> 00:02:34.537
that looks like the point
-10, maybe it looks like 3.4.
00:02:36.330 --> 00:02:38.630
Well, then that means
if we swap that x and y
00:02:38.630 --> 00:02:40.640
it'll be on the graph of f inverse.
00:02:40.640 --> 00:02:45.640
So if we go to 3.4, and then -10,
00:02:45.970 --> 00:02:47.830
so it gets us right about there,
00:02:47.830 --> 00:02:51.090
that would be on the graph of f inverse.
00:02:51.090 --> 00:02:53.927
Now, if we went to, let's say
00:02:53.927 --> 00:02:57.060
let's say this point right over here.
00:02:57.060 --> 00:03:01.470
This is the point -2,3.
00:03:01.470 --> 00:03:04.610
So if -2,3 is on the graph of f,
00:03:04.610 --> 00:03:08.150
then 3,-2 would be on the inverse.
00:03:08.150 --> 00:03:13.150
So 3,-2 would be on the
inverse right over there.
00:03:14.210 --> 00:03:16.160
Let's pick a few more points.
00:03:16.160 --> 00:03:19.290
So we have this point right over here, 4,2
00:03:19.290 --> 00:03:21.100
which would be on the graph of f,
00:03:21.100 --> 00:03:23.770
which means that 2,4 is on the inverse.
00:03:23.770 --> 00:03:28.020
So 2,4, which would be right over there.
00:03:28.020 --> 00:03:29.520
And then if we look at
this point over here
00:03:29.520 --> 00:03:32.700
which looks like roughly nine,
00:03:32.700 --> 00:03:35.620
let's just call it 9,-10
00:03:35.620 --> 00:03:37.530
maybe it's 9.1,-10.
00:03:37.530 --> 00:03:40.080
If that's on the graph of f,
00:03:40.080 --> 00:03:45.080
then if we swap that -10, maybe 9.1
00:03:45.590 --> 00:03:49.970
would be on the inverse
-10,9.1, right over there.
00:03:49.970 --> 00:03:52.170
And so then we could connect the dots
00:03:52.170 --> 00:03:55.330
to try to sketch out
what the inverse function
00:03:55.330 --> 00:03:58.350
is going to look like, the
graph of the inverse function.
00:03:58.350 --> 00:04:03.350
So it's going to look something like that.
00:04:04.580 --> 00:04:06.470
And you might notice, it looks like
00:04:06.470 --> 00:04:10.150
it's a reflection about the line y=x.
00:04:10.150 --> 00:04:12.540
It looks like it's a
reflection about that line,
00:04:12.540 --> 00:04:13.753
which is exactly right.
|
Using matrices to manipulate data: Game show | https://www.youtube.com/watch?v=NKG6DifB3OA | vtt | https://www.youtube.com/api/timedtext?v=NKG6DifB3OA&ei=6VWUZeuIIPGIp-oPr5uf0AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=789EB427A3D4A6940F9F64333CE979C2AEA12454.9638CE426348B552ADB4CDA704D1CB5DC714DB64&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:01.410
- [Instructor] We're
told, in the beginning
00:00:01.410 --> 00:00:03.520
of each episode of a certain game show,
00:00:03.520 --> 00:00:07.120
each contestant picks a certain
door out of three doors.
00:00:07.120 --> 00:00:09.070
Then the game show host randomly picks
00:00:09.070 --> 00:00:11.450
one of the two prize bundles.
00:00:11.450 --> 00:00:14.900
After each round, each
contestant receives a prize
00:00:14.900 --> 00:00:16.570
based on the door they picked
00:00:16.570 --> 00:00:18.910
and the bundle the host picked.
00:00:18.910 --> 00:00:21.590
Matrix A represents the possible prizes
00:00:21.590 --> 00:00:22.740
for the first round.
00:00:22.740 --> 00:00:24.460
All right, so for example,
00:00:24.460 --> 00:00:26.690
if the contestant picks door three
00:00:26.690 --> 00:00:30.900
and the host picks bundle
one, the prize is $300,
00:00:30.900 --> 00:00:32.870
but if the contestant picks door three
00:00:32.870 --> 00:00:34.960
and the host picks bundle two,
00:00:34.960 --> 00:00:37.870
the prize would be $0, all right.
00:00:37.870 --> 00:00:40.550
And then they say matrix B
represents the possible prizes
00:00:40.550 --> 00:00:41.700
for the second round.
00:00:41.700 --> 00:00:43.340
All right, that's fair.
00:00:43.340 --> 00:00:46.100
They also tell us the
second round can also
00:00:46.100 --> 00:00:47.970
be a lightning round.
00:00:47.970 --> 00:00:52.420
In this case, the prizes are doubled.
00:00:52.420 --> 00:00:55.330
Matrix C represents the possible prizes
00:00:55.330 --> 00:00:57.540
during a lightning round.
00:00:57.540 --> 00:01:00.110
Complete matrix C.
00:01:00.110 --> 00:01:02.560
So pause this video and see
if you can figure that out
00:01:02.560 --> 00:01:05.190
and then we'll work through this together.
00:01:05.190 --> 00:01:08.860
All right, so matrix C is a
scenario where we're dealing
00:01:08.860 --> 00:01:10.090
with a lightning round,
00:01:10.090 --> 00:01:13.130
and remember in a lightning
round, the prizes are doubled
00:01:13.130 --> 00:01:14.060
but it's the second round.
00:01:14.060 --> 00:01:16.800
It's doubled relative to
what it would have been
00:01:16.800 --> 00:01:18.320
in the second round.
00:01:18.320 --> 00:01:22.330
So what it would have been in
the second round is matrix B.
00:01:22.330 --> 00:01:23.840
So another way to think about it is,
00:01:23.840 --> 00:01:28.840
matrix C is going to be
equal to two times matrix B.
00:01:30.700 --> 00:01:33.404
And we know when we multiply a matrix
00:01:33.404 --> 00:01:36.100
times a scalar like this,
times just a number,
00:01:36.100 --> 00:01:39.180
we just multiply each of
these entries by that number.
00:01:39.180 --> 00:01:40.600
So let's do that.
00:01:40.600 --> 00:01:43.950
If we take $600 and multiply that by two,
00:01:43.950 --> 00:01:46.600
that is going to be $1,200.
00:01:46.600 --> 00:01:47.433
And that makes sense.
00:01:47.433 --> 00:01:50.150
We just said for each
corresponding scenario
00:01:50.150 --> 00:01:52.700
the prizes are doubled
in a lightning round.
00:01:52.700 --> 00:01:54.720
So if the contestant picks door one,
00:01:54.720 --> 00:01:56.970
host picks bundle one, instead of $600
00:01:56.970 --> 00:01:59.210
it's going to be $1,200.
00:01:59.210 --> 00:02:04.210
Keep going, instead of
$200, it's going to be $400.
00:02:04.340 --> 00:02:08.800
All I'm doing here is I'm
multiplying each of these entries
00:02:08.800 --> 00:02:12.950
by two to get the corresponding
entry in matrix C.
00:02:12.950 --> 00:02:15.950
Keep going, instead of $300 here,
00:02:15.950 --> 00:02:19.280
multiply that by two,
you're going to get $600.
00:02:19.280 --> 00:02:24.130
Instead of $300 here,
you're going to get $600.
00:02:25.380 --> 00:02:26.890
We're almost there.
00:02:26.890 --> 00:02:28.110
Instead of $0 here,
00:02:28.110 --> 00:02:31.920
well, zero times two is still $0.
00:02:31.920 --> 00:02:33.860
And then last but not least,
00:02:33.860 --> 00:02:35.810
instead of $400 right over here,
00:02:35.810 --> 00:02:39.600
that times two is going to be $800.
00:02:39.600 --> 00:02:41.050
Now there's one more question
00:02:41.050 --> 00:02:43.160
that they have below the
screen right over here.
00:02:43.160 --> 00:02:45.110
Let me scroll up a little bit.
00:02:45.110 --> 00:02:48.850
So they tell us matrix
D is defined as follows:
00:02:48.850 --> 00:02:51.650
D is equal to A plus B.
00:02:51.650 --> 00:02:54.810
What does matrix D represent?
00:02:54.810 --> 00:02:57.460
So pause the video and think
about that for a second.
00:02:58.330 --> 00:03:00.320
Well, if we add two matrices,
00:03:00.320 --> 00:03:03.050
we're going to add all
the corresponding entries.
00:03:03.050 --> 00:03:07.880
And so what it tells you is
what is the combined prize
00:03:07.880 --> 00:03:10.430
for both rounds one and two
00:03:10.430 --> 00:03:15.240
based on what the contestant
picks and what the host picks.
00:03:15.240 --> 00:03:18.690
So matrix D, that top
left entry will tell you,
00:03:18.690 --> 00:03:21.670
okay, in total, if the
contestant picked door number one
00:03:21.670 --> 00:03:24.000
and the host pick bundle
number one, what would you get?
00:03:24.000 --> 00:03:26.600
Cause it would be $100 dollars plus $600.
00:03:26.600 --> 00:03:29.580
So it would be total
for rounds one and two,
00:03:29.580 --> 00:03:31.410
assuming we don't have the lightning round
00:03:31.410 --> 00:03:33.313
like we had in matrix C.
|
Using matrices to manipulate data: Pet store | https://www.youtube.com/watch?v=g-ljbR62EAQ | vtt | https://www.youtube.com/api/timedtext?v=g-ljbR62EAQ&ei=6VWUZe3DHcbkmLAP29emyA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=CE6DF2F5BC2066FDFB1ADF8091B59A5D43F2C466.75AF8A5A24986B2457B2F565A018960FABDE21AF&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.880 --> 00:00:02.210
- [Instructor] We're told
a certain pet store chain
00:00:02.210 --> 00:00:03.970
has three types of dog food
00:00:03.970 --> 00:00:08.430
and each comes in bags
of two different sizes.
00:00:08.430 --> 00:00:13.170
Matrix A represents the store's
inventory at location A,
00:00:13.170 --> 00:00:18.170
where rows are food types
and columns are bag sizes.
00:00:18.780 --> 00:00:19.990
So let's see, it's store A.
00:00:19.990 --> 00:00:21.810
That's what matrix A is telling us.
00:00:21.810 --> 00:00:26.510
They're telling us we have
three different types of food,
00:00:26.510 --> 00:00:28.110
three different types of dog food,
00:00:28.110 --> 00:00:30.620
and then they each come
in two different sizes.
00:00:30.620 --> 00:00:34.430
So for example, type 1 dog food in size 1,
00:00:34.430 --> 00:00:39.060
they have five bags of
that while type 2 dog food
00:00:39.060 --> 00:00:41.080
in size 2, they have nine bags of that.
00:00:41.080 --> 00:00:42.620
All right. That's fair enough.
00:00:42.620 --> 00:00:46.390
Matrix B represents the store's
inventory at location B.
00:00:46.390 --> 00:00:48.860
All right, same thing for store B.
00:00:48.860 --> 00:00:52.900
Matrix C represents
how many more, or less,
00:00:52.900 --> 00:00:55.570
bags of each type and size there are
00:00:55.570 --> 00:01:00.570
in location A relative to location B.
00:01:00.690 --> 00:01:03.690
Complete matrix C.
00:01:03.690 --> 00:01:06.200
So pause this video and see
if you can have a go at that.
00:01:06.200 --> 00:01:11.083
So we need to fill in the
entries here of matrix C.
00:01:13.490 --> 00:01:15.040
All right, now let's do this together.
00:01:15.040 --> 00:01:17.000
So let me just review
what it just told us.
00:01:17.000 --> 00:01:22.000
Matrix C represents how many
more bags of each type and size
00:01:22.530 --> 00:01:27.530
there are in location A
relative to location B.
00:01:27.750 --> 00:01:30.950
So for example, this first
entry right over here,
00:01:30.950 --> 00:01:35.950
we wanna know how many
more bags of type 1, size 1
00:01:36.100 --> 00:01:40.520
there are in location A than
there are in location B?
00:01:40.520 --> 00:01:43.830
Well, I would take the number
that there are in location A
00:01:43.830 --> 00:01:46.060
and then from that subtract how many
00:01:46.060 --> 00:01:47.180
there are in location B.
00:01:47.180 --> 00:01:50.170
That would tell me how many
more I have in location A.
00:01:50.170 --> 00:01:55.170
So if I take five minus
eight, what am I going to get?
00:01:56.210 --> 00:02:00.760
Well, I'm going to get
negative three right over here,
00:02:00.760 --> 00:02:03.250
and you might already be
recognizing what's happening.
00:02:03.250 --> 00:02:05.200
For every corresponding entry,
00:02:05.200 --> 00:02:07.240
I'm gonna subtract the entry from matrix B
00:02:07.240 --> 00:02:09.530
from the entry in matrix A,
00:02:09.530 --> 00:02:11.290
or another way to think about it is,
00:02:11.290 --> 00:02:16.290
if I take matrix A and
I subtract matrix B,
00:02:16.390 --> 00:02:18.600
I am going to get matrix C.
00:02:18.600 --> 00:02:21.610
I'm just gonna subtract all
of the corresponding entries.
00:02:21.610 --> 00:02:26.230
So if I do seven minus six,
and that is going to be one,
00:02:26.230 --> 00:02:27.380
I'm just gonna color code this.
00:02:27.380 --> 00:02:32.380
If I do three minus 10, that's
going to be negative seven.
00:02:32.950 --> 00:02:36.020
If I do, I'm running out of colors.
00:02:36.020 --> 00:02:39.100
If I do nine minus 12,
00:02:39.100 --> 00:02:44.100
that is also going to be negative three.
00:02:44.320 --> 00:02:48.090
And then if I do this brown color,
00:02:48.090 --> 00:02:52.650
10 minus five, that is
going to be positive five.
00:02:52.650 --> 00:02:57.650
And then if I do 15 minus
nine, that is positive six.
00:02:58.640 --> 00:03:02.470
So we can see that, for
example, type 1, size 2,
00:03:02.470 --> 00:03:06.050
we have one more in store
A than we have in store B.
00:03:06.050 --> 00:03:10.150
But if we think about type 2, size 1,
00:03:10.150 --> 00:03:14.510
it shows us that store A
has actually seven fewer
00:03:14.510 --> 00:03:17.430
of that than store B does.
00:03:17.430 --> 00:03:21.830
Now we have one last question
here that is below the screen,
00:03:21.830 --> 00:03:24.180
but let me scroll down here.
00:03:24.180 --> 00:03:27.730
So they tell us that matrix
D is defined as follows,
00:03:27.730 --> 00:03:29.740
or is defines as follows. (chuckles)
00:03:29.740 --> 00:03:31.150
Make a little grammatical.
00:03:31.150 --> 00:03:36.140
Is defined as follows:
D is equal to A plus B.
00:03:36.140 --> 00:03:38.260
What does matrix D represent?
00:03:38.260 --> 00:03:40.780
So they're not asking us
to calculate A plus B.
00:03:40.780 --> 00:03:42.430
Not asking us to add the matrices,
00:03:42.430 --> 00:03:43.263
but you know how to do it.
00:03:43.263 --> 00:03:44.850
You would add the corresponding entries.
00:03:44.850 --> 00:03:47.403
But what does D represent?
00:03:48.850 --> 00:03:50.940
Well, if you add the
corresponding entries,
00:03:50.940 --> 00:03:53.180
remember, this is the
inventory of store A,
00:03:53.180 --> 00:03:55.350
this is the inventory of store B.
00:03:55.350 --> 00:03:56.510
So if you were to add them,
00:03:56.510 --> 00:03:59.730
the matrix D would tell you
the combined inventories
00:03:59.730 --> 00:04:04.443
of A and B, for each
of the types and sizes.
|
Magnetism and Magnetic Fields | https://www.youtube.com/watch?v=HFhTV4vzqOI | vtt | https://www.youtube.com/api/timedtext?v=HFhTV4vzqOI&ei=6VWUZbeLHKWrp-oPzqyOiAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6E1D811E9AAF2B544FA2946278D59FB190FD75EF.27A233ACF6A0EEAD8E26BC26934C03FA0B42C44A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.450 --> 00:00:02.330
- [Instructor] Let's talk
a little bit about magnets
00:00:02.330 --> 00:00:05.480
and magnetic fields and right
over here we have a picture
00:00:05.480 --> 00:00:08.420
of what today we would call a magnet
00:00:08.420 --> 00:00:11.540
where we have these metal
nails all being attracted
00:00:11.540 --> 00:00:14.100
to the stone and the stone,
00:00:14.100 --> 00:00:17.340
the modern name for it is magnetite,
00:00:17.340 --> 00:00:19.280
and human beings have known
00:00:19.280 --> 00:00:22.530
about magnetite for thousands of years
00:00:22.530 --> 00:00:25.750
in fact the name comes
from Ancient Greece,
00:00:25.750 --> 00:00:27.480
there was the Magnetes people
00:00:27.480 --> 00:00:30.520
who settled actually areas
that are often talked
00:00:30.520 --> 00:00:32.910
about in the origin of the name magnet,
00:00:32.910 --> 00:00:35.940
which are now referred to as Magnesia,
00:00:35.940 --> 00:00:38.270
and depending on the
historical count you see
00:00:38.270 --> 00:00:40.720
it was one of those Magnesia's
00:00:40.720 --> 00:00:43.860
where the Ancient Greeks
were able to find a lot
00:00:43.860 --> 00:00:45.420
of what we would call magnetite,
00:00:45.420 --> 00:00:48.650
and actually the element
magnesium which is not related
00:00:48.650 --> 00:00:51.030
to magnetite was also found in that area,
00:00:51.030 --> 00:00:53.140
which is where it got its name.
00:00:53.140 --> 00:00:55.820
But it wasn't just some interesting thing
00:00:55.820 --> 00:00:57.230
that would attract metal,
00:00:57.230 --> 00:00:59.790
and then they also obviously
observed other properties
00:00:59.790 --> 00:01:04.410
that if you had two pieces
of magnetized magnetite
00:01:04.410 --> 00:01:08.270
it actually turns out that not
all magnetite is magnetized,
00:01:08.270 --> 00:01:10.840
something interesting has
to happen to it we believe
00:01:10.840 --> 00:01:12.120
it's actually lightning strikes
00:01:12.120 --> 00:01:14.330
that magnetizes it naturally,
00:01:14.330 --> 00:01:16.300
that the orientation matters,
00:01:16.300 --> 00:01:19.410
if you're in one orientation
they might attract each other.
00:01:19.410 --> 00:01:21.450
And then if you're in another
orientation if you were
00:01:21.450 --> 00:01:23.930
to spin this one around
00:01:23.930 --> 00:01:26.980
they might actually repel each other.
00:01:26.980 --> 00:01:29.250
And this notion of the orientation
00:01:29.250 --> 00:01:32.410
that there might be some
polarity made it more than just
00:01:32.410 --> 00:01:34.710
an interesting thing to observe,
00:01:34.710 --> 00:01:37.410
an Ancient Han China
roughly 2000 years ago
00:01:37.410 --> 00:01:40.280
they invented the first
compass, where they realized
00:01:40.280 --> 00:01:44.740
that if you took some magnetized magnetite
00:01:44.740 --> 00:01:47.690
which the historical
name for it a lodestone,
00:01:47.690 --> 00:01:49.420
and you allow it to freely move
00:01:49.420 --> 00:01:52.230
and you could do that by
either hanging it from a string
00:01:52.230 --> 00:01:55.290
or have it float on some
still water say in bucket,
00:01:55.290 --> 00:01:58.150
that it will consistently orient itself,
00:01:58.150 --> 00:02:00.370
so that it points in the same direction.
00:02:00.370 --> 00:02:02.950
And so you can use that
for things like navigation
00:02:02.950 --> 00:02:06.460
which the Chinese did
roughly a 1000 years ago,
00:02:06.460 --> 00:02:09.850
and that helped us realize
that the Earth itself is acting
00:02:09.850 --> 00:02:11.410
as a magnet,
00:02:11.410 --> 00:02:15.790
and just like a small magnet
has different sides to it,
00:02:15.790 --> 00:02:18.050
the Earth does too and
that's where the convention
00:02:18.050 --> 00:02:22.220
for a North and South Pole
of a magnet came from.
00:02:22.220 --> 00:02:24.010
But there's probably a
question in your mind
00:02:24.010 --> 00:02:26.420
from the first time that
you noticed a magnet.
00:02:26.420 --> 00:02:29.220
If you have some piece of metal out here,
00:02:29.220 --> 00:02:31.230
that's not touching the magnet
00:02:31.230 --> 00:02:33.020
and in a future video we can even talk
00:02:33.020 --> 00:02:35.950
what touching even means at
a microphone scopic level,
00:02:35.950 --> 00:02:38.840
but if you have a nail out
here that's not touching it,
00:02:38.840 --> 00:02:40.530
but there's some force that's acting
00:02:40.530 --> 00:02:42.840
at a distance on that nail,
00:02:42.840 --> 00:02:46.210
how does that nail know to be
pulled towards that magnet?
00:02:46.210 --> 00:02:48.330
It doesn't have eyes,
it doesn't have ears,
00:02:48.330 --> 00:02:49.420
it doesn't say that there's a magnet
00:02:49.420 --> 00:02:53.070
there I better somehow
move myself towards it.
00:02:53.070 --> 00:02:54.490
There's something about that region
00:02:54.490 --> 00:02:58.220
of space that is
interacting with that nail.
00:02:58.220 --> 00:03:00.000
Or if you think about magnets,
00:03:00.000 --> 00:03:01.670
how does it know the orientation
00:03:01.670 --> 00:03:04.870
of the other magnet to
either be attracted to it
00:03:04.870 --> 00:03:05.703
or repel it?
00:03:05.703 --> 00:03:07.770
How does it even know that
other magnet is there?
00:03:07.770 --> 00:03:11.860
And that's where the concept
of a magnetic field is useful.
00:03:11.860 --> 00:03:14.370
And this was introduced by Michael Faraday
00:03:14.370 --> 00:03:16.520
in the 19th century,
00:03:16.520 --> 00:03:18.180
as a way of at least thinking
00:03:18.180 --> 00:03:21.720
about giving us a framework
for this force at a distance.
00:03:21.720 --> 00:03:24.710
It doesn't exactly tell us what it is,
00:03:24.710 --> 00:03:27.950
but it does gives us a way
of predicting and thinking
00:03:27.950 --> 00:03:30.210
about what is happening.
00:03:30.210 --> 00:03:34.010
And one way to visualize a magnetic field,
00:03:34.010 --> 00:03:38.700
is to take a bar magnet or I
could even say a bar lodestone,
00:03:38.700 --> 00:03:41.300
and put it underneath a piece of paper,
00:03:41.300 --> 00:03:44.750
and then putting metal
filings on top of that piece
00:03:44.750 --> 00:03:47.070
of paper, and you will
see something like this,
00:03:47.070 --> 00:03:50.340
in fact I encourage you to do
this to observe this yourself,
00:03:50.340 --> 00:03:52.150
and you see what look like lines
00:03:52.150 --> 00:03:54.753
that are essentially connecting the North
00:03:54.753 --> 00:03:57.870
and South Poles like that.
00:03:57.870 --> 00:03:59.850
And this notion of field lines we can draw
00:03:59.850 --> 00:04:02.870
it a little bit clearer
in something like this,
00:04:02.870 --> 00:04:05.300
was introduced by Michael
Faraday and he says okay
00:04:05.300 --> 00:04:07.530
there's this thing called a field,
00:04:07.530 --> 00:04:11.560
that tells us for every point
in space around the magnet,
00:04:11.560 --> 00:04:14.270
what it would do to
something that is interactive
00:04:14.270 --> 00:04:17.210
with the magnet another magnet
or maybe a piece of metal,
00:04:17.210 --> 00:04:22.210
so for example, if you were to
put a small bar magnet right
00:04:22.830 --> 00:04:26.920
over here, the North side
is going to be repelled
00:04:26.920 --> 00:04:29.400
from the North side of
this bigger bar magnet,
00:04:29.400 --> 00:04:32.500
and the South side is going
to be attracted to it,
00:04:32.500 --> 00:04:35.470
and so what you could do is
you could put a freely moving,
00:04:35.470 --> 00:04:37.540
magnet or you could put a compass,
00:04:37.540 --> 00:04:40.050
to actually see what the orientation is
00:04:40.050 --> 00:04:42.080
which direction will accomplish point,
00:04:42.080 --> 00:04:44.930
and it will point in the
direction of these field lines,
00:04:44.930 --> 00:04:47.110
and if you were to put it over here,
00:04:47.110 --> 00:04:49.670
it would orient this way if
you allow it to freely move,
00:04:49.670 --> 00:04:51.060
where this is the Northern end,
00:04:51.060 --> 00:04:52.250
and this is the Southern end,
00:04:52.250 --> 00:04:53.660
and if you were to put it here
00:04:53.660 --> 00:04:55.850
and you were allow it to
freely move let's say as part
00:04:55.850 --> 00:04:56.683
of a compass,
00:04:56.683 --> 00:04:58.620
and if this is the Northern end
00:04:58.620 --> 00:04:59.730
and this is the Southern end,
00:04:59.730 --> 00:05:01.220
it would orient like that.
00:05:01.220 --> 00:05:03.320
And so that helps you draw the field lines
00:05:03.320 --> 00:05:04.780
and also know the direction.
00:05:04.780 --> 00:05:07.760
And just by convention the
direction is where coming
00:05:07.760 --> 00:05:10.600
from the North Pole into the South Pole.
00:05:10.600 --> 00:05:13.130
And what Faraday said is not only does
00:05:13.130 --> 00:05:15.610
this tell you the direction
of the magnetic field,
00:05:15.610 --> 00:05:17.300
it tells you the magnitude based
00:05:17.300 --> 00:05:19.380
on the density of these field lines.
00:05:19.380 --> 00:05:23.480
So for example, the magnetic
field is stronger here,
00:05:23.480 --> 00:05:25.040
where in that unit area
00:05:25.040 --> 00:05:27.690
that I just made you have
very dense field lines,
00:05:27.690 --> 00:05:30.910
while it would be weaker right over here,
00:05:30.910 --> 00:05:32.800
I have fewer field lines.
00:05:32.800 --> 00:05:35.030
Now another amazing thing about magnets
00:05:35.030 --> 00:05:36.060
and their polarity
00:05:36.060 --> 00:05:38.650
that people have noticed
since ancient times is,
00:05:38.650 --> 00:05:41.490
you would think at least initially,
00:05:41.490 --> 00:05:44.810
that if this has a North
Pole and a South Pole,
00:05:44.810 --> 00:05:46.780
then maybe you could
separate these two things,
00:05:46.780 --> 00:05:48.680
maybe if you were to break this in half,
00:05:48.680 --> 00:05:51.380
then you could have a
pure North Pole magnet
00:05:51.380 --> 00:05:54.120
and you could have a
pure South Pole magnet,
00:05:54.120 --> 00:05:57.040
but that's not what happens
when you break this in half,
00:05:57.040 --> 00:06:02.040
instead you have two magnets
each with their own North
00:06:02.870 --> 00:06:05.840
and South Poles, and then
you can keep doing this,
00:06:05.840 --> 00:06:08.100
and early scientists just
kept doing it and said
00:06:08.100 --> 00:06:09.380
there might not be any limit
00:06:09.380 --> 00:06:11.220
to how much you can cut this obviously,
00:06:11.220 --> 00:06:13.770
when you keep cutting
and cannot cut any more
00:06:13.770 --> 00:06:15.330
while retaining the properties
00:06:15.330 --> 00:06:18.770
of the magnetite you're getting
down to the molecular level,
00:06:18.770 --> 00:06:20.670
and in future videos
we'll think about how even
00:06:20.670 --> 00:06:25.490
at a molecular level you can
still have a little tiny magnet
00:06:25.490 --> 00:06:28.470
that has a polarity to it.
00:06:28.470 --> 00:06:30.290
Now another really interesting thing
00:06:30.290 --> 00:06:32.220
about magnets is this connection
00:06:32.220 --> 00:06:35.750
between magnetism and electricity.
00:06:35.750 --> 00:06:37.110
People have also observed
00:06:37.110 --> 00:06:40.520
that if you took a current carrying wire
00:06:40.520 --> 00:06:42.130
and the current is going from the positive
00:06:42.130 --> 00:06:47.130
to the negative end so it
is going in this direction,
00:06:47.170 --> 00:06:48.003
and if you make it go
00:06:48.003 --> 00:06:50.680
through a piece of paper
that has metal filings,
00:06:50.680 --> 00:06:54.520
it looks like field
lines are forming here,
00:06:54.520 --> 00:06:57.670
magnetic field lines, it
turns out it does interact
00:06:57.670 --> 00:06:59.770
with the types of things
that tend to interact
00:06:59.770 --> 00:07:01.580
it will interact with magnets
00:07:01.580 --> 00:07:04.810
and so this is a magnetic
field that is being formed
00:07:04.810 --> 00:07:06.640
by an electrical current,
00:07:06.640 --> 00:07:09.970
and so that was the major
clue that the phenomena
00:07:09.970 --> 00:07:13.750
of electricity and magnetism
are in fact related,
00:07:13.750 --> 00:07:15.800
and this relationship is what allows us
00:07:15.800 --> 00:07:18.500
to do things like have electric motors,
00:07:18.500 --> 00:07:23.500
or generate electricity
from wind or water turbines,
00:07:23.600 --> 00:07:25.160
and it's out of the scope of this video
00:07:25.160 --> 00:07:26.830
but I'll give you a little bit of a clue
00:07:26.830 --> 00:07:29.050
of how these things are connected.
00:07:29.050 --> 00:07:31.280
We know that things
they're made up of atoms
00:07:31.280 --> 00:07:34.960
which are made up of particles
like electrons and protons,
00:07:34.960 --> 00:07:37.600
which are charged and
we know that a current,
00:07:37.600 --> 00:07:40.240
an electric current is
based on the movement
00:07:40.240 --> 00:07:42.070
of charged particles,
00:07:42.070 --> 00:07:44.880
that when something is not magnetic,
00:07:44.880 --> 00:07:47.810
say a non-magnetic piece of magnetite,
00:07:47.810 --> 00:07:50.990
all of those charges are
moving more chaotically,
00:07:50.990 --> 00:07:52.670
but if something happens to it,
00:07:52.670 --> 00:07:54.070
maybe a lightning strike,
00:07:54.070 --> 00:07:57.170
it can align how they
move so that they act
00:07:57.170 --> 00:08:01.240
in concert to have a more
coherent magnetic field.
00:08:01.240 --> 00:08:03.760
So leave I'll there I'm
already getting a little bit,
00:08:03.760 --> 00:08:05.600
ahead of our skis so to speak,
00:08:05.600 --> 00:08:08.350
but I do think it's really
interesting to appreciate
00:08:08.350 --> 00:08:10.630
how all of these puzzle pieces that we see
00:08:10.630 --> 00:08:12.393
in nature, fit together.
|
Introduction to Momentum | https://www.youtube.com/watch?v=iptKZt4FHRo | vtt | https://www.youtube.com/api/timedtext?v=iptKZt4FHRo&ei=6VWUZfaAGqiJp-oPgcKYgAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=992F0A39974D5BA45BA194BF93338D1D85FD56E2.C4603B0C8832DEC6AF026D77B4BA92995BA797F2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.290 --> 00:00:01.123
- [Instructor] In this video,
00:00:01.123 --> 00:00:04.060
we're going to talk a
little bit about momentum.
00:00:04.060 --> 00:00:05.150
And I encourage you to think about
00:00:05.150 --> 00:00:07.780
what does momentum mean
in everyday language.
00:00:07.780 --> 00:00:12.290
If I were to tell you that a
business has a lot of momentum,
00:00:12.290 --> 00:00:14.050
many people would imagine that means
00:00:14.050 --> 00:00:15.520
that it's doing really well,
00:00:15.520 --> 00:00:18.650
it's hard to stop that
business from succeeding.
00:00:18.650 --> 00:00:20.520
If I were to tell you that,
00:00:20.520 --> 00:00:23.330
and let's say a movie star
has a lot of momentum,
00:00:23.330 --> 00:00:25.040
it means that they keep making really,
00:00:25.040 --> 00:00:26.220
really, really good movies,
00:00:26.220 --> 00:00:27.740
it's hard to stop them.
00:00:27.740 --> 00:00:31.150
And in physics, momentum
essentially has that same notion.
00:00:31.150 --> 00:00:34.100
In fact, these everyday
language versions of momentum
00:00:34.100 --> 00:00:36.920
really came from the
physics version of it,
00:00:36.920 --> 00:00:39.860
and an informal definition
you could think of it is
00:00:39.860 --> 00:00:44.860
how hard to stop something.
00:00:45.140 --> 00:00:47.050
Stop something.
00:00:47.050 --> 00:00:48.990
So with that very informal definition,
00:00:48.990 --> 00:00:51.650
we'll get a little bit more
mathy in a few seconds.
00:00:51.650 --> 00:00:53.300
I have two pictures here.
00:00:53.300 --> 00:00:56.920
And let's say both of these vehicles,
00:00:56.920 --> 00:00:59.000
so we have a big 18-wheeler truck here,
00:00:59.000 --> 00:01:01.020
and here we have a Formula One car.
00:01:01.020 --> 00:01:05.170
Let's say that they both have a velocity
00:01:05.170 --> 00:01:08.313
of 20 meters per second.
00:01:09.260 --> 00:01:10.690
Positive 20 meters per second.
00:01:10.690 --> 00:01:12.110
We'll just think in one dimension.
00:01:12.110 --> 00:01:13.410
So let's say it's going to the right
00:01:13.410 --> 00:01:14.660
at 20 meters per second,
00:01:14.660 --> 00:01:17.010
so that's a magnitude and a direction.
00:01:17.010 --> 00:01:18.810
Okay, I could put a positive
here to make it clear
00:01:18.810 --> 00:01:20.680
that I'm giving a direction here.
00:01:20.680 --> 00:01:23.800
So they're both going in
the positive direction
00:01:23.800 --> 00:01:26.500
at 20 meters per second.
00:01:26.500 --> 00:01:29.740
But you can imagine their
masses are very different.
00:01:29.740 --> 00:01:32.120
This large truck would have a mass
00:01:32.120 --> 00:01:37.050
of let's just say 30,000 kilograms.
00:01:37.050 --> 00:01:40.100
That's roughly actually what
an 18-wheeler truck's mass is,
00:01:40.100 --> 00:01:41.490
I looked it up before this video.
00:01:41.490 --> 00:01:42.520
And let's say the mass
00:01:42.520 --> 00:01:46.727
of this Formula One car
is about 1,000 kilograms.
00:01:48.220 --> 00:01:49.730
Now pause this video and think about
00:01:49.730 --> 00:01:53.663
which one do you think
would have more momentum.
00:01:55.660 --> 00:01:57.890
All right, well, you're
probably imagining trying
00:01:57.890 --> 00:01:59.040
to stop either of these,
00:01:59.040 --> 00:02:03.030
and I guess either of these
would be difficult to stop,
00:02:03.030 --> 00:02:07.170
but a truck going at 20 meters
per second seems a lot harder
00:02:07.170 --> 00:02:08.820
than the Formula One car.
00:02:08.820 --> 00:02:10.510
This thing seems like
it would just be able
00:02:10.510 --> 00:02:12.810
to drive through anything.
00:02:12.810 --> 00:02:15.080
So if you picked the truck
having a higher momentum
00:02:15.080 --> 00:02:17.950
when it's going at the same
velocity as a Formula One car,
00:02:17.950 --> 00:02:19.340
you'd be right.
00:02:19.340 --> 00:02:20.490
But an interesting question is well,
00:02:20.490 --> 00:02:22.550
how can I quantify that?
00:02:22.550 --> 00:02:25.330
And that's where we have
the mathematical definition
00:02:25.330 --> 00:02:29.490
of momentum, and momentum is defined
00:02:29.490 --> 00:02:34.463
as mass times velocity.
00:02:35.680 --> 00:02:38.420
And because velocity is a vector,
00:02:38.420 --> 00:02:39.590
it's not just a magnitude,
00:02:39.590 --> 00:02:40.550
we assigned a direction,
00:02:40.550 --> 00:02:42.060
so we said in the positive direction.
00:02:42.060 --> 00:02:42.893
If we were in one dimension,
00:02:42.893 --> 00:02:44.040
if we said in the negative direction,
00:02:44.040 --> 00:02:45.130
we'd be going to the left.
00:02:45.130 --> 00:02:46.940
That's maybe the convention we could use.
00:02:46.940 --> 00:02:50.200
And since it's a scalar, which is mass,
00:02:50.200 --> 00:02:53.340
times a vector, momentum is
also going to be a vector.
00:02:53.340 --> 00:02:57.360
You're going to have a momentum
in a certain direction.
00:02:57.360 --> 00:02:58.670
So pause this video and see
00:02:58.670 --> 00:03:00.180
if you can calculate the momentum
00:03:00.180 --> 00:03:01.800
for each of these vehicles.
00:03:01.800 --> 00:03:03.070
And see also if you can figure out
00:03:03.070 --> 00:03:04.620
what the units are going to be.
00:03:05.770 --> 00:03:07.640
All right, now let's
think about the momentum
00:03:07.640 --> 00:03:09.060
for this 18 wheeler.
00:03:09.060 --> 00:03:11.700
It is going to be its mass,
00:03:11.700 --> 00:03:16.320
which is 30,000 kilograms,
00:03:16.320 --> 00:03:17.990
times its velocity,
00:03:17.990 --> 00:03:22.370
which is positive 20 meters per second.
00:03:22.370 --> 00:03:24.820
And so when I multiply those two things,
00:03:24.820 --> 00:03:25.940
I am going to get,
00:03:25.940 --> 00:03:27.410
let's see, I'm going to get a six
00:03:27.410 --> 00:03:30.590
with one, two, three, four, five zeros.
00:03:30.590 --> 00:03:34.510
One, two, three, four, five zeros.
00:03:34.510 --> 00:03:37.400
600,000, and then the units are
00:03:37.400 --> 00:03:40.080
kilogram times meter per second.
00:03:40.080 --> 00:03:43.890
Kilogram meter per second.
00:03:46.530 --> 00:03:48.470
That's the momentum of the truck.
00:03:48.470 --> 00:03:50.040
Now what about the Formula One car?
00:03:50.040 --> 00:03:53.300
Pause the video and try to
calculate that momentum.
00:03:53.300 --> 00:03:55.100
All right, well, same notion.
00:03:55.100 --> 00:03:56.850
I'll have to squeeze
it in right over here.
00:03:56.850 --> 00:04:01.373
The momentum here is the
mass, 1,000 kilograms.
00:04:02.870 --> 00:04:06.140
1,000 kilograms
00:04:06.140 --> 00:04:07.670
times the velocity,
00:04:07.670 --> 00:04:10.560
positive 20 meters per second.
00:04:10.560 --> 00:04:12.630
I'm stressing the positive
because we're in one dimension,
00:04:12.630 --> 00:04:14.120
and I'm saying positive is one direction,
00:04:14.120 --> 00:04:15.130
negative is the other direction.
00:04:15.130 --> 00:04:16.800
So I am giving it a direction here.
00:04:16.800 --> 00:04:20.940
And so this momentum
is going to be equal to
00:04:20.940 --> 00:04:25.883
20,000 kilogram meters per second.
00:04:28.300 --> 00:04:30.620
Kilogram meters per second.
00:04:30.620 --> 00:04:33.110
And so when you evaluate the momentums,
00:04:33.110 --> 00:04:35.050
it's clear mathematically
00:04:35.050 --> 00:04:38.010
that the truck has much more momentum
00:04:38.010 --> 00:04:40.180
than this Formula One car.
00:04:40.180 --> 00:04:43.350
It has 30 times the momentum.
00:04:43.350 --> 00:04:45.480
Now I know what some
of y'all are thinking.
00:04:45.480 --> 00:04:47.230
Well, this is just from
the reference frame
00:04:47.230 --> 00:04:49.440
if I'm standing still on the ground
00:04:49.440 --> 00:04:52.490
while this truck and car are moving by.
00:04:52.490 --> 00:04:54.540
But what if I were moving along with them?
00:04:54.540 --> 00:04:56.690
Would they have the same momentum?
00:04:56.690 --> 00:04:58.780
And if you were asking that question,
00:04:58.780 --> 00:04:59.613
it's a very good one,
00:04:59.613 --> 00:05:00.490
and the answer is no,
00:05:00.490 --> 00:05:03.570
the momentum depends on
the frame of reference.
00:05:03.570 --> 00:05:04.870
So let's say that you are able
00:05:04.870 --> 00:05:07.100
to travel very quickly in,
00:05:07.100 --> 00:05:09.460
well, let's say you're in a car here.
00:05:09.460 --> 00:05:14.460
And you're also going at
positive 20 meters per second,
00:05:14.560 --> 00:05:17.030
so you're going in the same
direction as the truck.
00:05:17.030 --> 00:05:18.860
Well, relative to you,
00:05:18.860 --> 00:05:21.830
the truck's velocity is now zero.
00:05:21.830 --> 00:05:24.010
So from your frame of reference,
00:05:24.010 --> 00:05:25.610
if you wanted to calculate momentum,
00:05:25.610 --> 00:05:28.470
you'd have the mass of the
truck, 30,000 kilograms.
00:05:28.470 --> 00:05:29.960
But from your frame of reference,
00:05:29.960 --> 00:05:32.350
the velocity would now be zero.
00:05:32.350 --> 00:05:35.720
So if you're traveling in
this car at the same velocity
00:05:35.720 --> 00:05:40.650
as that truck, the momentum
you would calculate is zero.
00:05:40.650 --> 00:05:42.740
Now, what would then have momentum?
00:05:42.740 --> 00:05:43.810
Well, in that world,
00:05:43.810 --> 00:05:47.770
let's say that there's a
big rock over here that,
00:05:47.770 --> 00:05:52.700
let's say this thing's 100,000 kilograms.
00:05:52.700 --> 00:05:54.460
Well, when you are standing on the ground,
00:05:54.460 --> 00:05:56.030
that thing would have no momentum,
00:05:56.030 --> 00:05:58.540
but now that you're moving
20 meters per second
00:05:58.540 --> 00:06:01.470
to the right, positive
20 meters per second,
00:06:01.470 --> 00:06:04.400
the rock in your frame of
reference would look like
00:06:04.400 --> 00:06:06.780
it's going at negative
20 meters per second.
00:06:06.780 --> 00:06:09.550
It would look like it's
going 20 meters per second
00:06:09.550 --> 00:06:10.900
to the left.
00:06:10.900 --> 00:06:13.370
And so this would now, if you're moving
00:06:13.370 --> 00:06:15.870
in the same frame of
reference as that truck,
00:06:15.870 --> 00:06:17.600
this rock would then look like
00:06:17.600 --> 00:06:19.860
it has a very negative momentum,
00:06:19.860 --> 00:06:22.430
and I encourage you to
calculate it if you like.
00:06:22.430 --> 00:06:23.600
But I'll leave you there.
00:06:23.600 --> 00:06:26.060
This is really just an
introduction to momentum.
00:06:26.060 --> 00:06:27.800
But once you get an intuition for it,
00:06:27.800 --> 00:06:30.310
all sorts of interesting
things in physics start
00:06:30.310 --> 00:06:31.483
to emerge from it.
|
Systems and Objects | https://www.youtube.com/watch?v=WLoBo-enxAw | vtt | https://www.youtube.com/api/timedtext?v=WLoBo-enxAw&ei=6VWUZcCKJcaJmLAPssudkAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2B6DE7F55712906CF654469963129380556807EB.051A586DC272E86F6CE4C1A805031364C847A5E8&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.190 --> 00:00:02.650
- [Instructor] Our world is
extraordinarily complicated.
00:00:02.650 --> 00:00:06.060
So in physics we're going to
have to make simplifications.
00:00:06.060 --> 00:00:08.110
Even things in our world that seems simple
00:00:08.110 --> 00:00:09.550
are extraordinarily complicated.
00:00:09.550 --> 00:00:12.720
So consider a basketball
seems simple enough,
00:00:12.720 --> 00:00:15.810
but it's composed of an
extraordinarily large number
00:00:15.810 --> 00:00:19.300
of air molecules bouncing
around inside, colliding
00:00:19.300 --> 00:00:22.080
with the outside leather
and rubber membrane,
00:00:22.080 --> 00:00:26.800
which itself is composed of an
extraordinarily large number
00:00:26.800 --> 00:00:29.470
of atoms and molecules all bonded together
00:00:29.470 --> 00:00:32.020
holding on tight, trying
to prevent themselves
00:00:32.020 --> 00:00:35.990
from being ripped apart and
exploded by the pressure inside.
00:00:35.990 --> 00:00:39.490
So do we have to keep track
of every atom and molecule
00:00:39.490 --> 00:00:42.770
in this ball to include
it in a physics problem?
00:00:42.770 --> 00:00:45.390
Typically not, nor would
we ever really want to.
00:00:45.390 --> 00:00:48.430
I mean, we can't keep track
of all that info, not yet,
00:00:48.430 --> 00:00:50.120
nor would you want to for most scenarios.
00:00:50.120 --> 00:00:52.500
So for instance, if you were an astronaut,
00:00:52.500 --> 00:00:53.670
you went to the moon,
00:00:53.670 --> 00:00:56.120
you took your basketball and
you were going to drop it.
00:00:56.120 --> 00:00:58.650
If all you wanted to know
was how long it's gonna take
00:00:58.650 --> 00:01:01.980
for this ball to strike
the lunar surface below,
00:01:01.980 --> 00:01:04.270
you don't need to know
about the ideal gas law,
00:01:04.270 --> 00:01:06.880
you don't need to know about
the structural integrity
00:01:06.880 --> 00:01:09.310
of the rubber leather membrane.
00:01:09.310 --> 00:01:11.180
You could solve this by
treating the basketball
00:01:11.180 --> 00:01:13.350
as if there was no internal
structure whatsoever.
00:01:13.350 --> 00:01:14.960
Like you were dropping a rock that had
00:01:14.960 --> 00:01:18.600
no interesting internal
structure whatsoever.
00:01:18.600 --> 00:01:21.250
So in physics, the good
news is we can typically get
00:01:21.250 --> 00:01:23.070
away with making a lot of simplifications
00:01:23.070 --> 00:01:24.980
and ignoring the internal structure
00:01:24.980 --> 00:01:27.820
if it isn't relevant to the
problem that we're asking.
00:01:27.820 --> 00:01:30.150
Sometimes it will be relevant though.
00:01:30.150 --> 00:01:32.590
So here was a case where
it wasn't relevant.
00:01:32.590 --> 00:01:34.240
The internal structure wasn't relevant.
00:01:34.240 --> 00:01:36.170
So we could ignore that
internal structure,
00:01:36.170 --> 00:01:38.660
but other questions like
if you were an astronaut,
00:01:38.660 --> 00:01:40.300
I mean if I was an
astronaut, and I was bringing
00:01:40.300 --> 00:01:42.870
my basketball to the moon,
I'd be like, wait a minute,
00:01:42.870 --> 00:01:44.570
there's no atmosphere on the moon.
00:01:44.570 --> 00:01:48.080
That means there is no pressure
pushing in from the outside.
00:01:48.080 --> 00:01:49.980
That means all this air
pressure's still pushing
00:01:49.980 --> 00:01:53.950
out from the inside is my
basketball just gonna explode?
00:01:53.950 --> 00:01:55.500
I'd want to know this before
I brought it out there.
00:01:55.500 --> 00:01:57.170
I don't wanna carry a little bomb out
00:01:57.170 --> 00:01:59.020
that's going to like blow up in my face
00:01:59.020 --> 00:02:00.630
and I don't want to lose a basketball.
00:02:00.630 --> 00:02:02.050
If you wanted to know if your basketball
00:02:02.050 --> 00:02:04.150
was going to explode,
okay now it does depend.
00:02:04.150 --> 00:02:07.140
That question does depend
on the internal structure.
00:02:07.140 --> 00:02:08.570
It depends on the pressure inside
00:02:08.570 --> 00:02:09.800
which is fundamentally related
00:02:09.800 --> 00:02:14.030
to the force of the collisions
between these air molecules
00:02:14.030 --> 00:02:17.690
and the rubber membrane and
then it depends also on,
00:02:17.690 --> 00:02:20.360
well, how strong are the bonds
between these rubber membrane
00:02:20.360 --> 00:02:21.800
and leather molecules?
00:02:21.800 --> 00:02:25.270
How much force can they
withstand before they burst?
00:02:25.270 --> 00:02:27.060
For that question you
would have to consider
00:02:27.060 --> 00:02:28.690
the internal structure.
00:02:28.690 --> 00:02:30.920
So, in some questions you get to ignore
00:02:30.920 --> 00:02:33.370
the internal structure and
other questions you don't.
00:02:33.370 --> 00:02:35.880
It's just context and question-dependent
00:02:35.880 --> 00:02:38.300
and in physics, we have
terminology to sort of
00:02:38.300 --> 00:02:41.270
sort this out and the
terminology we use is the idea
00:02:41.270 --> 00:02:43.240
of a system or the idea of an object.
00:02:43.240 --> 00:02:45.650
So the idea of a system
is just a collection
00:02:45.650 --> 00:02:49.430
of objects, that's the definition
of a system in physics.
00:02:49.430 --> 00:02:50.670
But that begs the question,
00:02:50.670 --> 00:02:52.680
well what do we mean by an object?
00:02:52.680 --> 00:02:55.330
By an object, we mean
anything that you could treat
00:02:55.330 --> 00:02:58.260
as if it had no internal structure.
00:02:58.260 --> 00:03:01.180
We don't mean that objects
have no internal structure.
00:03:01.180 --> 00:03:04.870
They typically do, the only
things that don't truly
00:03:04.870 --> 00:03:06.720
have an internal structures
as far as we know
00:03:06.720 --> 00:03:10.830
are truly fundamental particles
like electrons or neutrinos,
00:03:10.830 --> 00:03:13.510
these fundamental particles
in particle physics
00:03:13.510 --> 00:03:15.950
that as far as we know,
have no internal structure.
00:03:15.950 --> 00:03:18.190
So unless you're doing particle physics,
00:03:18.190 --> 00:03:20.340
you're probably don't have a true object,
00:03:20.340 --> 00:03:22.290
but you can treat things like an object.
00:03:22.290 --> 00:03:24.420
We can treat this
basketball like an object.
00:03:24.420 --> 00:03:26.510
That is to say, we can act as if it has
00:03:26.510 --> 00:03:29.210
no internal structure if
that internal structure
00:03:29.210 --> 00:03:30.690
isn't relevant to the problem.
00:03:30.690 --> 00:03:34.170
So to make this a little more meaningful
00:03:34.170 --> 00:03:35.490
just imagine another example.
00:03:35.490 --> 00:03:40.490
Say you collide two objects
so you collide a putty here.
00:03:40.590 --> 00:03:43.600
Let's say this is three kilogram object
00:03:43.600 --> 00:03:45.300
and it comes in with a certain speed
00:03:45.300 --> 00:03:49.070
and it collides with a
five kilogram object.
00:03:49.070 --> 00:03:52.050
If all you want to know is
when they stick together,
00:03:52.050 --> 00:03:54.160
say these stick together and move off
00:03:54.160 --> 00:03:55.830
with some common speed.
00:03:55.830 --> 00:03:57.950
If all you want to know is
what is that common speed
00:03:57.950 --> 00:04:00.690
that they move off with
after they stick together?
00:04:00.690 --> 00:04:02.050
Notice what you don't need to know.
00:04:02.050 --> 00:04:03.700
I don't need to tell
you that this was made
00:04:03.700 --> 00:04:07.170
out of gold here or that this
one was made out of copper
00:04:07.170 --> 00:04:08.460
as long as you know, the masses and that
00:04:08.460 --> 00:04:10.290
they stick together,
physics will let you solve
00:04:10.290 --> 00:04:13.440
for how fast they'll move off
with a common speed afterward
00:04:13.440 --> 00:04:15.380
if you tell me that they stick together.
00:04:15.380 --> 00:04:17.230
So if that's all you want to know
00:04:17.230 --> 00:04:19.710
doesn't matter what the
internal structure is.
00:04:19.710 --> 00:04:22.070
However, for other questions,
if you wanted to know
00:04:22.070 --> 00:04:25.690
if this was going to set off
some nuclear explosion, okay
00:04:25.690 --> 00:04:28.980
well then it really is going
to matter if these are made
00:04:28.980 --> 00:04:32.320
out of gold, made out of
copper, made out of clay
00:04:32.320 --> 00:04:34.610
or if they're made out
of uranium, so to speak.
00:04:34.610 --> 00:04:37.070
So for that question, you do need to know
00:04:37.070 --> 00:04:38.680
about the internal structure.
00:04:38.680 --> 00:04:40.040
So the idea of a system and the idea
00:04:40.040 --> 00:04:42.580
of an object is an
important one in physics
00:04:42.580 --> 00:04:46.240
and it's not just important
conceptually or abstractly
00:04:46.240 --> 00:04:48.210
it can actually help
you in problem solving.
00:04:48.210 --> 00:04:51.350
So let me show you a more
like, tangible example
00:04:51.350 --> 00:04:52.400
of where this might help you
00:04:52.400 --> 00:04:55.150
in solving a problem you might encounter
00:04:55.150 --> 00:04:56.420
in your physics courses.
00:04:56.420 --> 00:04:58.540
So let's say they're two boxes
00:04:58.540 --> 00:05:00.650
and they're just too big
and unwieldy to handle.
00:05:00.650 --> 00:05:02.350
So you're going to push
them across the floor.
00:05:02.350 --> 00:05:05.190
They're not heavy, they're just
like shaped weird, let's say
00:05:05.190 --> 00:05:07.640
and let's say the floor
has been newly waxed.
00:05:07.640 --> 00:05:09.980
So it's real slick against these boxes
00:05:09.980 --> 00:05:12.650
which are also slick and
there's negligible friction.
00:05:12.650 --> 00:05:14.360
You could ignore the
friction between the boxes
00:05:14.360 --> 00:05:16.220
and the floor, so let's say you come up
00:05:16.220 --> 00:05:17.730
and you're gonna push on these things.
00:05:17.730 --> 00:05:19.570
Push them into the
corner of some warehouse,
00:05:19.570 --> 00:05:22.060
you're working in the
warehouse here, earning
00:05:22.060 --> 00:05:23.610
your pay for the day
and you're going to go
00:05:23.610 --> 00:05:25.890
push these over here and
you're going to exert,
00:05:25.890 --> 00:05:28.310
let's just say nine newtons of force
00:05:28.310 --> 00:05:30.680
on this one kilogram
box and then that pushes
00:05:30.680 --> 00:05:31.930
into the two kilogram box
00:05:31.930 --> 00:05:33.470
and they move off to the right.
00:05:33.470 --> 00:05:35.270
So can we treat this system
00:05:35.270 --> 00:05:37.400
of boxes as if it were a single object?
00:05:37.400 --> 00:05:39.570
Well, like we said,
it's question-dependent.
00:05:39.570 --> 00:05:43.040
If the question we want to ask
is, what's the acceleration
00:05:43.040 --> 00:05:45.630
of these boxes as they slide to the right?
00:05:45.630 --> 00:05:47.560
Well, they're going to
move at the same rate
00:05:47.560 --> 00:05:49.740
because as you push on
this one kilogram box
00:05:49.740 --> 00:05:52.610
that one kilogram box pushes
on the two kilogram box
00:05:52.610 --> 00:05:53.770
and they're going to move together.
00:05:53.770 --> 00:05:57.020
As I keep pushing with nine
newtons, the velocity of both
00:05:57.020 --> 00:05:59.200
of these boxes are going
to be the same to the right
00:05:59.200 --> 00:06:00.790
and the acceleration of the boxes
00:06:00.790 --> 00:06:01.900
are going to be the same to the right.
00:06:01.900 --> 00:06:03.660
They're never going to become separated.
00:06:03.660 --> 00:06:06.060
What that means is the fact
that there were two boxes
00:06:06.060 --> 00:06:09.050
didn't matter, I can treat
this system of two boxes
00:06:09.050 --> 00:06:12.840
as if it were a single three kilogram box.
00:06:12.840 --> 00:06:14.240
I don't even need to know
that they were actually
00:06:14.240 --> 00:06:16.330
a division here, 'cause
they're never going to become
00:06:16.330 --> 00:06:18.960
separated for this question
that I'm asking here.
00:06:18.960 --> 00:06:20.520
So I could treat this whole system
00:06:20.520 --> 00:06:24.330
as if it were just one
big three kilogram object
00:06:24.330 --> 00:06:26.460
and this is an important idea.
00:06:26.460 --> 00:06:28.080
The properties of a system,
00:06:28.080 --> 00:06:30.660
like the mass of the
system, are determined
00:06:30.660 --> 00:06:33.180
by the properties of the
objects in that system.
00:06:33.180 --> 00:06:36.350
So I put a three here and this
is legal, this is allowed.
00:06:36.350 --> 00:06:39.700
The properties of this total
mass of my system is determined
00:06:39.700 --> 00:06:42.080
by the mass of the individual
objects in my system.
00:06:42.080 --> 00:06:44.030
So you really can just add up these masses
00:06:44.030 --> 00:06:47.010
to determine the total mass of the system
00:06:47.010 --> 00:06:49.120
that you're going to be
treating as a single object.
00:06:49.120 --> 00:06:51.210
And now that I get to treat
this as a single object
00:06:51.210 --> 00:06:54.680
I'm in luck, I can use
Newton's second law.
00:06:54.680 --> 00:06:56.470
The acceleration is going
to equal the net force
00:06:56.470 --> 00:06:59.870
over the mass, we'll do this
for the horizontal direction.
00:06:59.870 --> 00:07:01.470
I'm just going to put a mass of three.
00:07:01.470 --> 00:07:04.600
I could ignore the fact
that this was a one and two
00:07:04.600 --> 00:07:06.570
and the total mass of
my system is going to be
00:07:06.570 --> 00:07:09.910
three kilograms and the
only force on my system
00:07:09.910 --> 00:07:11.180
that I'm treating as an object here
00:07:11.180 --> 00:07:12.560
is the nine Newton force.
00:07:12.560 --> 00:07:14.110
I could ignore, in other words,
00:07:14.110 --> 00:07:17.920
I can ignore the internal
forces between these boxes.
00:07:17.920 --> 00:07:19.580
I don't care about the
one pushing on the two
00:07:19.580 --> 00:07:21.820
or the two pushing on the
one I'm treating the system
00:07:21.820 --> 00:07:24.890
like an object and I'm ignoring
that internal structure
00:07:24.890 --> 00:07:26.520
that makes this problem really easy
00:07:26.520 --> 00:07:27.780
when I solve for the acceleration
00:07:27.780 --> 00:07:31.090
I just get three meters
per second squared.
00:07:31.090 --> 00:07:33.330
So for this question I
could treat the system
00:07:33.330 --> 00:07:34.640
as a single object.
00:07:34.640 --> 00:07:37.260
What question would I not
be able to treat the system
00:07:37.260 --> 00:07:38.610
as a single object for?
00:07:38.610 --> 00:07:41.470
Well, if I wanted to know,
let's say the question was
00:07:41.470 --> 00:07:44.270
with how much force does
the one kilogram box exert
00:07:44.270 --> 00:07:46.330
on the two kilogram box?
00:07:46.330 --> 00:07:48.380
And you might think, oh,
it's just nine, but it isn't.
00:07:48.380 --> 00:07:50.420
So stay tuned, hold on.
00:07:50.420 --> 00:07:51.910
It's counterintuitive. I know,
00:07:51.910 --> 00:07:53.590
but the main idea I'm
trying to stress here
00:07:53.590 --> 00:07:58.150
is that this force on two
by one is fundamentally
00:07:58.150 --> 00:08:00.660
a question about an internal force.
00:08:00.660 --> 00:08:02.350
So if the question you're asking is about
00:08:02.350 --> 00:08:04.920
the internal structure,
clearly you're not allowed
00:08:04.920 --> 00:08:07.120
to ignore the internal structure.
00:08:07.120 --> 00:08:10.110
So for this question we
cannot treat the system
00:08:10.110 --> 00:08:13.180
of two boxes as if it were a single mass.
00:08:13.180 --> 00:08:14.980
We'll have to focus on
the internal structure.
00:08:14.980 --> 00:08:18.170
So again, consider this a
one and a two separate boxes
00:08:18.170 --> 00:08:19.530
and we'll do the same formula.
00:08:19.530 --> 00:08:22.910
Acceleration's going to equal
the net force over the mass,
00:08:22.910 --> 00:08:25.700
but this time we do have
to focus on a single mass.
00:08:25.700 --> 00:08:29.870
So we'll focus just on
the two kilogram mass
00:08:29.870 --> 00:08:32.590
the only horizontal force
on this two kilogram mass
00:08:32.590 --> 00:08:34.310
if this really is frictionless
00:08:34.310 --> 00:08:37.860
is this force that we want to
find the force onto by one.
00:08:37.860 --> 00:08:39.470
And that's the only force that's exerted
00:08:39.470 --> 00:08:41.030
on the two kilogram mass.
00:08:41.030 --> 00:08:43.780
This nine newtons is
exerted directly on the one.
00:08:43.780 --> 00:08:45.380
So it's not directly exerted on the two.
00:08:45.380 --> 00:08:46.500
We don't draw that up here.
00:08:46.500 --> 00:08:47.520
We don't include that here.
00:08:47.520 --> 00:08:50.300
These are only forces
directly on the two, and then
00:08:50.300 --> 00:08:52.730
we'd have to put the acceleration
of the two kilogram mass,
00:08:52.730 --> 00:08:55.340
but we already found that this
three was the acceleration
00:08:55.340 --> 00:08:57.590
of the one, the two and the entire system.
00:08:57.590 --> 00:08:59.240
Everything was accelerating
at the same rate.
00:08:59.240 --> 00:09:02.130
So I can put my three meters
per second squared here
00:09:02.130 --> 00:09:04.510
and I find out that the force exerted
00:09:04.510 --> 00:09:08.320
on the two by the one is six newtons.
00:09:08.320 --> 00:09:11.070
So it's not as big and
this isn't surprising.
00:09:11.070 --> 00:09:13.550
It takes more newtons from the left here
00:09:13.550 --> 00:09:16.100
this nine newtons to
accelerate the entire system
00:09:16.100 --> 00:09:18.890
of three kilograms than it does to just
00:09:18.890 --> 00:09:21.080
accelerate the two
kilogram mass over here.
00:09:21.080 --> 00:09:24.300
So the fact that this force
is accelerating less mass
00:09:24.300 --> 00:09:26.030
means it doesn't have to be as big.
00:09:26.030 --> 00:09:28.010
But the key idea is that to find that,
00:09:28.010 --> 00:09:30.410
we could not treat, to
find this force here,
00:09:30.410 --> 00:09:33.640
we could not treat this entire
system as a single mass.
00:09:33.640 --> 00:09:37.550
So recapping, if the question
being asked does not depend
00:09:37.550 --> 00:09:40.190
on the internal structure,
you can simplify your life
00:09:40.190 --> 00:09:42.160
by treating that structure and that system
00:09:42.160 --> 00:09:44.840
as if it were a single
object, in which case,
00:09:44.840 --> 00:09:46.680
the properties of that will be determined
00:09:46.680 --> 00:09:48.920
by the properties of the
objects in that system.
00:09:48.920 --> 00:09:51.590
But if the question being
asked does depend on
00:09:51.590 --> 00:09:53.470
the internal structure,
then you cannot treat
00:09:53.470 --> 00:09:55.420
that system as a single object.
00:09:55.420 --> 00:09:57.953
You will have to focus on
the internal structure.
|
Contact Forces | https://www.youtube.com/watch?v=BtQnTyGq4sI | vtt | https://www.youtube.com/api/timedtext?v=BtQnTyGq4sI&ei=6VWUZcO6IP2VvdIPnu2Y2Ak&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7EF998C19060E0310A25FE9E8DF47D45974B72CA.71D597638B61D072DE0CE55284847B9E96DAEFDE&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.330 --> 00:00:01.370
- [Instructor] There are
a lot of different types
00:00:01.370 --> 00:00:02.550
of forces in physics,
00:00:02.550 --> 00:00:03.540
but for the most part,
00:00:03.540 --> 00:00:07.240
all forces can be
categorized as either being
00:00:07.240 --> 00:00:10.950
a contact force or a long range force.
00:00:10.950 --> 00:00:13.640
So contact forces as the name suggests
00:00:13.640 --> 00:00:14.790
requires the two objects
00:00:14.790 --> 00:00:16.310
that are exerting a force on each other
00:00:16.310 --> 00:00:19.130
to be touching or in contact.
00:00:19.130 --> 00:00:22.010
So tension, the normal
force, frictional forces,
00:00:22.010 --> 00:00:26.000
these are all common everyday
examples of contact forces.
00:00:26.000 --> 00:00:29.260
So, you know, this wire from this crane
00:00:29.260 --> 00:00:31.860
can exert a contact force
i.e. attention force
00:00:31.860 --> 00:00:34.400
on the wrecking ball but that wire
00:00:34.400 --> 00:00:36.810
can only exert that tension
force on the wrecking ball
00:00:36.810 --> 00:00:39.190
if the wire is actually connected to
00:00:39.190 --> 00:00:41.350
i.e. touching the wrecking ball,
00:00:41.350 --> 00:00:43.870
if you forgot to tie the
wire to the wrecking ball,
00:00:43.870 --> 00:00:46.000
that wire is not gonna exert any tension
00:00:46.000 --> 00:00:47.440
on the wrecking ball.
00:00:47.440 --> 00:00:51.310
So these contact forces are
to be distinguished from
00:00:51.310 --> 00:00:52.660
long range forces.
00:00:52.660 --> 00:00:55.950
Sometimes these are called
action at a distance forces
00:00:55.950 --> 00:00:57.520
because they can be exerted
00:00:57.520 --> 00:00:59.690
on objects that are far
away from each other,
00:00:59.690 --> 00:01:01.453
so gravity is a common example,
00:01:02.480 --> 00:01:05.390
the earth can exert a
gravitational force on the moon
00:01:05.390 --> 00:01:07.560
even though the earth and
the moon aren't touching.
00:01:07.560 --> 00:01:09.560
So that's a group long range force.
00:01:09.560 --> 00:01:12.840
Similarly, the electric force
can exert a repulsive force
00:01:12.840 --> 00:01:15.130
on two charges if they're not touching,
00:01:15.130 --> 00:01:17.380
so not a contact force,
00:01:17.380 --> 00:01:19.420
and magnets can attract each other
00:01:19.420 --> 00:01:20.690
even if they're not touching,
00:01:20.690 --> 00:01:24.420
so those are all long range or
action at a distance forces.
00:01:24.420 --> 00:01:26.290
But I'll be honest with you here,
00:01:26.290 --> 00:01:29.410
this distinction is not
nearly as fundamental
00:01:29.410 --> 00:01:31.010
as it might seem at first.
00:01:31.010 --> 00:01:34.620
All of these forces that
we call contact forces
00:01:34.620 --> 00:01:38.880
are really just an enormous
number of long range forces
00:01:38.880 --> 00:01:40.190
in disguise.
00:01:40.190 --> 00:01:42.930
In other words, these contact
forces, tension, normal force
00:01:42.930 --> 00:01:46.740
and friction are all arising
microscopically due to
00:01:46.740 --> 00:01:48.620
a bunch of long range forces
00:01:48.620 --> 00:01:50.910
acting over really short distances.
00:01:50.910 --> 00:01:53.250
So just cause they're
called long range forces
00:01:53.250 --> 00:01:56.640
doesn't mean they can't exert
force over small distances,
00:01:56.640 --> 00:01:59.510
and in fact, all those forces arise,
00:01:59.510 --> 00:02:01.330
you know, cause all these forces to arise.
00:02:01.330 --> 00:02:03.720
So let me go through and explain
how all these come about.
00:02:03.720 --> 00:02:06.000
So we'll start with tension here.
00:02:06.000 --> 00:02:07.450
Where does tension come from?
00:02:07.450 --> 00:02:09.960
Well, tension is the
force exerted by a wire
00:02:09.960 --> 00:02:12.840
or a cable or a string,
something like that.
00:02:12.840 --> 00:02:14.130
And so these strings,
00:02:14.130 --> 00:02:15.780
they're made out of atoms and molecules,
00:02:15.780 --> 00:02:17.400
I'm trying to represent that over here.
00:02:17.400 --> 00:02:20.690
Your string is probably
more than three atoms wide,
00:02:20.690 --> 00:02:22.790
but I didn't wanna have to
draw an enormous number here,
00:02:22.790 --> 00:02:24.550
so I imagine you've got
a certain number of atoms
00:02:24.550 --> 00:02:26.810
and molecules in your string,
00:02:26.810 --> 00:02:29.500
well, these atoms and molecules
are all bonded together,
00:02:29.500 --> 00:02:30.770
chemically bonded together,
00:02:30.770 --> 00:02:33.543
those are all electromagnetic bonds here,
00:02:35.103 --> 00:02:38.200
they don't wanna move away from
their equilibrium position,
00:02:38.200 --> 00:02:40.490
they have a position and if
they get displaced from there,
00:02:40.490 --> 00:02:42.450
they wanna go back to that spot.
00:02:42.450 --> 00:02:44.560
So that's what it means
to be in a solid here.
00:02:44.560 --> 00:02:48.100
So this wire, if you connect
to a heavy load to it
00:02:48.100 --> 00:02:49.200
like a wrecking ball,
00:02:49.200 --> 00:02:51.270
that wrecking ball is gonna
try to rip these atoms
00:02:51.270 --> 00:02:52.540
and molecules apart,
00:02:52.540 --> 00:02:55.230
it's gonna try to pull
them away from each other,
00:02:55.230 --> 00:02:56.500
but they don't wanna move
away from each other,
00:02:56.500 --> 00:02:59.390
in other words, they try
to restore themselves
00:02:59.390 --> 00:03:01.720
as this distance between these atoms
00:03:01.720 --> 00:03:03.180
and molecules gets bigger,
00:03:03.180 --> 00:03:05.720
and it does, you'll stretch
your string or your wire
00:03:05.720 --> 00:03:08.590
sometimes imperceptibly, but a little bit,
00:03:08.590 --> 00:03:10.340
these distances get bigger,
00:03:10.340 --> 00:03:13.090
that force holding them
together gets bigger,
00:03:13.090 --> 00:03:14.900
so more tension force occurs
00:03:14.900 --> 00:03:18.840
and this is the microscopic
origin of that tension force.
00:03:18.840 --> 00:03:21.030
These atoms and molecules
wanna restore themselves
00:03:21.030 --> 00:03:23.890
to their previous length and
00:03:23.890 --> 00:03:25.530
to do that they have to
pull harder and harder.
00:03:25.530 --> 00:03:27.070
Now, this won't last forever,
00:03:27.070 --> 00:03:29.200
you hang a heavy enough load over here,
00:03:29.200 --> 00:03:31.810
you'll overwhelm these
electromagnetic bonds
00:03:31.810 --> 00:03:34.600
and you'll rip these molecules apart
00:03:34.600 --> 00:03:36.260
and that's what happens
when your string breaks.
00:03:36.260 --> 00:03:38.680
So that's the microscopic
origin of tension
00:03:38.680 --> 00:03:42.860
but you don't have to draw an
Avogadro's number of arrows,
00:03:42.860 --> 00:03:45.430
we just represent the
tension with one arrow up,
00:03:45.430 --> 00:03:47.290
it turns out you can pretty much summarize
00:03:47.290 --> 00:03:51.250
all of those microscopic
electromagnetic chemical bonds
00:03:51.250 --> 00:03:54.420
with one arrow that we call tension.
00:03:54.420 --> 00:03:56.580
So how about the normal force,
where does that come from?
00:03:56.580 --> 00:03:58.060
Well, this is kind of the opposite.
00:03:58.060 --> 00:03:59.600
Tension is a pulling force,
00:03:59.600 --> 00:04:02.930
the normal force is the force
that tries to prevent two
00:04:02.930 --> 00:04:05.390
objects from getting
smashed into each other.
00:04:05.390 --> 00:04:07.100
So now instead of the atoms and molecules
00:04:07.100 --> 00:04:08.470
trying to get ripped apart,
00:04:08.470 --> 00:04:11.300
the atoms and molecules
in this green box here
00:04:11.300 --> 00:04:13.960
due to its weight are
trying to get shoved into
00:04:13.960 --> 00:04:15.590
the atoms and molecules this table,
00:04:15.590 --> 00:04:17.330
so I've tried to represent that here,
00:04:17.330 --> 00:04:19.340
again, the box and the
table are made out of more
00:04:19.340 --> 00:04:21.500
than these number of atoms and molecules,
00:04:21.500 --> 00:04:24.290
but you've got your atoms
molecules of the box,
00:04:24.290 --> 00:04:26.820
atoms and molecules of the table,
00:04:26.820 --> 00:04:28.900
they won't get moved into each other,
00:04:28.900 --> 00:04:31.110
there's gonna be an electron cloud
00:04:31.110 --> 00:04:33.120
around these atoms and
molecules of the box
00:04:33.120 --> 00:04:35.010
and similarly for the table,
00:04:35.010 --> 00:04:37.420
there's gonna be an
electromagnetic repulsion
00:04:37.420 --> 00:04:38.890
when they try to overlap
00:04:38.890 --> 00:04:40.840
and other quantum mechanical effects,
00:04:40.840 --> 00:04:43.820
it turns out it's surprisingly
complicated to explain
00:04:43.820 --> 00:04:47.020
why matter is solid and it
can't penetrate each other,
00:04:47.020 --> 00:04:50.240
but the enormous number of
electromagnetic interactions
00:04:50.240 --> 00:04:52.970
and other quantum mechanical
effects between these
00:04:52.970 --> 00:04:56.190
atoms and molecules are
the microscopic origin
00:04:56.190 --> 00:04:57.200
of the normal force.
00:04:57.200 --> 00:04:59.880
So again, it's, you know,
action at a distance
00:04:59.880 --> 00:05:01.710
over a small scale,
00:05:01.710 --> 00:05:04.583
which really bugs people out,
they're like, wait a minute,
00:05:05.659 --> 00:05:07.550
are two things ever actually touching?
00:05:07.550 --> 00:05:09.300
You know, as you sit in a chair,
00:05:09.300 --> 00:05:12.440
do the atoms and molecules of your pants
00:05:12.440 --> 00:05:14.690
actually physically touch?
00:05:14.690 --> 00:05:17.800
Hard to actually define
what it means touching here,
00:05:17.800 --> 00:05:20.440
you know, you've got these
amorphous electron clouds,
00:05:20.440 --> 00:05:22.430
how do you define
whether they're touching?
00:05:22.430 --> 00:05:24.930
Hard to do, but good news,
we don't have to do it,
00:05:24.930 --> 00:05:27.400
we can actually just
summarize microscopically
00:05:27.400 --> 00:05:29.620
all of these microscopic interactions
00:05:29.620 --> 00:05:33.960
as one big normal force and that helps us
00:05:33.960 --> 00:05:36.330
both calculationally and conceptually
00:05:36.330 --> 00:05:38.470
knock it to at last here.
00:05:38.470 --> 00:05:39.760
Now, you might be disturbed here,
00:05:39.760 --> 00:05:40.650
you might be like, wait a minute,
00:05:40.650 --> 00:05:43.160
this whole video is about contact forces,
00:05:43.160 --> 00:05:43.993
you're telling me,
00:05:43.993 --> 00:05:46.310
we don't even know if two
surfaces are in contact,
00:05:46.310 --> 00:05:48.170
well, I'm saying it's hard to define
00:05:48.170 --> 00:05:50.370
but here's a good way to define it,
00:05:50.370 --> 00:05:52.370
your pants, atoms and molecules
00:05:52.370 --> 00:05:56.050
are contacting the seat's
atom molecules as soon as
00:05:56.050 --> 00:05:57.650
you notice that force
00:05:57.650 --> 00:05:59.760
preventing them from
moving into each other.
00:05:59.760 --> 00:06:01.830
So as soon as you could
detect this normal force,
00:06:01.830 --> 00:06:03.040
that's as good a way as any
00:06:03.040 --> 00:06:06.460
to define two surfaces
as being in contact.
00:06:06.460 --> 00:06:08.680
So let's look at some other forces.
00:06:08.680 --> 00:06:10.640
So how about the frictional force?
00:06:10.640 --> 00:06:13.180
What are the microscopic
origins of the frictional force?
00:06:13.180 --> 00:06:15.800
Well, you know, the frictional
force is the force that
00:06:15.800 --> 00:06:19.660
resist two surfaces from being
dragged across each other.
00:06:19.660 --> 00:06:21.220
Why is there a resistive force?
00:06:21.220 --> 00:06:23.920
Well, if you zoomed in on these surfaces,
00:06:23.920 --> 00:06:25.800
a table, no matter how smooth it looks,
00:06:25.800 --> 00:06:27.400
even if you just wiped it down,
00:06:27.400 --> 00:06:28.570
if you zoomed in close enough,
00:06:28.570 --> 00:06:30.570
you'd be shocked at all the little
00:06:30.570 --> 00:06:32.890
crevices and cracks and valleys involved,
00:06:32.890 --> 00:06:34.600
the whole world you don't know about
00:06:34.600 --> 00:06:36.280
unless you look at it microscopically,
00:06:36.280 --> 00:06:39.380
and similarly for this purple
box, maybe it's cardboard,
00:06:39.380 --> 00:06:41.960
if you zoomed in microscopically,
00:06:41.960 --> 00:06:45.730
again, it's astonishing how
not smooth those surfaces are.
00:06:45.730 --> 00:06:48.467
So obviously, if you tried
to drag one across the other
00:06:48.467 --> 00:06:49.970
and these are bumping into each other,
00:06:49.970 --> 00:06:52.570
these hills and valleys are
running into each other,
00:06:52.570 --> 00:06:53.940
that's gonna be a problem
00:06:53.940 --> 00:06:55.650
that's gonna cause a resistive force.
00:06:55.650 --> 00:06:59.150
You might break this, you
know, yellow hill off,
00:06:59.150 --> 00:07:00.500
sometimes they just bust off,
00:07:00.500 --> 00:07:04.270
yep, that's gonna be a
resistive cause of friction.
00:07:04.270 --> 00:07:05.380
Sometimes they don't bust off,
00:07:05.380 --> 00:07:07.410
maybe they just like bend and bounce back
00:07:07.410 --> 00:07:08.980
but even if they do,
00:07:08.980 --> 00:07:10.500
still gonna cause a frictional force
00:07:10.500 --> 00:07:12.300
and add to this friction,
00:07:12.300 --> 00:07:15.330
and it's not just that
but sometimes even like
00:07:15.330 --> 00:07:17.800
the atoms and molecules
in the surface over here,
00:07:17.800 --> 00:07:19.380
look, this pot doesn't look too bad,
00:07:19.380 --> 00:07:20.960
it looks like they could
slide across each other
00:07:20.960 --> 00:07:22.300
pretty well,
00:07:22.300 --> 00:07:25.760
but there can be adhesion
like molecular bonds that form
00:07:25.760 --> 00:07:28.110
between those atoms and molecules
that are near each other,
00:07:28.110 --> 00:07:30.410
that can also contribute to friction.
00:07:30.410 --> 00:07:32.350
So again, astonishingly complicated,
00:07:32.350 --> 00:07:35.080
there's actually lots of
questions to still be answered
00:07:35.080 --> 00:07:36.220
in studying friction,
00:07:36.220 --> 00:07:39.150
and the study of friction
is called tribology.
00:07:39.150 --> 00:07:42.210
Shockingly, a lot of
questions to this day but,
00:07:42.210 --> 00:07:44.110
the good news is you can summarize
00:07:44.110 --> 00:07:47.840
all of those microscopic
interactions as one force
00:07:47.840 --> 00:07:50.090
we call friction that resists
00:07:50.090 --> 00:07:52.570
the two surfaces from
sliding over each other.
00:07:52.570 --> 00:07:54.970
So you don't have to do
a lot of calculations
00:07:54.970 --> 00:07:57.750
and microscopically
zoom in on the surface,
00:07:57.750 --> 00:07:59.510
we can pretty much account for all of it
00:07:59.510 --> 00:08:01.930
by simply drawing it as
one big resistive force
00:08:01.930 --> 00:08:03.770
of friction backwards.
00:08:03.770 --> 00:08:06.670
So recapping, contact
forces are those forces
00:08:06.670 --> 00:08:09.510
that require the two objects
interacting to be touching
00:08:09.510 --> 00:08:11.190
for that force to occur,
00:08:11.190 --> 00:08:13.860
but we've seen that these
contact forces are actually due
00:08:13.860 --> 00:08:17.580
to a mind bogglingly large
number of long range forces
00:08:17.580 --> 00:08:19.790
all acting over a very short distance,
00:08:19.790 --> 00:08:22.210
but you can summarize all
those long range forces
00:08:22.210 --> 00:08:24.560
as a single contact force
00:08:24.560 --> 00:08:28.083
when doing most introductory
physics problems.
|
Using matrices to represent data: Payoffs | https://www.youtube.com/watch?v=2ObBIZoZnJ0 | vtt | https://www.youtube.com/api/timedtext?v=2ObBIZoZnJ0&ei=6VWUZaKkHv29mLAP_JytmA0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5A695C42BACF3F5C555E37C32EF0EE3EF3BF6C98.C089855412D3CB7B1DDB2DA1FD04BED1A73E8FCE&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.400 --> 00:00:01.280
- [Instructor] We're told Violet
00:00:01.280 --> 00:00:05.210
and Lennox play an elaborated
version of rock paper scissors
00:00:05.210 --> 00:00:08.280
where each combination of shape choices
00:00:08.280 --> 00:00:10.780
earns a different number
of points for the winner.
00:00:10.780 --> 00:00:12.840
So rock paper scissors, the game,
00:00:12.840 --> 00:00:16.410
of course, where rock beats scissors,
00:00:16.410 --> 00:00:19.470
scissors beats paper,
and paper beats rock,
00:00:19.470 --> 00:00:21.560
and then they give us
this elaborate version
00:00:21.560 --> 00:00:22.393
right over here.
00:00:22.393 --> 00:00:24.350
When Violet wins, she gets two points.
00:00:24.350 --> 00:00:27.000
When Lennox wins with
rock, she gets three.
00:00:27.000 --> 00:00:29.700
When Lennox wins with
paper, she gets two points.
00:00:29.700 --> 00:00:32.290
When Lennox wins with
scissors, she gets one point.
00:00:32.290 --> 00:00:35.230
And if they choose the same
shape, nobody gets any points
00:00:35.230 --> 00:00:37.290
'cause no one wins that round.
00:00:37.290 --> 00:00:40.980
Complete the matrix so it
represents their scoring system.
00:00:40.980 --> 00:00:45.140
It shows the number of points Violet gets,
00:00:45.140 --> 00:00:48.590
a negative number means
Lennox gets those points,
00:00:48.590 --> 00:00:51.390
where rows are Violet's chosen shape
00:00:51.390 --> 00:00:54.650
and columns are Lennox's chosen shape.
00:00:54.650 --> 00:00:56.670
So here we have the
matrix right over here.
00:00:56.670 --> 00:00:58.940
I encourage you to pause this video
00:00:58.940 --> 00:01:00.670
and see if you can have
a go at this on your own
00:01:00.670 --> 00:01:02.090
if you have a piece of paper
in front of you, alright?
00:01:02.090 --> 00:01:04.210
I encourage you to get a piece of paper.
00:01:04.210 --> 00:01:06.450
All right, now let's do this together.
00:01:06.450 --> 00:01:08.040
So, how many points,
00:01:08.040 --> 00:01:10.570
remember, this matrix is
how many points Violet gets.
00:01:10.570 --> 00:01:14.290
And if Lennox gets points, then
it's a negative for Violet.
00:01:14.290 --> 00:01:18.180
So, if Violet chooses a rock
and Lennox chooses a rock,
00:01:18.180 --> 00:01:20.130
so that is this entry right over here,
00:01:20.130 --> 00:01:20.963
what's going to happen?
00:01:20.963 --> 00:01:22.890
How many points is Violet going to get?
00:01:23.830 --> 00:01:25.860
Well, if both players
choose the same shape,
00:01:25.860 --> 00:01:28.320
nobody gets any points.
00:01:28.320 --> 00:01:31.700
So if they both get rock, rock
will get a zero right there.
00:01:31.700 --> 00:01:33.590
And we also know that's going to be true
00:01:33.590 --> 00:01:35.900
if Violet picks paper
and Lennox picks paper,
00:01:35.900 --> 00:01:38.060
you're gonna get a zero
points for Violet there.
00:01:38.060 --> 00:01:41.170
And if they both pick
scissors, that entry there,
00:01:41.170 --> 00:01:43.550
you're also going to get a zero.
00:01:43.550 --> 00:01:46.280
All right, now, what if Violet picks rock
00:01:46.280 --> 00:01:48.460
and Lennox picks paper?
00:01:48.460 --> 00:01:49.293
What should I put there?
00:01:49.293 --> 00:01:50.320
Pause the video and think about it.
00:01:50.320 --> 00:01:52.763
Violet picks rock and Lennox picks paper.
00:01:53.860 --> 00:01:57.460
Well, we know that paper beats rock.
00:01:57.460 --> 00:02:01.530
So this is a situation where
Lennox wins with paper.
00:02:01.530 --> 00:02:03.780
And so that's this
scenario right over here,
00:02:03.780 --> 00:02:06.140
so Lennox will get two points.
00:02:06.140 --> 00:02:07.550
So if Lennox gets two points,
00:02:07.550 --> 00:02:09.840
remember this matrix is
what does Violet get,
00:02:09.840 --> 00:02:12.300
Violet gets negative two
points right over here
00:02:12.300 --> 00:02:14.110
'cause Lennox got them.
00:02:14.110 --> 00:02:15.730
All right, now what about this entry?
00:02:15.730 --> 00:02:17.640
What does that represent?
00:02:17.640 --> 00:02:19.750
Well, that represents Violet picking rock
00:02:19.750 --> 00:02:22.530
and Lennox picking scissors.
00:02:22.530 --> 00:02:25.680
And we know that rock beats scissors
00:02:25.680 --> 00:02:27.610
so this is a situation where Violet wins,
00:02:27.610 --> 00:02:31.610
and we know whenever Violet
wins, she gets two points.
00:02:31.610 --> 00:02:34.690
So this will be a positive
two points right over here.
00:02:34.690 --> 00:02:36.180
Now, what about this entry?
00:02:36.180 --> 00:02:38.200
What does that represent?
00:02:38.200 --> 00:02:40.550
Well, that represents Violet picking paper
00:02:40.550 --> 00:02:42.400
and Lennox picking rock.
00:02:42.400 --> 00:02:44.510
And we know that paper beats rock,
00:02:44.510 --> 00:02:47.410
so this is another
situation where Violet wins
00:02:47.410 --> 00:02:50.350
and she gets two points in
any scenario where she wins.
00:02:50.350 --> 00:02:51.780
So that's two points.
00:02:51.780 --> 00:02:54.390
And now, what about this one over here?
00:02:54.390 --> 00:02:57.163
Pause this video and think
about what number goes there.
00:02:58.340 --> 00:03:01.040
Well, this is a situation
where Violet picks paper
00:03:01.040 --> 00:03:03.130
and Lennox picks scissors.
00:03:03.130 --> 00:03:05.270
We know scissors beats paper
00:03:05.270 --> 00:03:06.950
'cause it can cut it up, I guess,
00:03:06.950 --> 00:03:09.360
and so Lennox has won with scissors.
00:03:09.360 --> 00:03:12.070
And we see here, I'll do
it in a different color,
00:03:12.070 --> 00:03:15.180
Lennox wins with scissors,
she gets one point.
00:03:15.180 --> 00:03:17.320
So you might be tempted
to write a one here
00:03:17.320 --> 00:03:19.410
but remember, that's
Lennox getting a point.
00:03:19.410 --> 00:03:21.610
So this is all about how
many points does Violet get
00:03:21.610 --> 00:03:23.910
and we said that would
be negative one point
00:03:23.910 --> 00:03:26.290
if it's going to Lennox.
00:03:26.290 --> 00:03:30.200
And then, let's think
about this last row here.
00:03:30.200 --> 00:03:31.650
What does this entry represent?
00:03:31.650 --> 00:03:32.740
What number should go there?
00:03:32.740 --> 00:03:34.490
Pause the video and think about it.
00:03:35.520 --> 00:03:37.460
Well, this is Violet picking scissors
00:03:37.460 --> 00:03:39.070
and Lennox picking rock.
00:03:39.070 --> 00:03:41.150
Now, we know that rock beats scissors
00:03:41.150 --> 00:03:42.890
'cause I guess it can bash it up,
00:03:42.890 --> 00:03:46.700
and so Lennox in this
scenario has won with rock,
00:03:46.700 --> 00:03:49.130
and we know, I'll pick another color here,
00:03:49.130 --> 00:03:52.500
when Lennox wins with rock,
she gets three points.
00:03:52.500 --> 00:03:54.300
So Lennox is getting three points here.
00:03:54.300 --> 00:03:56.030
This matrix is all about
what does Violet get
00:03:56.030 --> 00:03:58.000
so we wanna put a negative three here
00:03:58.000 --> 00:03:59.690
'cause that's three points for Lennox.
00:03:59.690 --> 00:04:03.590
Remember, a negative number
means Lennox gets those points.
00:04:03.590 --> 00:04:07.873
And one last entry, what do
you think should go there?
00:04:09.550 --> 00:04:11.860
Well, this is Violet picking scissors
00:04:11.860 --> 00:04:14.550
and Lennox picking paper.
00:04:14.550 --> 00:04:17.230
So we know that scissors beats paper
00:04:17.230 --> 00:04:18.330
'cause it can cut it up,
00:04:18.330 --> 00:04:21.040
and we know that in any
situation where Violet wins,
00:04:21.040 --> 00:04:23.740
'cause she won with scissors
here, she gets two points.
00:04:23.740 --> 00:04:27.320
So that is two points, just like that.
00:04:27.320 --> 00:04:28.620
So we filled in the matrix
00:04:28.620 --> 00:04:30.230
and now we have to answer this question.
00:04:30.230 --> 00:04:33.980
Assuming Lennox picks her
shape entirely at random,
00:04:33.980 --> 00:04:38.090
what shape should Violet
choose to maximize her chances
00:04:38.090 --> 00:04:40.130
of getting the most points?
00:04:40.130 --> 00:04:43.000
So pause the video and see
if this matrix is helpful
00:04:43.000 --> 00:04:44.800
for figuring out the answer to that.
00:04:46.190 --> 00:04:47.150
All right.
00:04:47.150 --> 00:04:50.030
So, this obviously isn't
an exercise on probability,
00:04:50.030 --> 00:04:52.210
but just as a little bit of a review,
00:04:52.210 --> 00:04:55.330
one way to think about it
is when Violet picks rock,
00:04:55.330 --> 00:04:57.010
here are the scenarios,
00:04:57.010 --> 00:04:59.400
here are the outcomes that might happen.
00:04:59.400 --> 00:05:02.430
Now, they're telling us
that Lennox picks at random
00:05:02.430 --> 00:05:04.840
so there would be a 1/3
chance that Lennox picks rock,
00:05:04.840 --> 00:05:07.270
1/3 paper, 1/3 scissors.
00:05:07.270 --> 00:05:09.490
And since these are equally likely
00:05:09.490 --> 00:05:12.330
'cause they're saying that
Lennox is picking at random,
00:05:12.330 --> 00:05:13.310
you can get the,
00:05:13.310 --> 00:05:16.070
what is sometimes known as
the expected value here,
00:05:16.070 --> 00:05:19.000
by taking the average
of these three numbers.
00:05:19.000 --> 00:05:19.940
Another way to think about it would be
00:05:19.940 --> 00:05:24.940
1/3 X 0 + 1/3 X -2 + 1/3 X 2.
00:05:25.700 --> 00:05:27.900
If you wanna go dig deeper
into expected value,
00:05:27.900 --> 00:05:29.880
there's a lot of that on Khan Academy,
00:05:29.880 --> 00:05:31.910
but we can really just take
the average of these numbers.
00:05:31.910 --> 00:05:33.300
Add them up and divide by three
00:05:33.300 --> 00:05:34.660
is another way to think about it.
00:05:34.660 --> 00:05:37.000
And so, here the expected value
00:05:37.000 --> 00:05:39.110
is going to be if we take the sum,
00:05:39.110 --> 00:05:41.260
we get 0 + -2 + 2.
00:05:41.260 --> 00:05:42.780
Well, that all sums up to 0,
00:05:42.780 --> 00:05:45.370
divided by 3, you get to 0.
00:05:45.370 --> 00:05:48.090
So I'll just write this 0
here as the expected value
00:05:48.090 --> 00:05:51.820
when Violet picks rock and
Lennox picks at random.
00:05:51.820 --> 00:05:56.130
Now, in this second scenario,
let's take the average.
00:05:56.130 --> 00:05:58.370
If we add all three of these up,
00:05:58.370 --> 00:06:02.070
you get 2 + 0 + -1,
which is 1, divide by 3,
00:06:02.070 --> 00:06:05.640
you're gonna get 1/3 as the expected value
00:06:05.640 --> 00:06:07.210
of the points for Violet.
00:06:07.210 --> 00:06:09.800
And then in that last scenario,
00:06:09.800 --> 00:06:13.270
if you add all of these up, you get -1,
00:06:13.270 --> 00:06:14.270
divide by 3 is -1/3.
00:06:16.300 --> 00:06:19.690
So it looks like the best
expected value for Violet,
00:06:19.690 --> 00:06:22.110
assuming that Lennox is
going to pick at random,
00:06:22.110 --> 00:06:23.510
is to go with paper.
00:06:23.510 --> 00:06:26.640
You have a positive 1/3 expected value.
00:06:26.640 --> 00:06:29.220
So what shape should Violet
choose to maximize her chances
00:06:29.220 --> 00:06:30.940
of getting the most points?
00:06:30.940 --> 00:06:32.150
Paper.
00:06:32.150 --> 00:06:33.630
Now, of course that's assuming Lennox
00:06:33.630 --> 00:06:35.050
always picks at random.
00:06:35.050 --> 00:06:36.730
Obviously, if Lennox catches on
00:06:36.730 --> 00:06:38.030
that Violet keeps picking paper,
00:06:38.030 --> 00:06:39.970
Lennox would adjust their strategy.
00:06:39.970 --> 00:06:41.670
But that gets a little bit deeper.
|
Using matrices to represent data: Networks | https://www.youtube.com/watch?v=IxmFLAPSx5I | vtt | https://www.youtube.com/api/timedtext?v=IxmFLAPSx5I&ei=6VWUZafpKYa3vdIP9NOowAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D8E7696AFD81B0B4D7EC199765EE2DBC03258158.CBFD3BBBEB5D7A8FD8E01B147B8C5483894BDE30&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.620 --> 00:00:02.330
- [Instructor] We're
told this network diagram
00:00:02.330 --> 00:00:06.040
represents the different train
routes between three cities.
00:00:06.040 --> 00:00:09.690
Each node is a city
and each directed arrow
00:00:09.690 --> 00:00:14.160
represents a direct bus
route from city to city.
00:00:14.160 --> 00:00:19.160
So for example, this
arrow right over here,
00:00:19.200 --> 00:00:21.840
I guess would represent a direct bus route
00:00:21.840 --> 00:00:25.990
that starts in city three
and ends in city one,
00:00:25.990 --> 00:00:30.360
while this arrow that has
an arrow on both sides
00:00:30.360 --> 00:00:33.120
shows a route that both starts
00:00:33.120 --> 00:00:35.320
in city three and ends in city one,
00:00:35.320 --> 00:00:40.320
and a route that starts in city
one and ends in city three.
00:00:40.430 --> 00:00:43.080
So it says, complete the
matrix so it represents
00:00:43.080 --> 00:00:46.120
the number of direct
routes between the cities,
00:00:46.120 --> 00:00:50.270
where rows are starting points
and columns are end points.
00:00:50.270 --> 00:00:52.250
So this is the matrix right over here.
00:00:52.250 --> 00:00:54.130
I encourage you if you feel so inspired,
00:00:54.130 --> 00:00:55.940
and I encourage you to feel so inspired,
00:00:55.940 --> 00:00:57.480
pause this video and see if you can
00:00:57.480 --> 00:00:59.580
fill out this matrix right over here.
00:00:59.580 --> 00:01:01.960
You have nine entries in this matrix
00:01:01.960 --> 00:01:03.330
for each of these combinations
00:01:03.330 --> 00:01:05.430
between the starting city and ending city.
00:01:06.280 --> 00:01:07.640
All right, now let's do it together.
00:01:07.640 --> 00:01:09.360
So, what would go here?
00:01:09.360 --> 00:01:11.350
This would be the number of direct routes
00:01:11.350 --> 00:01:15.550
that start at city one
and end at city one.
00:01:15.550 --> 00:01:18.690
So if we start at city one,
00:01:18.690 --> 00:01:22.230
are there any things that
then end at city one?
00:01:22.230 --> 00:01:23.063
Well, no.
00:01:23.063 --> 00:01:24.300
It doesn't look like there's anything
00:01:24.300 --> 00:01:26.860
that starts at city one
and ends at city one.
00:01:26.860 --> 00:01:29.000
So I'll put a zero there.
00:01:29.000 --> 00:01:31.220
What about this one right over here?
00:01:31.220 --> 00:01:34.690
Well it needs to start at
city one and end at city two.
00:01:34.690 --> 00:01:35.523
So let's see.
00:01:35.523 --> 00:01:39.710
This starts at city one and
ends at city two, so that's one.
00:01:39.710 --> 00:01:41.850
We get two.
00:01:41.850 --> 00:01:44.320
And then we get three.
00:01:44.320 --> 00:01:47.430
And then we get four, 'cause
you can start at city one here
00:01:47.430 --> 00:01:50.170
and then end at city two.
00:01:50.170 --> 00:01:51.533
So we get four.
00:01:52.510 --> 00:01:55.800
Now how many start at city
one and end at city three?
00:01:55.800 --> 00:01:58.540
Pause this video and think
about that, actually.
00:01:58.540 --> 00:02:00.000
All right, we're gonna start at city one
00:02:00.000 --> 00:02:02.100
and end at city three.
00:02:02.100 --> 00:02:03.800
I'm going to get another color out here.
00:02:03.800 --> 00:02:06.210
So I could start here and go on this route
00:02:06.210 --> 00:02:09.480
and 'cause this arrow ends
at city three, so that's one.
00:02:09.480 --> 00:02:12.610
This middle one does not start at city one
00:02:12.610 --> 00:02:13.530
and end at city three.
00:02:13.530 --> 00:02:16.100
It goes the other way around,
so I'm not gonna count that.
00:02:16.100 --> 00:02:19.030
This one right over here,
I can go either way,
00:02:19.030 --> 00:02:21.510
so I could start at city
one and end at city three,
00:02:21.510 --> 00:02:23.304
'cause we have that arrow there.
00:02:23.304 --> 00:02:25.330
And those look like the only two
00:02:25.330 --> 00:02:29.760
that start at city one
and end at city three.
00:02:29.760 --> 00:02:32.980
So that looks like, go
back to the original color,
00:02:32.980 --> 00:02:35.080
two routes right over there.
00:02:35.080 --> 00:02:38.623
Now what about starting at city
two and ending at city one?
00:02:39.610 --> 00:02:43.260
Well, if we start at city
two and end at city one,
00:02:43.260 --> 00:02:44.500
these three over here,
00:02:44.500 --> 00:02:46.870
all of these start at one and end at two.
00:02:46.870 --> 00:02:48.340
They don't go the other way.
00:02:48.340 --> 00:02:50.580
But this one on top with the double arrows
00:02:50.580 --> 00:02:51.413
you can go either way.
00:02:51.413 --> 00:02:56.413
So you could start at city
two and end at city one.
00:02:56.700 --> 00:02:59.400
So there's one route here.
00:02:59.400 --> 00:03:00.659
Let's see.
00:03:00.659 --> 00:03:02.420
Start at city two, end at city two.
00:03:02.420 --> 00:03:04.450
Well, I don't see anything that looks
00:03:04.450 --> 00:03:06.460
like that for city two,
00:03:06.460 --> 00:03:08.730
so this is going to be a zero.
00:03:08.730 --> 00:03:11.370
And then starts at city
two, ends at city three.
00:03:11.370 --> 00:03:14.600
So starts at city two, ends at city three.
00:03:14.600 --> 00:03:16.250
This arrow doesn't count, 'cause this
00:03:16.250 --> 00:03:18.870
starts at three, ends at two,
not the other way around.
00:03:18.870 --> 00:03:21.060
So we get a zero there as well.
00:03:21.060 --> 00:03:23.260
And then let's go to city three.
00:03:23.260 --> 00:03:26.470
How many start at three and end at one?
00:03:26.470 --> 00:03:29.420
So start at three and end at one?
00:03:29.420 --> 00:03:31.810
So this two-way arrow, you could do that.
00:03:31.810 --> 00:03:35.940
You could start at three and
end at one, so that's one.
00:03:35.940 --> 00:03:38.640
Then this one right over
here starts at three
00:03:38.640 --> 00:03:41.140
and ends at one because
we can see the arrow
00:03:41.140 --> 00:03:43.390
points to one right over there.
00:03:43.390 --> 00:03:48.110
And then it looks like,
and actually this one,
00:03:48.110 --> 00:03:49.530
I have so much that I've written here
00:03:49.530 --> 00:03:51.860
that I actually can't see
too well the original.
00:03:51.860 --> 00:03:54.390
Let me erase it actually,
so I can make sure
00:03:54.390 --> 00:03:55.570
I'm seeing things properly.
00:03:55.570 --> 00:03:58.310
Yeah, that one, too, looks like,
00:03:58.310 --> 00:04:02.070
so this one I can do, and then this one
00:04:02.070 --> 00:04:07.070
I can start at city three
and end at city one, as well.
00:04:07.390 --> 00:04:11.580
So it looks like we
have three paths there.
00:04:11.580 --> 00:04:14.220
Now start at city three, end at city two.
00:04:14.220 --> 00:04:16.190
That one's a little bit
more straight forward.
00:04:16.190 --> 00:04:19.530
That's that path there, so that is one.
00:04:19.530 --> 00:04:21.900
And then starts at city
three, ends at city three.
00:04:21.900 --> 00:04:23.850
Well, we have this one right over here.
00:04:24.780 --> 00:04:27.130
That's the only one, so I would put one.
00:04:27.130 --> 00:04:27.963
So there you have it.
00:04:27.963 --> 00:04:30.920
We have filled in this matrix.
00:04:30.920 --> 00:04:34.560
So which city has the
most incoming routes?
00:04:34.560 --> 00:04:36.410
Pause the video and think about that.
00:04:37.260 --> 00:04:39.870
So the city with the most incoming routes,
00:04:39.870 --> 00:04:43.230
we can look at the cities
that are the end points,
00:04:43.230 --> 00:04:48.070
and so city one has a total
of zero plus one plus three,
00:04:48.070 --> 00:04:50.250
has four incoming routes.
00:04:50.250 --> 00:04:54.940
City two has a total of four
plus one, five incoming routes.
00:04:54.940 --> 00:04:58.480
And city three has a total
of two plus zero plus one,
00:04:58.480 --> 00:05:00.300
has three incoming routes.
00:05:00.300 --> 00:05:05.140
So it looks like this would be city two
00:05:05.140 --> 00:05:07.000
with five incoming routes.
00:05:07.000 --> 00:05:09.400
Which city has the most outgoing routes?
00:05:09.400 --> 00:05:11.260
Well, then we would
just look the other way.
00:05:11.260 --> 00:05:14.000
Actually, pause the video
and think about that.
00:05:14.000 --> 00:05:15.400
Well, it looks like city one
00:05:16.500 --> 00:05:19.040
has six outgoing routes.
00:05:19.040 --> 00:05:21.960
City two only has one outgoing route.
00:05:21.960 --> 00:05:23.690
I'm just adding up along the row.
00:05:23.690 --> 00:05:28.450
And city three has, looks
like five outgoing routes.
00:05:28.450 --> 00:05:31.200
So city one was zero plus four plus two.
00:05:31.200 --> 00:05:33.630
There's a total of six
routes that start at city one
00:05:33.630 --> 00:05:38.630
and go out of the city, so that
is city one with six routes.
|
Human population dynamics | https://www.youtube.com/watch?v=jKfojKK-8Zk | vtt | https://www.youtube.com/api/timedtext?v=jKfojKK-8Zk&ei=6VWUZfjxHNGdp-oP6Kq-iAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7E2283C43E6063F1A6BD670E97D5A5F401C49EA7.C529CBF727BED96BCDD137F62FF83CC9788F2CFE&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.720 --> 00:00:01.560
- [Instructor] What we have here
00:00:01.560 --> 00:00:03.660
is a really interesting visual
00:00:03.660 --> 00:00:06.470
that shows world population growth
00:00:06.470 --> 00:00:09.940
from 1750 all the way to 2100.
00:00:09.940 --> 00:00:12.070
And obviously this isn't 2100 yet.
00:00:12.070 --> 00:00:15.480
So it's doing some projecting
for roughly the next 80 years.
00:00:15.480 --> 00:00:18.390
It also shows the
absolute world population
00:00:18.390 --> 00:00:19.940
over that time period.
00:00:19.940 --> 00:00:22.570
So just to make sure we're
understanding this graphic,
00:00:22.570 --> 00:00:26.540
our horizontal axis here, we
can see the years going by.
00:00:26.540 --> 00:00:30.280
You can view that as our time
axis, starting with the 1750
00:00:30.280 --> 00:00:33.100
right over here, going
all the way to 2100.
00:00:33.100 --> 00:00:35.730
Now we are here in, when
I'm making this video
00:00:35.730 --> 00:00:39.850
is 2021 but this graphic was made in 2015.
00:00:39.850 --> 00:00:44.850
So everything beyond 2015 is
considered to be a projection.
00:00:45.220 --> 00:00:48.090
Now on this left-hand vertical axis,
00:00:48.090 --> 00:00:51.950
this is really the rate of
world population growth,
00:00:51.950 --> 00:00:53.740
the growth rate that it has here.
00:00:53.740 --> 00:00:57.300
And I could write that down
just to make it more clear.
00:00:57.300 --> 00:01:00.460
This is the growth rate axis
00:01:00.460 --> 00:01:03.130
and we have a right vertical axis here
00:01:03.130 --> 00:01:04.740
because we're really showing
two different things.
00:01:04.740 --> 00:01:06.240
We're showing the annual growth rate
00:01:06.240 --> 00:01:07.800
of world population in red.
00:01:07.800 --> 00:01:10.470
And then we're showing the
absolute world population
00:01:10.470 --> 00:01:12.350
in this blue curve right over here.
00:01:12.350 --> 00:01:17.350
And so we could view this
axis as world population.
00:01:19.990 --> 00:01:22.130
Now there's a bunch of really
interesting things here.
00:01:22.130 --> 00:01:23.170
One, you might just wonder, well
00:01:23.170 --> 00:01:26.550
what was the world population around 1750?
00:01:26.550 --> 00:01:29.180
And if you look at this and
these are obviously estimates
00:01:29.180 --> 00:01:32.820
because you did not have a
global census back in 1750,
00:01:32.820 --> 00:01:36.190
it was around seven or 800 million people.
00:01:36.190 --> 00:01:39.890
Now what's interesting is
that's not a lot larger
00:01:39.890 --> 00:01:42.740
than the number of people
that we had at say the time
00:01:42.740 --> 00:01:44.280
of Jesus, which is also the time
00:01:44.280 --> 00:01:47.660
of the Roman empire and Han
China, where it's estimated
00:01:47.660 --> 00:01:50.890
that at around that time
period around 2000 years ago
00:01:50.890 --> 00:01:54.340
the world population was
around 300 million people.
00:01:54.340 --> 00:01:56.460
But then we see something
interesting happening
00:01:56.460 --> 00:01:59.380
over the next several centuries from 1750
00:01:59.380 --> 00:02:02.610
it seems to start growing
pretty dramatically.
00:02:02.610 --> 00:02:04.150
And we could see why that is.
00:02:04.150 --> 00:02:08.650
We can see the growth rate
of population for a while.
00:02:08.650 --> 00:02:11.850
If we look at this red
curve, the growth rate
00:02:11.850 --> 00:02:16.660
of world population was
around 0.6%, but it looks
00:02:16.660 --> 00:02:20.910
like in the early 20th
century, right around here,
00:02:20.910 --> 00:02:24.380
the rate of growth of
world population starts
00:02:24.380 --> 00:02:28.320
to really increase where
at least based on this
00:02:28.320 --> 00:02:33.320
it looks like around the 1970s,
00:02:33.370 --> 00:02:38.000
world population the growth
rate peaked out at 2.1%.
00:02:38.000 --> 00:02:40.580
Now the question might be,
why was this happening?
00:02:40.580 --> 00:02:43.480
Why did the rate of
growth increased so much?
00:02:43.480 --> 00:02:46.390
Well, the main argument
is as we became a more
00:02:46.390 --> 00:02:49.560
industrial society, healthcare
would have improved.
00:02:49.560 --> 00:02:52.370
So child mortality would have gone down.
00:02:52.370 --> 00:02:54.680
People would have died of fewer diseases.
00:02:54.680 --> 00:02:55.630
At the same time
00:02:55.630 --> 00:02:58.480
we would have gotten more
efficient with agriculture.
00:02:58.480 --> 00:03:02.310
We would have had farming
methods, so more people
00:03:02.310 --> 00:03:03.510
so food would get cheaper.
00:03:03.510 --> 00:03:04.410
It would be more abundant.
00:03:04.410 --> 00:03:06.530
More people would have access to nutrition
00:03:06.530 --> 00:03:10.630
and all of those would
drive the growth rate up.
00:03:10.630 --> 00:03:12.650
Now, an interesting question
that folks have been thinking
00:03:12.650 --> 00:03:15.990
about for many hundreds
of years, is there a limit
00:03:15.990 --> 00:03:19.720
to how much human population
the earth can sustain?
00:03:19.720 --> 00:03:21.700
And so they've introduced this idea
00:03:21.700 --> 00:03:24.130
known as carrying capacity.
00:03:24.130 --> 00:03:27.680
Why do we use the letter K for
capacity when capacity starts
00:03:27.680 --> 00:03:31.660
with a C, because a version
of that word in German starts
00:03:31.660 --> 00:03:33.970
with a K and there's
always been this notion
00:03:33.970 --> 00:03:35.240
that for a given species
00:03:35.240 --> 00:03:38.430
there's gotta be some maximum capacity
00:03:38.430 --> 00:03:41.120
that an ecosystem can sustain.
00:03:41.120 --> 00:03:42.940
And there's folks like Thomas Malthus,
00:03:42.940 --> 00:03:45.300
who's theorized that
there must be some limit
00:03:45.300 --> 00:03:47.440
to how many people there
could be on the planet.
00:03:47.440 --> 00:03:48.940
Just based on how much land there is,
00:03:48.940 --> 00:03:52.450
how much nutrition or how
much resources there are.
00:03:52.450 --> 00:03:53.760
But the carrying capacity
00:03:53.760 --> 00:03:56.750
for humanity is really an open question
00:03:56.750 --> 00:03:59.610
because our technology is
constantly on the move.
00:03:59.610 --> 00:04:01.360
We constantly are getting better
00:04:01.360 --> 00:04:04.190
at using our resources more efficiently
00:04:04.190 --> 00:04:05.940
going into new ecosystems.
00:04:05.940 --> 00:04:07.010
Now it's a huge debate.
00:04:07.010 --> 00:04:08.550
How sustainable is that?
00:04:08.550 --> 00:04:10.110
And as we become more efficient
00:04:10.110 --> 00:04:13.150
are we also trashing certain
parts of our ecosystem
00:04:13.150 --> 00:04:14.840
but the carrying capacity of humans,
00:04:14.840 --> 00:04:16.640
we really don't know how many people
00:04:16.640 --> 00:04:19.080
the planet earth could sustain.
00:04:19.080 --> 00:04:21.780
But we could see that the
rate of population growth
00:04:21.780 --> 00:04:24.810
starts to decline after 1970.
00:04:24.810 --> 00:04:26.880
And the main argument for this,
00:04:26.880 --> 00:04:28.970
and we've seen this and
recover this in other videos
00:04:28.970 --> 00:04:31.830
when we study countries
that are still developing
00:04:31.830 --> 00:04:33.810
and countries that would
be considered industrial
00:04:33.810 --> 00:04:35.290
or even post-industrial,
00:04:35.290 --> 00:04:38.710
is that as countries
develop and become wealthier
00:04:38.710 --> 00:04:41.680
you might have more women
entering into the workforce.
00:04:41.680 --> 00:04:43.820
You might have more family planning.
00:04:43.820 --> 00:04:45.780
Women have more control
over their destiny,
00:04:45.780 --> 00:04:49.890
get education longer, and
people just have fewer children.
00:04:49.890 --> 00:04:52.660
And so as people have fewer children
00:04:52.660 --> 00:04:54.330
you could see that the world that,
00:04:54.330 --> 00:04:56.490
especially we see this in industrial
00:04:56.490 --> 00:04:58.030
and post-industrial countries,
00:04:58.030 --> 00:05:00.280
the growth rate starts to come down.
00:05:00.280 --> 00:05:02.980
And so the aggregate growth
rate is coming down, arguably
00:05:02.980 --> 00:05:05.410
because more and more countries
are becoming wealthier,
00:05:05.410 --> 00:05:08.000
have better healthcare,
better rights for women.
00:05:08.000 --> 00:05:11.160
And we even see today that
when you look at countries
00:05:11.160 --> 00:05:16.160
that are developed being their
growth rate is around 1.2%
00:05:16.410 --> 00:05:18.680
while more economically developed nations
00:05:18.680 --> 00:05:20.767
aren't around 0.2%.
00:05:20.767 --> 00:05:23.120
So there's definitely that
correlation between the two.
00:05:23.120 --> 00:05:25.810
And of course, this growth
rate that you see in red
00:05:25.810 --> 00:05:28.290
is going to affect the
absolute population.
00:05:28.290 --> 00:05:31.070
And so it's no coincidence
that at the same time
00:05:31.070 --> 00:05:34.060
that the growth rate
started to go up like that.
00:05:34.060 --> 00:05:36.120
We see that the population
00:05:36.120 --> 00:05:38.630
in absolute terms starts to accelerate.
00:05:38.630 --> 00:05:42.320
And just over, let's say
the last hundred years
00:05:42.320 --> 00:05:45.300
we've gone from 1.6, 5 billion.
00:05:45.300 --> 00:05:47.260
I guess if we go back
a hundred years to 1920
00:05:47.260 --> 00:05:49.710
it looks like we're
approaching 2 billion folks.
00:05:49.710 --> 00:05:50.700
And now we're sitting
00:05:50.700 --> 00:05:53.140
at roughly seven and a half billion folks.
00:05:53.140 --> 00:05:55.540
So the world population roughly doubled
00:05:55.540 --> 00:05:59.810
over the, last let's 2000
years prior to this chart.
00:05:59.810 --> 00:06:04.560
But then over this chart
over just the last 270 years
00:06:04.560 --> 00:06:07.750
our world population has grown pretty much
00:06:07.750 --> 00:06:09.750
by a factor of 10.
00:06:09.750 --> 00:06:11.660
Now we don't know how
sustainable that would be
00:06:11.660 --> 00:06:13.540
if our growth rate were to continue,
00:06:13.540 --> 00:06:16.950
but it does look like that
growth rate is moderating
00:06:16.950 --> 00:06:19.140
and at least the projections in this chart
00:06:19.140 --> 00:06:22.790
have a starting to approach
11 billion, maybe over time
00:06:22.790 --> 00:06:26.090
12 billion and maybe stabilize
someplace around there.
00:06:26.090 --> 00:06:28.583
But it's an interesting
thing to think about.
|
Khan Kickoff Pep Talk: Brandi Chastain | https://www.youtube.com/watch?v=bGSCMJmbMUI | vtt | https://www.youtube.com/api/timedtext?v=bGSCMJmbMUI&ei=6VWUZeL9HYuWvdIPhKy4kAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2FE898555B3358B86E6C3ECC8259404C0600C23D.EEE8CCACDA0206F74A5B073F79ED0F126AB32E3F&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.521 --> 00:00:02.860
- Hello, Khan Academy students.
00:00:02.860 --> 00:00:04.038
This is Brandi Chastain,
00:00:04.038 --> 00:00:07.090
former U.S. Women's National Team member,
00:00:07.090 --> 00:00:10.068
Olympic gold medalist
and World Cup champion.
00:00:10.068 --> 00:00:13.991
And I'm here to say to you that
00:00:13.991 --> 00:00:17.090
what you're doing is not easy.
00:00:17.090 --> 00:00:19.970
Trying to learn in an adverse environment,
00:00:19.970 --> 00:00:23.700
to be a champion takes
a lot of determination,
00:00:23.700 --> 00:00:28.016
desire, resiliency, it
takes a lot of falling down
00:00:28.016 --> 00:00:29.496
and getting back up
00:00:29.496 --> 00:00:32.533
and I want you to know that anything
00:00:32.533 --> 00:00:35.988
that is worthwhile is worth fighting for,
00:00:35.988 --> 00:00:40.988
is worth getting dirty, it's
worth getting a couple scrapes.
00:00:41.070 --> 00:00:43.974
And if it were easy,
everybody would be doing it
00:00:43.974 --> 00:00:45.950
and it wouldn't be a big deal,
00:00:45.950 --> 00:00:47.420
but what you're doing is a big deal.
00:00:47.420 --> 00:00:50.555
You're challenging yourselves
to learn like champions,
00:00:50.555 --> 00:00:54.447
and to be a champion takes
time, it's a process,
00:00:54.447 --> 00:00:56.874
it's not always going to be smooth
00:00:56.874 --> 00:01:01.060
and most of the time success
isn't this upward ascension,
00:01:01.060 --> 00:01:04.310
straight line to gold medals.
00:01:04.310 --> 00:01:07.030
So remember that what you're doing
00:01:08.869 --> 00:01:12.540
is really a life's work
and a life's journey.
00:01:12.540 --> 00:01:15.560
And when you get to be my age, (chuckles)
00:01:15.560 --> 00:01:17.465
you'll understand that
maybe a little bit more,
00:01:17.465 --> 00:01:20.500
but you can look back and
say, "I stuck with it,
00:01:20.500 --> 00:01:24.479
it wasn't easy, sometimes
I wanted to give up".
00:01:24.479 --> 00:01:28.820
I know that along my journey
to playing in the Olympics
00:01:28.820 --> 00:01:31.501
and being on the World Cup team
00:01:31.501 --> 00:01:34.120
and scoring that final penalty kick goal,
00:01:34.120 --> 00:01:37.263
where I got to do a little celebrating,
00:01:39.690 --> 00:01:40.580
it wasn't easy.
00:01:40.580 --> 00:01:44.452
I was on the team, cut from the team.
00:01:44.452 --> 00:01:46.493
I made the team in a different position
00:01:46.493 --> 00:01:48.450
which I'd never played before.
00:01:48.450 --> 00:01:52.437
And when that was presented
to me, I had a choice.
00:01:52.437 --> 00:01:54.503
Did I wanna be on the team
00:01:54.503 --> 00:01:59.489
and try to make a contribution
to a positive outcome,
00:01:59.489 --> 00:02:02.610
or was I more prideful and say,
"No, that's not my position,
00:02:02.610 --> 00:02:03.930
I wanna play my position".
00:02:03.930 --> 00:02:06.550
And I realized that being on the team
00:02:06.550 --> 00:02:08.050
and having a chance to get
00:02:08.050 --> 00:02:10.052
into the game was really what I wanted.
00:02:10.052 --> 00:02:11.925
So I want you to remember
00:02:11.925 --> 00:02:16.925
that when things just
get tough, you got this.
00:02:17.770 --> 00:02:21.963
You got to remember, you
are talented, you're smart.
00:02:23.040 --> 00:02:26.062
We all have a competitor inside of us
00:02:26.062 --> 00:02:28.750
and you have to be willing to allow it
00:02:28.750 --> 00:02:32.555
to come out and don't
settle, never settle.
00:02:32.555 --> 00:02:35.448
Becoming a gold medalist is
definitely not about settling,
00:02:35.448 --> 00:02:39.038
and you in 2021, we'll be champions.
00:02:39.038 --> 00:02:42.730
So I'm going to hopefully give you
00:02:42.730 --> 00:02:44.555
your first gold medal ever.
00:02:44.555 --> 00:02:48.490
So if you bow your head,
here comes the gold medal.
00:02:48.490 --> 00:02:50.320
There it is.
00:02:50.320 --> 00:02:54.480
You are now on team
Brandi and we are strong
00:02:54.480 --> 00:02:57.960
and we are resilient
and we get the job done.
00:02:57.960 --> 00:02:59.551
So all the best to you in 2021.
00:02:59.551 --> 00:03:02.486
Hopefully at some point
we'll meet on a soccer field
00:03:02.486 --> 00:03:04.670
or somewhere else near you.
00:03:04.670 --> 00:03:05.503
Take care.
|
Types of catalysts | https://www.youtube.com/watch?v=5Tw9Yp-YuVU | vtt | https://www.youtube.com/api/timedtext?v=5Tw9Yp-YuVU&ei=6VWUZYC0GvTnxN8PjNCh4A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8AE68DDD9C6C45E11A180CC2B45852BAFEDDA4A4.90154CF410A6BD19FD198124FAB34A2DD78FCDC6&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.520 --> 00:00:02.240
- [Instructor] A catalyst
speeds up a reaction
00:00:02.240 --> 00:00:04.550
by lowering the activation energy.
00:00:04.550 --> 00:00:05.740
And there are many types of catalysts.
00:00:05.740 --> 00:00:07.630
And first we're going to look at enzymes
00:00:07.630 --> 00:00:10.984
which are biological catalysts.
00:00:10.984 --> 00:00:13.884
Let's say that this represents our enzyme,
00:00:13.884 --> 00:00:17.294
and the place where the reaction occurs
00:00:17.294 --> 00:00:19.677
is called the active site of the enzyme.
00:00:19.677 --> 00:00:23.160
So right in here, let's say
this is our active site.
00:00:23.160 --> 00:00:26.165
And then the substance that
reacts at the active site
00:00:26.165 --> 00:00:28.908
is called the substrate.
00:00:28.908 --> 00:00:33.298
So this little picture here
with two triangles together,
00:00:33.298 --> 00:00:36.382
that's the substrate for our reaction.
00:00:36.382 --> 00:00:37.700
In the next step,
00:00:37.700 --> 00:00:42.640
the substrate binds to the
enzyme at the active site.
00:00:42.640 --> 00:00:44.560
And when the substrate binds,
00:00:44.560 --> 00:00:46.940
the substrate can produce
changes in the shape
00:00:46.940 --> 00:00:49.732
of the active site, that
allow for better binding.
00:00:49.732 --> 00:00:52.366
So on the left here, we
can see how the shape
00:00:52.366 --> 00:00:55.367
of the active site changes slightly
00:00:55.367 --> 00:00:58.688
when the substrate binds to it.
00:00:58.688 --> 00:01:02.686
This formation of the
enzyme substrate complex
00:01:02.686 --> 00:01:06.562
is called the induced fit model.
00:01:06.562 --> 00:01:10.322
The substrate interacts with the enzyme
00:01:10.322 --> 00:01:13.926
through non-covalent
interactions in the active site.
00:01:13.926 --> 00:01:15.827
So things like hydrogen bonding
00:01:15.827 --> 00:01:18.299
or dipole-dipole interactions.
00:01:18.299 --> 00:01:20.618
Perhaps some of these
non-covalent interactions
00:01:20.618 --> 00:01:22.990
cause a shift in electron density
00:01:22.990 --> 00:01:24.001
which make it easier
00:01:24.001 --> 00:01:27.770
to reach the transition
state for the reaction.
00:01:27.770 --> 00:01:30.346
Therefore lowering the activation energy
00:01:30.346 --> 00:01:34.030
and speeding up the overall reaction.
00:01:34.030 --> 00:01:37.050
Next let's say the bond between
the two triangles breaks
00:01:37.050 --> 00:01:39.410
and we get our two products here.
00:01:39.410 --> 00:01:41.520
So two individual triangles.
00:01:41.520 --> 00:01:44.725
And the enzyme active site
goes back to the original shape
00:01:44.725 --> 00:01:48.750
and it's ready to
catalyze another reaction.
00:01:48.750 --> 00:01:51.145
Next, let's talk about
a homogeneous catalyst,
00:01:51.145 --> 00:01:52.813
which is a catalyst that's present
00:01:52.813 --> 00:01:57.256
in the same phase as the
reactants in a reaction mixture.
00:01:57.256 --> 00:02:01.014
So let's look at the hydrolysis of sucrose
00:02:01.014 --> 00:02:04.803
to turn into glucose and fructose.
00:02:04.803 --> 00:02:06.850
This reaction can be catalyzed
00:02:06.850 --> 00:02:09.620
by the hydronium ion H30+.
00:02:09.620 --> 00:02:13.080
And since sucrose, our reactant
is an aqueous solution,
00:02:13.080 --> 00:02:14.922
and so as the hydronium ion,
00:02:14.922 --> 00:02:19.435
we can say that the hydronium
ion is a homogeneous catalyst.
00:02:19.435 --> 00:02:21.220
And it's a source of protons
00:02:21.220 --> 00:02:23.840
to catalyze this hydrolysis reaction.
00:02:23.840 --> 00:02:26.660
This is a drawing of the sucrose molecule,
00:02:26.660 --> 00:02:30.740
which is a disaccharide
composed of two monosaccharides.
00:02:30.740 --> 00:02:32.300
Glucose is over here on the left
00:02:32.300 --> 00:02:34.978
and fructose is over here on the right.
00:02:34.978 --> 00:02:37.804
And these two monosaccharides are joined
00:02:37.804 --> 00:02:39.418
by an ether linkage.
00:02:39.418 --> 00:02:41.586
So we can see, we can see this,
00:02:41.586 --> 00:02:43.290
this connection here, alright?
00:02:43.290 --> 00:02:46.227
This oxygen in between
our two monosaccharides
00:02:46.227 --> 00:02:47.740
isn't ether linkage.
00:02:47.740 --> 00:02:49.823
And ethers are fairly nonreactive.
00:02:50.965 --> 00:02:54.116
Since ethers are generally unreactive,
00:02:54.116 --> 00:02:57.700
the hydrolysis of sucrose
is a pretty slow reaction.
00:02:57.700 --> 00:03:00.870
And to speed it up, we need
to add an acid catalyst.
00:03:00.870 --> 00:03:02.360
So if we add an acid catalyst
00:03:02.360 --> 00:03:05.238
and we have hydronium
ions in aqueous solution,
00:03:05.238 --> 00:03:08.874
a lone pair of electrons
on the oxygen on the ether,
00:03:08.874 --> 00:03:10.258
will take this proton
00:03:10.258 --> 00:03:13.653
and these electrons move in to form water.
00:03:14.500 --> 00:03:15.805
Protonation of the oxygen,
00:03:15.805 --> 00:03:18.760
gives the oxygen a plus one formal charge.
00:03:18.760 --> 00:03:22.526
And allows an acid catalyzed
mechanism to proceed.
00:03:22.526 --> 00:03:24.530
And there are more steps to the mechanism
00:03:24.530 --> 00:03:28.860
but ultimately sucrose is
broken down to form glucose
00:03:28.860 --> 00:03:33.860
and fructose in this acid
catalyzed hydrolysis of sucrose.
00:03:34.690 --> 00:03:38.374
Honey bees actually have the
enzyme to convert sucrose
00:03:38.374 --> 00:03:43.374
which is table sugar,
into glucose and fructose.
00:03:43.450 --> 00:03:47.524
And since fructose is
sweeter than sucrose,
00:03:47.524 --> 00:03:51.220
honey is sweeter than table sugar.
00:03:51.220 --> 00:03:54.440
A heterogeneous catalyst is
a catalyst that's present
00:03:54.440 --> 00:03:55.590
in a different phase
00:03:55.590 --> 00:03:58.397
from the reactants in a reaction mixture.
00:03:58.397 --> 00:04:02.370
As an example, let's look
at a hydrogenation reaction.
00:04:02.370 --> 00:04:05.715
And this reaction ethene
reacts with hydrogen
00:04:05.715 --> 00:04:09.903
on a surface of platinum to form ethane.
00:04:09.903 --> 00:04:13.080
Now, since the platinum
is in the solid form
00:04:13.080 --> 00:04:15.843
and our reactants are
in the gaseous state,
00:04:15.843 --> 00:04:20.220
the platinum is an example
of a heterogeneous catalyst.
00:04:20.220 --> 00:04:23.610
So here in our picture, we have
our piece of platinum metal
00:04:23.610 --> 00:04:28.610
and both the ethene molecule
and hydrogen are adsorbed
00:04:29.165 --> 00:04:32.319
to the surface of the platinum metal.
00:04:32.319 --> 00:04:36.580
Next the bond between the
two hydrogen atoms breaks
00:04:36.580 --> 00:04:39.470
and we get the two individual
hydrogen atoms bonded
00:04:39.470 --> 00:04:41.930
to the surface of the platinum metal.
00:04:41.930 --> 00:04:43.360
Eventually these two hydrogens
00:04:43.360 --> 00:04:46.040
add across the double bond of ethene
00:04:46.040 --> 00:04:50.490
and form the ethane molecules C2H6.
00:04:50.490 --> 00:04:53.922
So the hydrogenation of
ethene to form ethane
00:04:53.922 --> 00:04:58.153
is catalyzed by the presence
of the platinum metal.
|
Multistep reaction energy profiles | https://www.youtube.com/watch?v=l4VCiJulLKw | vtt | https://www.youtube.com/api/timedtext?v=l4VCiJulLKw&ei=6VWUZdHJGqK-mLAPhaunkAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=3FF124B4B1EF52457C8F2CED6D357A6F91ACFC5B.EBC9CF1C72E1B8ECBD3E582BD5FC07A6F991553C&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:01.440
- [Instructor] Let's consider a reaction
00:00:01.440 --> 00:00:04.010
with the following multi-step mechanism.
00:00:04.010 --> 00:00:09.010
In step one, A reacts
with BC to form AC plus B.
00:00:09.670 --> 00:00:14.670
And in step two, AC reacts
with D to form A plus CD.
00:00:16.870 --> 00:00:19.050
If we add the two steps
of our mechanism together
00:00:19.050 --> 00:00:20.640
we can find the balanced equation
00:00:20.640 --> 00:00:23.130
for this hypothetical reaction.
00:00:23.130 --> 00:00:25.120
So we're gonna put all of our reactants
00:00:25.120 --> 00:00:27.560
on the left side here,
and we're gonna have
00:00:27.560 --> 00:00:30.800
all of our products on the right side.
00:00:30.800 --> 00:00:33.130
And we can see that AC is on the left
00:00:33.130 --> 00:00:36.450
and it's on the right side,
so we can cancel that out.
00:00:36.450 --> 00:00:38.600
A is also in the left and the right side,
00:00:38.600 --> 00:00:40.530
so we can cancel that out.
00:00:40.530 --> 00:00:45.360
So the overall equation would be BC plus D
00:00:46.940 --> 00:00:51.673
goes to B plus CD.
00:00:56.002 --> 00:00:58.850
We've just seen that BC
and D are our reactants
00:01:01.220 --> 00:01:05.480
and B and CD are the products
00:01:05.480 --> 00:01:07.980
for this hypothetical reaction.
00:01:07.980 --> 00:01:11.550
If we look at the mechanism,
A is there in the beginning
00:01:11.550 --> 00:01:13.330
and A is there in the end.
00:01:13.330 --> 00:01:16.040
But A is not a reactant or a product,
00:01:16.040 --> 00:01:19.363
therefore A must be a catalyst.
00:01:20.600 --> 00:01:24.260
Something else that's not a
reactant or a product is AC.
00:01:24.260 --> 00:01:26.150
You notice how AC was generated
00:01:26.150 --> 00:01:27.740
in the first step of our mechanism,
00:01:27.740 --> 00:01:31.630
and then AC is used up in the
second step of the mechanism.
00:01:31.630 --> 00:01:36.630
Therefore AC must be the
intermediate for this reaction.
00:01:41.860 --> 00:01:43.810
Next, let's look at the energy profile
00:01:43.810 --> 00:01:45.720
for this multi-step reaction.
00:01:45.720 --> 00:01:48.820
Energy profiles usually have
potential energy in the y-axis
00:01:48.820 --> 00:01:51.640
and then reaction progress on the x-axis.
00:01:51.640 --> 00:01:55.270
So as we move to the right on the x-axis,
00:01:55.270 --> 00:01:56.963
the reaction is occurring.
00:01:58.310 --> 00:02:00.750
This first line on our energy profile
00:02:00.750 --> 00:02:03.750
represents the energy
level of our reactants,
00:02:03.750 --> 00:02:06.330
which are BC and D.
00:02:06.330 --> 00:02:10.890
So let's go ahead and show
the bond between B and C.
00:02:11.750 --> 00:02:14.980
And then we also have D present.
00:02:14.980 --> 00:02:17.140
Our catalyst is also present
00:02:17.140 --> 00:02:19.210
at the very beginning of our reactions.
00:02:19.210 --> 00:02:23.883
So I'll go ahead and draw in
A above our two reactants.
00:02:26.408 --> 00:02:29.870
We can see in our energy
profile that we have two hills.
00:02:29.870 --> 00:02:32.440
The first Hill corresponds
to the first step
00:02:32.440 --> 00:02:34.190
of the mechanism and the second hill
00:02:34.190 --> 00:02:37.090
corresponds to the second step.
00:02:37.090 --> 00:02:40.950
So the peak of the first
hill is the transition state
00:02:40.950 --> 00:02:44.250
for the first step of the mechanism.
00:02:44.250 --> 00:02:47.330
And we can see in the first
step that the catalyst A,
00:02:47.330 --> 00:02:50.510
is colliding with BC or reacting with BC
00:02:50.510 --> 00:02:53.490
to form our intermediate AC.
00:02:53.490 --> 00:02:58.490
So A must collide with BC
and at the transition state,
00:02:59.030 --> 00:03:02.370
the bond between B and C is breaking,
00:03:02.370 --> 00:03:07.370
and at the same time, the bond
between A and C is forming.
00:03:10.380 --> 00:03:12.760
We would still have reactant D present
00:03:12.760 --> 00:03:14.330
at the top of this hill too.
00:03:14.330 --> 00:03:17.410
So I'll go ahead and draw in D here.
00:03:17.410 --> 00:03:22.410
When a collides with BC,
the collision has to have
00:03:22.660 --> 00:03:27.660
enough kinetic energy to
overcome the activation energy
00:03:28.280 --> 00:03:31.270
necessary for this reaction to occur.
00:03:31.270 --> 00:03:33.530
And on this energy profile,
00:03:33.530 --> 00:03:36.520
the activation energy is
the difference in energy
00:03:36.520 --> 00:03:41.520
between the reactants
and the transition state,
00:03:42.440 --> 00:03:44.000
so the very peak of the hill.
00:03:44.000 --> 00:03:46.900
So this difference in energy,
00:03:46.900 --> 00:03:49.310
corresponds to the activation energy
00:03:49.310 --> 00:03:53.403
for the first step of the
mechanism which we will call Ea1.
00:03:54.890 --> 00:03:57.760
If we assume that the collision
has enough kinetic energy
00:03:57.760 --> 00:04:00.260
to overcome the activation energy,
00:04:00.260 --> 00:04:04.610
we'll form our intermediate
AC, and we'd also form B.
00:04:04.610 --> 00:04:06.650
So let's go ahead and show the bond
00:04:06.650 --> 00:04:09.960
between A and C has now been formed.
00:04:09.960 --> 00:04:12.380
So this valley here between our two hills
00:04:12.380 --> 00:04:16.330
represents the energy
level of the intermediate.
00:04:16.330 --> 00:04:18.120
We would also have be present,
00:04:18.120 --> 00:04:20.990
so I can go ahead and
I'll just write in B here.
00:04:20.990 --> 00:04:23.130
And then we still have some D present,
00:04:23.130 --> 00:04:25.290
D still hasn't reacted yet.
00:04:25.290 --> 00:04:27.803
So I'll go ahead and draw in D as well.
00:04:30.440 --> 00:04:31.970
Next we're ready for the second hill
00:04:31.970 --> 00:04:34.360
or the second step of our mechanism.
00:04:34.360 --> 00:04:39.060
In the second step, AC the
intermediate AC reacts with D
00:04:39.060 --> 00:04:41.840
to form A and CD.
00:04:41.840 --> 00:04:45.160
So the top of this second hill
would be the transition state
00:04:45.160 --> 00:04:47.240
for this second step.
00:04:47.240 --> 00:04:51.970
So we can show the bond
between A and C braking,
00:04:51.970 --> 00:04:56.970
and at the same time the bond
between C and D is forming.
00:04:58.980 --> 00:05:02.120
The difference in energy
between the energy
00:05:02.120 --> 00:05:05.540
of the intermediate and the
energy of the transition state
00:05:05.540 --> 00:05:07.660
represents the activation energy
00:05:07.660 --> 00:05:09.900
for the second step of the mechanism,
00:05:09.900 --> 00:05:12.007
which we will call Ea2.
00:05:14.650 --> 00:05:19.390
So AC and D must collide
with enough kinetic energy
00:05:19.390 --> 00:05:24.390
to overcome the activation
energy for this second step.
00:05:24.450 --> 00:05:28.100
If AC and D collide with
enough kinetic energy,
00:05:28.100 --> 00:05:31.760
we would produce A and CD.
00:05:31.760 --> 00:05:35.130
So this line at the end here
represents the energy level
00:05:35.130 --> 00:05:37.910
of our products.
00:05:37.910 --> 00:05:42.910
So CD is one of our products,
so we'll write that in here.
00:05:43.530 --> 00:05:46.600
And remember B is our other products,
00:05:46.600 --> 00:05:51.330
which we formed from the
first step of the mechanisms.
00:05:51.330 --> 00:05:55.640
So let's go ahead and
write in here B plus CD.
00:05:55.640 --> 00:05:58.180
And we also reformed our catalyst,
00:05:58.180 --> 00:06:01.540
so A would be present here as well.
00:06:01.540 --> 00:06:04.910
Next let's compare the
first activation energy Ea1
00:06:04.910 --> 00:06:08.040
with the second activation energy Ea2.
00:06:08.040 --> 00:06:10.490
Looking at the energy
profile we can see that Ea1
00:06:11.741 --> 00:06:14.587
has a much greater
activation energy than Ea2.
00:06:15.550 --> 00:06:20.550
So let's go ahead and write
Ea1 is greater than Ea2.
00:06:20.890 --> 00:06:24.490
The smaller the activation
energy, the faster the reaction,
00:06:24.490 --> 00:06:26.910
and since there's a
smaller activation energy
00:06:26.910 --> 00:06:28.440
for the second step,
00:06:28.440 --> 00:06:32.320
the second step must be
the faster of the two.
00:06:32.320 --> 00:06:35.440
Since the first step has the
higher activation energy,
00:06:35.440 --> 00:06:40.440
the first step must be slow
compared to the second step.
00:06:42.150 --> 00:06:45.070
Since the first step of the
mechanism is the slow step,
00:06:45.070 --> 00:06:48.083
the first step is the
rate determining step.
00:06:48.960 --> 00:06:51.620
Finally, let's Find the
overall change in energy
00:06:51.620 --> 00:06:54.020
for our reaction.
00:06:54.020 --> 00:06:57.320
So to find the overall change
in energy, that's Delta E,
00:06:57.320 --> 00:06:59.640
which is final minus initial.
00:06:59.640 --> 00:07:02.220
So that would be the
energy of the products
00:07:02.220 --> 00:07:05.870
minus the energy of the reactants.
00:07:05.870 --> 00:07:09.320
So the energy level of
the products is right here
00:07:09.320 --> 00:07:11.100
and then the energy level of the reactants
00:07:11.100 --> 00:07:11.933
is at the beginning.
00:07:11.933 --> 00:07:14.210
So let me just extend
this dashed line here
00:07:14.210 --> 00:07:16.570
so we can better compare the two.
00:07:16.570 --> 00:07:18.540
Representing Delta E on a graph,
00:07:18.540 --> 00:07:20.300
it would be the difference in energy
00:07:20.300 --> 00:07:22.760
between these two lines.
00:07:22.760 --> 00:07:24.750
And since the energy of the products
00:07:24.750 --> 00:07:27.650
is greater than the
energy of the reactants,
00:07:27.650 --> 00:07:29.930
we would be subtracting a smaller number
00:07:29.930 --> 00:07:31.210
from a larger number
00:07:31.210 --> 00:07:34.360
and therefore Delta E would be positive
00:07:34.360 --> 00:07:37.010
for this hypothetical reaction.
00:07:37.010 --> 00:07:39.290
And since Delta E is positive,
00:07:39.290 --> 00:07:43.563
we know that this reaction
is an endothermic reaction.
|
Collision theory and the Maxwell–Boltzmann distribution | https://www.youtube.com/watch?v=L7R1HjA8BQ4 | vtt | https://www.youtube.com/api/timedtext?v=L7R1HjA8BQ4&ei=6VWUZdqaIMXTxN8Pj4mRqAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D363599B5F08862F2EC3F41D2BD7256D7CE4BAB0.4DB5322681EDB2DBE66D2A55C943445C2BD60D5C&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.400 --> 00:00:02.233
- [Instructor] Collision theory
00:00:02.233 --> 00:00:05.130
can be related to
Maxwell-Boltzmann distributions.
00:00:05.130 --> 00:00:07.590
And first we'll start
with collision theory.
00:00:07.590 --> 00:00:09.970
Collision theory says that
particles must collide
00:00:09.970 --> 00:00:13.860
in the proper orientation and
with enough kinetic energy
00:00:13.860 --> 00:00:17.370
to overcome the activation energy barrier.
00:00:17.370 --> 00:00:21.130
So let's look at the reaction
where A reacts with B and C
00:00:21.130 --> 00:00:24.420
to form AB plus C.
00:00:24.420 --> 00:00:28.240
On an energy profile, we
have the reactants over here
00:00:28.240 --> 00:00:29.580
in the left.
00:00:29.580 --> 00:00:33.660
So A, atom A is colored red,
00:00:33.660 --> 00:00:36.590
and we have molecule BC over here,
00:00:36.590 --> 00:00:39.790
So these two particles must collide
00:00:39.790 --> 00:00:43.150
for the reaction to occur,
00:00:43.150 --> 00:00:45.400
and they must collide with enough energy
00:00:45.400 --> 00:00:48.070
to overcome the activation energy barrier.
00:00:48.070 --> 00:00:51.210
So the activation energy
on an energy profile
00:00:51.210 --> 00:00:52.250
is the difference in energy
00:00:52.250 --> 00:00:56.010
between the peak here, which
is the transition state
00:00:56.010 --> 00:00:57.610
and the energy of the reactants.
00:00:57.610 --> 00:01:01.810
So this energy here is
our activation energy.
00:01:01.810 --> 00:01:04.030
The minimum amount of energy necessary
00:01:04.030 --> 00:01:06.770
for the reaction to occur.
00:01:06.770 --> 00:01:09.830
So if these particles
collide with enough energy,
00:01:09.830 --> 00:01:13.920
we can just get over this
activation energy barrier
00:01:13.920 --> 00:01:17.653
and the reactions can turn
into our two products.
00:01:20.020 --> 00:01:22.090
If our reactant particles
don't hit each other
00:01:22.090 --> 00:01:25.340
with enough energy, they
simply bounce off of each other
00:01:25.340 --> 00:01:27.070
and our reaction never occurs.
00:01:27.070 --> 00:01:30.820
We never overcome this
activation energy barrier.
00:01:30.820 --> 00:01:33.420
As an analogy, let's think
about hitting a golf ball.
00:01:33.420 --> 00:01:35.310
So let's imagine we have a hill,
00:01:35.310 --> 00:01:37.150
and on the right side of the hill,
00:01:37.150 --> 00:01:39.050
somewhere is the hole down here,
00:01:39.050 --> 00:01:42.700
and the left side of the
hill is our golf ball.
00:01:42.700 --> 00:01:45.720
So we know we have to hit this
golf ball with enough force
00:01:45.720 --> 00:01:47.920
to give it enough kinetic energy
00:01:47.920 --> 00:01:49.970
for it to reach the top of the hill
00:01:49.970 --> 00:01:53.050
and to roll over the hill
and go into the hole.
00:01:53.050 --> 00:01:55.320
So we can imagine this hill
00:01:55.320 --> 00:01:58.580
as being a hill of potential energy.
00:01:58.580 --> 00:02:02.080
And this golf ball needs to
have enough kinetic energy
00:02:02.080 --> 00:02:06.353
to turn into enough potential
energy to go over the hill.
00:02:09.390 --> 00:02:11.230
If we don't hit our golf ball hard enough,
00:02:11.230 --> 00:02:13.730
it might not have enough
energy to go over the hill.
00:02:13.730 --> 00:02:16.160
So if we hit it softly,
it might just roll halfway
00:02:16.160 --> 00:02:18.470
up the hill and roll back down again.
00:02:18.470 --> 00:02:23.470
Kinetic energy is equal to 1/2 MV squared.
00:02:24.770 --> 00:02:26.630
And so M would be the
mass of the golf ball
00:02:26.630 --> 00:02:28.790
and V would be the velocity.
00:02:28.790 --> 00:02:30.350
So we have to hit it with enough force
00:02:30.350 --> 00:02:33.770
so it has enough as a high enough velocity
00:02:33.770 --> 00:02:35.190
to have a high enough kinetic energy
00:02:35.190 --> 00:02:37.083
to get over the hill.
00:02:38.740 --> 00:02:40.160
Let's apply collision theory
00:02:40.160 --> 00:02:42.810
to a Maxwell-Boltzmann distribution.
00:02:42.810 --> 00:02:45.370
Usually a Maxwell-Boltzmann distribution
00:02:45.370 --> 00:02:48.400
has fractional particles or
relative numbers of particles
00:02:48.400 --> 00:02:52.790
on the y-axis and particle
speed on the x-axis.
00:02:52.790 --> 00:02:55.160
And a Maxwell-Boltzmann distribution
00:02:55.160 --> 00:03:00.160
shows us the range of speeds
available to the particles
00:03:01.380 --> 00:03:02.840
in a sample of gas.
00:03:02.840 --> 00:03:04.160
So let's say we have,
00:03:04.160 --> 00:03:06.420
here's a particulate diagram over here.
00:03:06.420 --> 00:03:07.820
Let's say we have a sample of gas
00:03:07.820 --> 00:03:10.290
at a particular temperature T.
00:03:10.290 --> 00:03:12.980
These particles aren't
traveling at the same speed,
00:03:12.980 --> 00:03:15.790
there's a range of
speeds available to them.
00:03:15.790 --> 00:03:19.820
So one particle might be
traveling really slowly
00:03:19.820 --> 00:03:22.090
so we'll draw a very short arrow here.
00:03:22.090 --> 00:03:24.450
A few more might be
traveling a little faster,
00:03:24.450 --> 00:03:28.190
so we'll draw the arrow longer
to indicate a faster speed.
00:03:28.190 --> 00:03:31.310
And maybe one particle
is traveling the fastest.
00:03:31.310 --> 00:03:34.293
So we'll give this
particle the longest arrow.
00:03:36.130 --> 00:03:38.400
We can think about the
area under the curve
00:03:38.400 --> 00:03:40.310
for a Maxwell-Boltzmann distribution
00:03:40.310 --> 00:03:43.850
as representing all of the
particles in our sample.
00:03:43.850 --> 00:03:47.920
So we had this one particle
here moving very slowly,
00:03:47.920 --> 00:03:50.450
and so if we look at
our curve and we think
00:03:50.450 --> 00:03:52.120
about the area under the curve
00:03:52.120 --> 00:03:54.073
that's at a low particle speed,
00:03:54.920 --> 00:03:57.410
this area is smaller than
other parts of the curve.
00:03:57.410 --> 00:03:59.640
So that's represented here
by only this one particle
00:03:59.640 --> 00:04:01.490
moving very slowly.
00:04:01.490 --> 00:04:03.620
We think about this
next part of the curve,
00:04:03.620 --> 00:04:06.610
most, this is a large
amount of area in here
00:04:06.610 --> 00:04:09.640
and these particles are
traveling at a higher speed.
00:04:09.640 --> 00:04:14.640
So maybe these three
particles here would represent
00:04:15.550 --> 00:04:17.870
the particles moving at a higher speed.
00:04:17.870 --> 00:04:21.670
And then finally, we had
this one particle here,
00:04:21.670 --> 00:04:23.610
We drew this arrow longer than the others.
00:04:23.610 --> 00:04:26.440
So this particle's traveling
faster than the other one.
00:04:26.440 --> 00:04:29.750
So maybe this area under the curve up here
00:04:29.750 --> 00:04:31.853
is represented by that one particle.
00:04:33.520 --> 00:04:34.890
We know from collision theory,
00:04:34.890 --> 00:04:37.760
that particles have to
have enough kinetic energy
00:04:37.760 --> 00:04:42.760
to overcome the activation
energy for a reaction to occur.
00:04:42.850 --> 00:04:46.610
So we can draw a line
representing the activation energy
00:04:46.610 --> 00:04:48.840
on a Maxwell-Boltzmann distribution.
00:04:48.840 --> 00:04:52.722
So if I draw this line,
this dotted line right here,
00:04:52.722 --> 00:04:57.060
this represents my activation energy.
00:04:57.060 --> 00:04:59.600
And instead of particle
speed, you could think
00:04:59.600 --> 00:05:02.400
about the x-axis as being
kinetic energy if you want.
00:05:02.400 --> 00:05:05.480
So the faster a particle is traveling,
00:05:05.480 --> 00:05:07.690
the higher its kinetic energy.
00:05:07.690 --> 00:05:11.390
And so the area under the curve
00:05:11.390 --> 00:05:13.010
to the right of this dash line,
00:05:13.010 --> 00:05:14.640
this represents all of the particles
00:05:14.640 --> 00:05:19.640
that have enough kinetic energy
for this reaction to occur.
00:05:21.820 --> 00:05:24.300
Next, let's think about what
happens to the particles
00:05:24.300 --> 00:05:27.770
in our sample when we
increase the temperature.
00:05:27.770 --> 00:05:29.240
So when we increase the temperature,
00:05:29.240 --> 00:05:32.350
the Maxwell-Boltzmann
distribution changes.
00:05:32.350 --> 00:05:36.030
So what happens is the peak height drops
00:05:36.030 --> 00:05:40.360
and our Maxwell-Boltzmann
distribution curve gets broader.
00:05:40.360 --> 00:05:43.373
So it looks something like
this at a higher temperature.
00:05:45.380 --> 00:05:47.210
So we still have some particles traveling
00:05:47.210 --> 00:05:48.820
at relatively low speeds, right?
00:05:48.820 --> 00:05:50.440
Remember it's the area under the curve.
00:05:50.440 --> 00:05:53.583
So maybe that's represented
by this one particle here,
00:05:54.440 --> 00:05:56.520
and next, let's think about the area
00:05:56.520 --> 00:06:00.180
to the left of this dash line for Ea.
00:06:00.180 --> 00:06:02.750
So we want to make these
particles green here
00:06:02.750 --> 00:06:05.180
as we have some particles traveling
00:06:05.180 --> 00:06:06.510
a little bit of faster speeds.
00:06:06.510 --> 00:06:09.250
So let me go ahead and draw
these arrows a little bit longer
00:06:09.250 --> 00:06:12.330
but notice what happens to
the right of this dash line.
00:06:12.330 --> 00:06:14.880
We think about the area under the curve
00:06:14.880 --> 00:06:17.960
for the magenta curve.
00:06:17.960 --> 00:06:21.350
Notice how the area is bigger
than in the previous example.
00:06:21.350 --> 00:06:24.450
So maybe this time we have
these two particles here
00:06:24.450 --> 00:06:25.900
traveling at a faster speed.
00:06:25.900 --> 00:06:28.150
So I'm gonna draw these arrows longer
00:06:28.150 --> 00:06:30.270
to indicate they're
traveling at a faster speed.
00:06:30.270 --> 00:06:33.780
And since they're to the
right of this dash line here,
00:06:33.780 --> 00:06:36.690
both of these particles
have enough kinetic energy
00:06:36.690 --> 00:06:40.840
to overcome the activation
energy for our reaction.
00:06:40.840 --> 00:06:44.530
So we can see when you
increase the temperature,
00:06:44.530 --> 00:06:46.730
you increase the number of particles
00:06:46.730 --> 00:06:48.580
that have enough kinetic energy
00:06:48.580 --> 00:06:51.323
to overcome the activation energy.
00:06:52.840 --> 00:06:54.090
It's important to point out
00:06:54.090 --> 00:06:56.770
that since the number of
particles hasn't changed,
00:06:56.770 --> 00:06:59.480
all we've done is increase
the temperature here,
00:06:59.480 --> 00:07:02.360
the area under the curve remains the same.
00:07:02.360 --> 00:07:06.420
So the area under the curve
for the curve in yellow,
00:07:06.420 --> 00:07:08.880
is the same as the area under the curve
00:07:08.880 --> 00:07:12.010
for the one drawn in magenta.
00:07:12.010 --> 00:07:14.640
The difference of course
is the one in magenta
00:07:14.640 --> 00:07:15.950
is at a higher temperature,
00:07:15.950 --> 00:07:18.370
and therefore there are more
particles with enough energy
00:07:18.370 --> 00:07:20.790
to overcome the activation energy.
00:07:20.790 --> 00:07:23.030
So increasing the temperature
00:07:23.030 --> 00:07:25.783
increases the rate of reaction.
|
The pre-equilibrium approximation | https://www.youtube.com/watch?v=4czm7qIbUjA | vtt | https://www.youtube.com/api/timedtext?v=4czm7qIbUjA&ei=6VWUZZKpIO2ghcIPut6P-AU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7625ED8AE39F62B94011FE083770E9A959D32D34.2BB13B67426D0DF71DB252377189AE0E12393499&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:02.370
- [Instructor] The
Pre-equilibrium Approximation
00:00:02.370 --> 00:00:03.770
is used to find the rate law
00:00:03.770 --> 00:00:06.740
for a mechanism with a fast initial step.
00:00:06.740 --> 00:00:08.940
As an example, let's look
at the reaction between
00:00:08.940 --> 00:00:11.383
nitric oxide and bromine.
00:00:12.770 --> 00:00:14.310
In the first step of the mechanism,
00:00:14.310 --> 00:00:17.323
nitric oxide combines with
bromine to form NOBr2.
00:00:18.663 --> 00:00:20.560
And in the second step of the mechanism,
00:00:20.560 --> 00:00:25.323
NOBr2 reacts with NO to
form our product 2NOBr.
00:00:28.570 --> 00:00:30.530
NOBr2 is generated
00:00:30.530 --> 00:00:33.400
from the first elementary
step of the mechanism.
00:00:33.400 --> 00:00:36.960
And then NOBr2 is used
up in the second step.
00:00:36.960 --> 00:00:39.790
Since NOBr2 wasn't there in the beginning
00:00:39.790 --> 00:00:41.270
and it's not there in the end,
00:00:41.270 --> 00:00:44.973
we call NOBr2 an intermediate.
00:00:50.310 --> 00:00:53.100
The first step of the mechanism is fast.
00:00:53.100 --> 00:00:55.360
And the second step of
the mechanism is slow.
00:00:55.360 --> 00:00:57.830
Since the second step of
the mechanism is slow,
00:00:57.830 --> 00:01:00.640
this is the rate determining step.
00:01:00.640 --> 00:01:04.420
And we can write the rate
law for the overall reaction
00:01:04.420 --> 00:01:07.540
by writing the rate law for
this elementary reaction
00:01:07.540 --> 00:01:10.750
that makes up step two of our mechanism.
00:01:10.750 --> 00:01:14.760
So we can write the rate
of reaction is equal to
00:01:14.760 --> 00:01:19.220
for step two, our rate constant is K2.
00:01:19.220 --> 00:01:21.940
And we multiply K2, the rate constant,
00:01:21.940 --> 00:01:24.460
by the concentration of our two reactants,
00:01:24.460 --> 00:01:27.253
which would be the concentration of NOBr2,
00:01:29.320 --> 00:01:32.323
and the concentration of NO.
00:01:33.370 --> 00:01:36.300
Since the coefficients
in our balanced equation
00:01:36.300 --> 00:01:40.400
are ones for NOBr2 and
one and a one for NO,
00:01:40.400 --> 00:01:41.790
we can take the coefficients
00:01:41.790 --> 00:01:44.860
and turn them into
exponents in our rate law.
00:01:44.860 --> 00:01:48.763
So we can do this because this
is an elementary reaction.
00:01:50.490 --> 00:01:52.320
However, we can't leave the rate law
00:01:52.320 --> 00:01:53.730
for the overall reaction,
00:01:53.730 --> 00:01:57.427
in terms of the concentration
of our intermediate, NOBr2.
00:01:58.360 --> 00:02:00.430
It's preferable to have rate laws
00:02:00.430 --> 00:02:03.230
written in terms of the
concentration of our reactants,
00:02:03.230 --> 00:02:04.447
which were NO and Br2.
00:02:07.430 --> 00:02:09.550
So we need some way of substituting N
00:02:09.550 --> 00:02:11.923
for the concentration of NOBr2.
00:02:13.832 --> 00:02:15.860
And we can do that by assuming that
00:02:15.860 --> 00:02:19.110
the first elementary step in our mechanism
00:02:19.110 --> 00:02:22.430
comes to a fast equilibrium.
00:02:22.430 --> 00:02:27.430
So if we assume the first step
comes to a fast equilibrium,
00:02:27.470 --> 00:02:31.283
we can use the
Pre-equilibrium Approximation.
00:02:32.370 --> 00:02:34.070
If we assume that the first step
00:02:34.070 --> 00:02:39.070
comes to a fast equilibrium,
or a pre equilibrium,
00:02:39.080 --> 00:02:40.090
we know at equilibrium,
00:02:40.090 --> 00:02:42.340
the rate of the forward reaction
00:02:42.340 --> 00:02:45.630
is equal to the rate of
the reverse reaction.
00:02:45.630 --> 00:02:48.390
So in the forward reaction for step one,
00:02:48.390 --> 00:02:50.953
NO combines with Br2 to form NOBr2.
00:02:52.350 --> 00:02:54.216
And in the reverse reaction,
00:02:54.216 --> 00:02:59.216
NOBr2 breaks apart to form NO and Br2.
00:02:59.310 --> 00:03:03.750
So if the rate of the forward reaction
00:03:03.750 --> 00:03:08.750
is equal to the rate of the
reverse reaction at equilibrium,
00:03:11.180 --> 00:03:13.770
let's go ahead and write the rate laws
00:03:13.770 --> 00:03:16.453
for the forward and the reverse reaction.
00:03:17.610 --> 00:03:21.250
The rate constant for the
forward reaction is K1.
00:03:21.250 --> 00:03:22.340
So we can go ahead and write
00:03:22.340 --> 00:03:25.810
the rate of the forward
reaction is equal to K1.
00:03:25.810 --> 00:03:29.730
And our two reactants are NO and Br2.
00:03:29.730 --> 00:03:33.110
So we have K1 times the
concentration of NO,
00:03:33.110 --> 00:03:36.260
times the concentration of Br2.
00:03:36.260 --> 00:03:38.640
Since the coefficients
in our balanced equation
00:03:38.640 --> 00:03:40.670
are both ones for these two reactants,
00:03:40.670 --> 00:03:43.040
we can raise the power of
these two concentrations
00:03:43.040 --> 00:03:44.070
to the first power.
00:03:44.070 --> 00:03:47.620
Since this is an elementary
reaction, we can do this.
00:03:47.620 --> 00:03:50.210
And we set this rate
of the forward reaction
00:03:50.210 --> 00:03:52.710
equal to the rate of the reverse reaction.
00:03:52.710 --> 00:03:56.600
The reverse reaction has a
rate constant of K minus one,
00:03:56.600 --> 00:04:00.750
and we have only NOBr2 with
a coefficient of one in it.
00:04:00.750 --> 00:04:02.360
So we multiply K minus one
00:04:02.360 --> 00:04:07.360
times the concentration of
NOBr2, to the first power.
00:04:09.150 --> 00:04:11.440
Next, our goal is to substitute N
00:04:11.440 --> 00:04:14.780
for the concentration of our intermediate.
00:04:14.780 --> 00:04:17.380
And so we can divide both sides
00:04:17.380 --> 00:04:20.480
of the equation by K minus one.
00:04:20.480 --> 00:04:22.330
So if we decide if we divide
00:04:22.330 --> 00:04:24.980
both sides of the equation by K minus one,
00:04:24.980 --> 00:04:27.460
on the right side, K
minus one cancels out.
00:04:27.460 --> 00:04:32.300
And we get that the concentration
of our intermediate NOBr2,
00:04:32.300 --> 00:04:33.780
is equal to K one
00:04:33.780 --> 00:04:36.870
times the concentration
of NO to the first power,
00:04:36.870 --> 00:04:39.520
times the concentration
of Br2 to the first power,
00:04:39.520 --> 00:04:42.410
divided by K minus one.
00:04:42.410 --> 00:04:44.730
Next, we can substitute all of this in
00:04:44.730 --> 00:04:48.083
for the concentration of our intermediate.
00:04:49.240 --> 00:04:52.930
That gives us the rate
of reaction is equal to,
00:04:52.930 --> 00:04:54.670
we still have this K2 in here,
00:04:54.670 --> 00:04:57.180
so we need to make sure to include it.
00:04:57.180 --> 00:04:59.890
And we're gonna substitute everything in
00:04:59.890 --> 00:05:02.410
all of this in for the
concentration of our intermediate.
00:05:02.410 --> 00:05:05.773
So that would be times K one,
00:05:07.000 --> 00:05:10.440
times the concentration
of NO to the first power,
00:05:10.440 --> 00:05:14.680
times the concentration
of Br2 to the first power,
00:05:14.680 --> 00:05:17.350
divided by K minus one.
00:05:17.350 --> 00:05:18.720
And then we still have this
00:05:18.720 --> 00:05:20.930
concentration of NO to the first power.
00:05:20.930 --> 00:05:25.310
So we have to make sure to
include that in our rate law.
00:05:25.310 --> 00:05:27.810
Let's think about what we would get
00:05:27.810 --> 00:05:30.650
if we multiply two constants together
00:05:30.650 --> 00:05:32.410
and then divide by a third constant.
00:05:32.410 --> 00:05:35.150
So multiplying K2 times K1,
00:05:35.150 --> 00:05:37.120
and then we divide by K minus one,
00:05:37.120 --> 00:05:39.310
that would just give us another constant,
00:05:39.310 --> 00:05:42.040
which we could just call K.
00:05:42.040 --> 00:05:46.350
So K is now the rate constant
for the overall reaction.
00:05:46.350 --> 00:05:48.990
So we have the rate law
for the overall reaction
00:05:48.990 --> 00:05:50.210
is equal to K,
00:05:50.210 --> 00:05:52.160
times the concentration of
00:05:52.160 --> 00:05:56.030
we have NO to the first power
times NO to the first power,
00:05:56.030 --> 00:06:00.470
which is just the concentration
of NO to the second power.
00:06:00.470 --> 00:06:02.310
And we still have to include
00:06:02.310 --> 00:06:06.130
the concentration of
bromine to the first power.
00:06:06.130 --> 00:06:10.600
So now we have a rate law
for our overall reaction
00:06:10.600 --> 00:06:13.640
in terms of the concentration
of our two reactants.
00:06:13.640 --> 00:06:16.500
The rate of reaction is
equal to the rate constant K,
00:06:16.500 --> 00:06:18.730
times the concentration of NO squared,
00:06:18.730 --> 00:06:21.553
times the concentration of
bromine to the first power.
00:06:22.980 --> 00:06:25.190
The experimentally determined rate law
00:06:25.190 --> 00:06:27.350
matches the rate law that we found
00:06:27.350 --> 00:06:31.157
using the Pre-equilibrium Approximation.
00:06:31.157 --> 00:06:33.190
And if you look at the coefficients
00:06:33.190 --> 00:06:34.880
for the overall equation,
00:06:34.880 --> 00:06:37.630
there's a two in front of NO
and a one in front of Br2,
00:06:38.480 --> 00:06:39.867
it might be tempting just to say,
00:06:39.867 --> 00:06:41.520
"Can't we just take those coefficients
00:06:41.520 --> 00:06:44.450
and turn them into exponents,
because in this case,
00:06:44.450 --> 00:06:47.640
they happen to match the
exponent in our rate law?"
00:06:47.640 --> 00:06:50.170
That's just a coincidence
for this reaction.
00:06:50.170 --> 00:06:53.060
We can't just take the coefficients
for an overall equation
00:06:53.060 --> 00:06:55.140
and turn them into
exponents in the rate law.
00:06:55.140 --> 00:06:57.750
We can only do that for
elementary reactions.
00:06:57.750 --> 00:06:59.350
Like the elementary reactions
00:06:59.350 --> 00:07:02.043
in the two steps of our mechanism.
00:07:02.960 --> 00:07:03.980
It's important to point out
00:07:03.980 --> 00:07:06.160
that if the rate of the forward reaction
00:07:06.160 --> 00:07:08.320
is equal to the rate of
the reverse reaction,
00:07:08.320 --> 00:07:10.461
the concentration of our intermediate,
00:07:10.461 --> 00:07:12.920
NOBr2 remains constant.
00:07:12.920 --> 00:07:17.920
And therefore we can use this
Pre-equilibrium Approximation
00:07:18.290 --> 00:07:20.580
to find the rate law for a reaction
00:07:20.580 --> 00:07:22.713
with a fast initial step.
|
Kinetics of radioactive decay | https://www.youtube.com/watch?v=Xnu--929bo4 | vtt | https://www.youtube.com/api/timedtext?v=Xnu--929bo4&ei=6VWUZcLVG4e3mLAP2vmG4AE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=660A23FFD381134253B85F9D0F446BA734A02570.3CBBEC6D213F32A9BBB77C6377DBAFB8FB9E9D3D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.240 --> 00:00:03.920
- [Instructor] Strontium-90
is a radioactive isotope
00:00:03.920 --> 00:00:05.743
that undergoes beta decay.
00:00:06.960 --> 00:00:10.230
Because radioactive decay
is a first-order process,
00:00:10.230 --> 00:00:13.773
radioactive isotopes
have constant half-lives.
00:00:15.450 --> 00:00:18.940
Half-life is symbolized by t1/2,
00:00:18.940 --> 00:00:22.580
and it's the time required
for 1/2 of a sample
00:00:22.580 --> 00:00:26.640
of a particular radioactive
isotope to decay.
00:00:26.640 --> 00:00:29.570
For example, the half-life of Strontium-90
00:00:29.570 --> 00:00:34.513
is equal to 28.8 years.
00:00:38.090 --> 00:00:40.250
Let's say we start with 10 grams
00:00:40.250 --> 00:00:45.250
of our Strontium-90 radioactive isotope.
00:00:45.270 --> 00:00:46.830
And on the y-axis,
00:00:46.830 --> 00:00:50.220
we're gonna put the mass of
our Strontium isotope in grams.
00:00:50.220 --> 00:00:53.260
And on the x-axis, we're
going to have time.
00:00:53.260 --> 00:00:56.230
So when time is equal to zero,
00:00:56.230 --> 00:00:59.483
we have 10 grams of our isotope.
00:01:00.810 --> 00:01:05.300
Since the half-life of
Strontium-90 is 28.8 years,
00:01:05.300 --> 00:01:09.130
if we wait 28.8 years,
00:01:09.130 --> 00:01:12.820
we'll go from 10 grams to five grams.
00:01:12.820 --> 00:01:17.820
So the next point on our
graph will be at five grams,
00:01:18.750 --> 00:01:23.260
and this time should be 28.8 years.
00:01:27.530 --> 00:01:30.720
If we wait another 28.8 years,
00:01:30.720 --> 00:01:33.300
we're gonna go from five
grams to half of that,
00:01:33.300 --> 00:01:35.350
which would be 2.5 grams.
00:01:35.350 --> 00:01:39.020
So the next point would be here at 2.5.
00:01:44.410 --> 00:01:47.230
If we wait another 28.8 years,
00:01:47.230 --> 00:01:50.393
we'd go from 2.5 grams down to 1.25,
00:01:52.350 --> 00:01:56.113
so approximately here on our graph.
00:01:57.180 --> 00:02:01.713
So this graph shows exponential decay.
00:02:03.130 --> 00:02:05.380
Let's say we were asked to find out
00:02:05.380 --> 00:02:08.300
how much of our radioactive
isotope Strontium is left
00:02:08.300 --> 00:02:11.940
after 115.2 years.
00:02:11.940 --> 00:02:15.790
So what we would do is take 115.2 years
00:02:15.790 --> 00:02:20.790
and divide that by the
half-life of 28.8 years.
00:02:21.960 --> 00:02:22.920
And by doing that,
00:02:22.920 --> 00:02:27.920
we realize that 115.2 is
really just four half-lives.
00:02:28.740 --> 00:02:30.270
So one approach with this problem
00:02:30.270 --> 00:02:32.360
would be starting with our 10 grams.
00:02:32.360 --> 00:02:36.030
And we think about one half-life
taking us to five grams,
00:02:36.030 --> 00:02:38.970
another half-life taking us to 2.5,
00:02:38.970 --> 00:02:41.250
another half-life taking us to 1.25,
00:02:42.520 --> 00:02:44.480
and then finally, one more half-life
00:02:44.480 --> 00:02:49.260
that takes us to 0.625 grams.
00:02:49.260 --> 00:02:51.330
So just doing the problem this way,
00:02:51.330 --> 00:02:55.760
we can see that's one, two,
three, four half-lives.
00:02:55.760 --> 00:02:56.920
So our final answer
00:02:56.920 --> 00:03:01.920
is 0.625 grams remain after 115.2 years.
00:03:03.770 --> 00:03:06.180
Another approach to do the same problem
00:03:06.180 --> 00:03:08.120
would be to start with our 10 grams,
00:03:08.120 --> 00:03:10.180
and we multiply that by 1/2
00:03:10.180 --> 00:03:13.230
to get the amount remaining
after one half-life.
00:03:13.230 --> 00:03:15.750
And we could do that three more times
00:03:15.750 --> 00:03:20.200
to get the amount that
remains after four half-lives.
00:03:20.200 --> 00:03:21.480
We could have also have written this
00:03:21.480 --> 00:03:26.480
as 10 times 1/2 to the fourth power
00:03:26.480 --> 00:03:29.500
since we needed to wait four half-lives.
00:03:29.500 --> 00:03:33.810
All these approaches will get
you the answer of 0.625 grams
00:03:33.810 --> 00:03:38.810
of our radioactive isotope
remaining after 115.2 years.
00:03:40.910 --> 00:03:44.300
For a chemical reaction with
reactant A that's first-order,
00:03:44.300 --> 00:03:46.710
the rate law says that
the rate of reaction
00:03:46.710 --> 00:03:48.540
is equal to the rate constant k
00:03:48.540 --> 00:03:52.623
times the concentration
of A to the first power.
00:03:53.580 --> 00:03:56.130
Since radioactive decay
is a first-order process,
00:03:56.130 --> 00:03:58.090
we can write that the rate of decay
00:03:58.090 --> 00:04:01.760
is equal to the rate constant
k times N to the first power,
00:04:01.760 --> 00:04:06.760
where N is the number of
radioactive nuclei in a sample.
00:04:07.420 --> 00:04:10.390
Since radioactive decay
is a first-order process,
00:04:10.390 --> 00:04:14.380
we can also use this equation
for the rate constant,
00:04:14.380 --> 00:04:16.610
which comes from first-order kinetics,
00:04:16.610 --> 00:04:20.320
which says that the rate
constant k is equal to 0.693
00:04:20.320 --> 00:04:22.283
divided by the half-life.
00:04:23.390 --> 00:04:26.250
For example, if we wanted
to find the rate constant
00:04:26.250 --> 00:04:29.840
for the radioactive decay of Strontium-90,
00:04:29.840 --> 00:04:34.840
the rate constant would be equal to 0.693
00:04:34.840 --> 00:04:38.060
divided by the half-life of Strontium-90,
00:04:38.060 --> 00:04:42.353
which we saw was 28.8 years.
00:04:43.510 --> 00:04:45.370
So when we do that math,
00:04:45.370 --> 00:04:49.597
we find that k is equal to 0.0241
00:04:51.200 --> 00:04:52.963
one over years.
00:04:54.020 --> 00:04:56.420
Another equation from first-order kinetics
00:04:56.420 --> 00:05:00.550
is the integrated rate law
for a first-order reaction.
00:05:00.550 --> 00:05:03.200
And the integrated rate law
says that the natural log
00:05:03.200 --> 00:05:06.400
of the concentration of
reactant A at some time t
00:05:06.400 --> 00:05:09.770
is equal to negative
kt plus the natural log
00:05:09.770 --> 00:05:13.860
of the initial
concentration of reactant A.
00:05:13.860 --> 00:05:15.020
Since we're using N,
00:05:15.020 --> 00:05:18.200
which is the number of
radioactive nuclei in our sample,
00:05:18.200 --> 00:05:20.700
instead of the concentration of A,
00:05:20.700 --> 00:05:22.570
we can write the integrated rate law
00:05:22.570 --> 00:05:26.060
for our first-order
radioactive decay process,
00:05:26.060 --> 00:05:27.800
which says the natural log
00:05:27.800 --> 00:05:31.180
of the number of radioactive
nuclei at some time t
00:05:31.180 --> 00:05:34.300
is equal to negative
kt plus the natural log
00:05:34.300 --> 00:05:37.043
of the initial number
of radioactive nuclei.
00:05:38.080 --> 00:05:41.523
So let's say we start with 1.000 grams
00:05:44.170 --> 00:05:47.590
of our Strontium-90 radioactive isotope,
00:05:47.590 --> 00:05:49.610
and our goal is to find out
00:05:49.610 --> 00:05:53.380
how much remains after two years.
00:05:53.380 --> 00:05:55.220
So we're gonna wait two years
00:05:55.220 --> 00:05:59.150
and find out how much of our
radioactive isotope remains.
00:05:59.150 --> 00:06:02.060
So we're going to use our equation
00:06:02.060 --> 00:06:04.850
for the integrated rate law.
00:06:04.850 --> 00:06:08.073
Let's go ahead and plug in what we know.
00:06:09.200 --> 00:06:10.510
We already know what k is,
00:06:10.510 --> 00:06:12.500
we found that in our earlier problem,
00:06:12.500 --> 00:06:16.980
so we can write this is
equal to negative times k,
00:06:16.980 --> 00:06:19.080
which is 0.0241.
00:06:22.340 --> 00:06:25.700
Next, we also know the time
period we're interested in.
00:06:25.700 --> 00:06:28.580
So we know what t is, t is two years,
00:06:28.580 --> 00:06:33.580
so let's go ahead and write
2.00 in here for the time.
00:06:34.520 --> 00:06:37.580
Next, we're gonna add the natural log
00:06:37.580 --> 00:06:42.380
of the initial number of
radioactive nuclei in our sample.
00:06:42.380 --> 00:06:44.550
And while we don't have
the initial number,
00:06:44.550 --> 00:06:45.990
we do have the mass.
00:06:45.990 --> 00:06:48.020
And since the mass is proportional
00:06:48.020 --> 00:06:50.180
to the number of radioactive nuclei,
00:06:50.180 --> 00:06:53.020
it's okay to go ahead and
plug that into our equation.
00:06:53.020 --> 00:06:56.763
So we're gonna plug in
the natural log of one.
00:06:58.750 --> 00:07:01.730
And all of this is
equal to the natural log
00:07:01.730 --> 00:07:05.300
of the initial number of
radioactive nuclei at some time t.
00:07:05.300 --> 00:07:08.253
So we have the natural log of that.
00:07:10.370 --> 00:07:13.720
The natural log of one is zero,
00:07:13.720 --> 00:07:17.740
so now we have the natural log of N
00:07:17.740 --> 00:07:19.450
is equal to,
00:07:19.450 --> 00:07:24.313
and when we do this math, we're
gonna get negative 0.0482.
00:07:26.290 --> 00:07:29.170
Next, we have to get
rid of the natural log.
00:07:29.170 --> 00:07:31.920
And we can do that by
taking e to both sides.
00:07:31.920 --> 00:07:36.050
So if we take e to both sides,
the natural log cancels out,
00:07:36.050 --> 00:07:39.650
and we get that N is equal
00:07:39.650 --> 00:07:44.650
to 0.953 grams.
00:07:45.650 --> 00:07:50.240
So that's how much of our
radioactive isotope remains
00:07:50.240 --> 00:07:51.973
after two years.
|
Zero-order reactions | https://www.youtube.com/watch?v=aXf3e8a1teo | vtt | https://www.youtube.com/api/timedtext?v=aXf3e8a1teo&ei=6VWUZZ7iHrmBhcIPxpOy-Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6AA3C41644B7CE405206F642023435445FB24CBA.113D07ABAA691C5B6024065DFC589AF3419F773F&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.125 --> 00:00:02.970
- [Instructor] Let's say we
have a hypothetical reaction
00:00:02.970 --> 00:00:06.440
where reactant A turns into products.
00:00:06.440 --> 00:00:10.970
And let's say the reaction is
zero order with respect to A.
00:00:10.970 --> 00:00:13.660
If it's zero order with
respect to A, we can write
00:00:13.660 --> 00:00:15.970
that the rate of the reaction is equal to
00:00:15.970 --> 00:00:19.440
the rate constant k, times
the concentration of A
00:00:19.440 --> 00:00:22.010
to the zero power.
00:00:22.010 --> 00:00:26.420
And since any number to the
zero power is equal to one,
00:00:26.420 --> 00:00:27.810
then the rate of the reaction
00:00:27.810 --> 00:00:31.413
would just be equal to
the rate constant k.
00:00:32.390 --> 00:00:34.580
We can also write that
the rate of the reaction
00:00:34.580 --> 00:00:36.760
is equal to the negative and the change
00:00:36.760 --> 00:00:40.143
in the concentration of A,
over the change in time.
00:00:41.290 --> 00:00:44.200
If we set these two ways of
writing the rate of reaction
00:00:44.200 --> 00:00:47.100
equal to each other, and
we use some calculus,
00:00:47.100 --> 00:00:49.990
including the concept of
integration, we will arrive
00:00:49.990 --> 00:00:53.920
at the integrated rate law
for a zero-order reaction,
00:00:53.920 --> 00:00:56.980
which says that the concentration
of A at time t is equal
00:00:56.980 --> 00:01:00.640
to the negative of the rate
constant k times the time,
00:01:00.640 --> 00:01:02.783
plus the initial concentration of A.
00:01:04.380 --> 00:01:05.980
Notice that the integrated rate law
00:01:05.980 --> 00:01:10.840
is in the form of Y is equal to mx plus b,
00:01:10.840 --> 00:01:13.680
which is the equation for a straight line.
00:01:13.680 --> 00:01:18.630
So if we graph the concentration
of A on the Y axis,
00:01:18.630 --> 00:01:21.830
and the time on the X axis,
00:01:21.830 --> 00:01:26.330
we will get a straight line
if the reaction is zero order.
00:01:26.330 --> 00:01:29.830
So if we write the concentration
of A on the Y axis,
00:01:29.830 --> 00:01:33.070
and time on the X axis,
00:01:33.070 --> 00:01:35.850
the graph will be a straight line,
00:01:35.850 --> 00:01:40.160
and the slope of that line
is equal to the negative
00:01:40.160 --> 00:01:42.970
of the rate constant k,
00:01:42.970 --> 00:01:46.703
so the slope is equal to -k,
00:01:48.130 --> 00:01:51.070
and the Y intercept of that line,
00:01:51.070 --> 00:01:56.070
so right where the line
intersects with the y-axis,
00:01:57.690 --> 00:02:01.900
this point is the initial
concentration of A.
00:02:01.900 --> 00:02:04.630
So everything we've talked
about assumes that there's a
00:02:04.630 --> 00:02:08.803
coefficient of 1 in front
of the concentration of A.
00:02:10.160 --> 00:02:12.890
However, let's say we
have a coefficient of 2
00:02:12.890 --> 00:02:15.620
in front of A in our balanced equation.
00:02:15.620 --> 00:02:20.620
That means we need a
stoichiometric coefficient of 1/2,
00:02:20.902 --> 00:02:23.152
which changes the math.
00:02:23.152 --> 00:02:26.985
Now, instead of getting
-kt, we would get -2kt
00:02:28.730 --> 00:02:33.400
after we integrate, which means
that the slope of the line,
00:02:33.400 --> 00:02:37.560
when we graph the
concentration of A versus time,
00:02:37.560 --> 00:02:39.760
the slope of the line
would be equal to -2k.
00:02:42.630 --> 00:02:45.020
It's important to note
that textbooks often just
00:02:45.020 --> 00:02:48.040
assume the coefficient
in front of A as a 1,
00:02:48.040 --> 00:02:51.700
which would give the slope as equal to -k.
00:02:51.700 --> 00:02:54.740
However, if the coefficient
in front of A is a 2,
00:02:54.740 --> 00:02:57.100
then technically the slope of the line
00:02:57.100 --> 00:02:59.670
should be equal to -2k
00:03:01.073 --> 00:03:03.510
As an example of a zero-order
reaction, let's look at
00:03:03.510 --> 00:03:08.380
the decomposition of ammonia
on a hot platinum surface
00:03:08.380 --> 00:03:11.970
to form nitrogen gas and hydrogen gas.
00:03:11.970 --> 00:03:16.210
In our diagram, we have
four ammonia molecules
00:03:16.210 --> 00:03:19.020
on the surface of our platinum catalyst,
00:03:19.020 --> 00:03:21.320
and then we have another four
00:03:21.320 --> 00:03:24.850
that are above the
surface of the catalyst.
00:03:24.850 --> 00:03:27.500
Only the ammonia molecules on
the surface of the catalyst
00:03:27.500 --> 00:03:30.770
can react and turn into
nitrogen and hydrogen,
00:03:30.770 --> 00:03:34.180
the ammonia molecules above
the surface can't react.
00:03:34.180 --> 00:03:38.010
And even if we were to add in
some more ammonia molecules,
00:03:38.010 --> 00:03:40.430
so let's just add in some more here,
00:03:40.430 --> 00:03:43.360
those molecules still can't
react, and therefore the rate
00:03:43.360 --> 00:03:46.730
of the reaction doesn't
change as we increase
00:03:46.730 --> 00:03:49.670
the concentration of ammonia.
00:03:49.670 --> 00:03:52.900
So we can write that the
rate of the reaction is equal
00:03:52.900 --> 00:03:57.900
to the rate constant k times
the concentration of ammonia,
00:03:58.280 --> 00:04:01.510
but since increasing the
concentration of ammonia
00:04:01.510 --> 00:04:03.760
has no effect on rate,
00:04:03.760 --> 00:04:07.520
that's why this is
raised to the zero power.
00:04:07.520 --> 00:04:09.480
And therefore we get
the rate of the reaction
00:04:09.480 --> 00:04:12.003
is just equal to the rate constant k.
00:04:12.960 --> 00:04:16.010
Normally, increasing the
concentration of a reactant
00:04:16.010 --> 00:04:18.770
increases the rate of the reaction.
00:04:18.770 --> 00:04:21.280
However, for this reaction,
since we're limited
00:04:21.280 --> 00:04:24.000
by the surface area of the catalyst,
00:04:24.000 --> 00:04:26.550
if the catalyst is covered
with ammonia molecules,
00:04:26.550 --> 00:04:29.070
increasing the concentration
of ammonia molecules
00:04:29.070 --> 00:04:32.850
will have no effect on
the rate of the reaction.
00:04:32.850 --> 00:04:34.800
And therefore this reaction,
00:04:34.800 --> 00:04:38.120
the decomposition of ammonia
on a hot platinum surface,
00:04:38.120 --> 00:04:41.263
is an example of a zero-order reaction.
|
Second-order reactions | https://www.youtube.com/watch?v=YgWmHssKVvQ | vtt | https://www.youtube.com/api/timedtext?v=YgWmHssKVvQ&ei=6VWUZfy4GtCihcIPgKWe-Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7C5452AFE6E6CC6B8DBD9EF27EB7895659B0099E.3983B875F57C1021724AE078FE835E57DB69B51A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.710 --> 00:00:01.543
- [Instructor] Let's say we have
00:00:01.543 --> 00:00:02.880
a hypothetical reaction
00:00:02.880 --> 00:00:06.120
where reactant A turns into products.
00:00:06.120 --> 00:00:08.080
And let's say the reaction is second order
00:00:08.080 --> 00:00:09.970
with respect to A.
00:00:09.970 --> 00:00:12.140
If the reaction is second
order with respect to A,
00:00:12.140 --> 00:00:14.840
then we can write the rate of the reaction
00:00:14.840 --> 00:00:18.230
is equal to the rate constant
k times the concentration
00:00:18.230 --> 00:00:20.460
of A to the second power
00:00:20.460 --> 00:00:23.293
since this is a second order reaction.
00:00:24.550 --> 00:00:26.960
We can also write that
the rate of the reaction
00:00:26.960 --> 00:00:29.160
is equal to the negative of the change
00:00:29.160 --> 00:00:32.543
in the concentration of A
over the change in time.
00:00:33.900 --> 00:00:36.220
If we set these two
ways of writing the rate
00:00:36.220 --> 00:00:38.210
of reaction equal to each other,
00:00:38.210 --> 00:00:40.030
and use of calculus,
00:00:40.030 --> 00:00:42.580
including the concept of integration,
00:00:42.580 --> 00:00:45.290
we will arrive at the integrated rate law
00:00:45.290 --> 00:00:47.553
for a second order reaction.
00:00:48.750 --> 00:00:51.730
The integrated rate law
for a second order reaction
00:00:51.730 --> 00:00:54.060
says that one over the concentration
00:00:54.060 --> 00:00:56.590
of reactant A at some time t,
00:00:56.590 --> 00:00:59.240
is equal to the rate
constant k times the time
00:00:59.240 --> 00:01:04.123
plus one over the initial
concentration of A.
00:01:05.270 --> 00:01:06.790
Notice how the integrated rate law
00:01:06.790 --> 00:01:10.907
has the form of y is equal to mx plus b,
00:01:12.360 --> 00:01:15.360
which is the equation for a straight line.
00:01:15.360 --> 00:01:18.990
So if we graph one over
the concentration of A
00:01:18.990 --> 00:01:23.530
on the y axis, and time on the x axis,
00:01:23.530 --> 00:01:25.160
so let's go ahead and put that in here,
00:01:25.160 --> 00:01:29.040
one over the concentration
of A on the y axis,
00:01:29.040 --> 00:01:33.670
and time on the x axis, we
will get a straight line
00:01:33.670 --> 00:01:35.910
and the slope of that line
00:01:35.910 --> 00:01:39.760
is equal to the rate constant k.
00:01:39.760 --> 00:01:44.760
So slope is equal to K and the y intercept
00:01:46.000 --> 00:01:50.210
is equal to one over the
initial concentration of A.
00:01:50.210 --> 00:01:54.520
So the point where our
line intersects the y axis
00:01:54.520 --> 00:01:59.500
is equal to one over the
initial concentration of A.
00:02:00.460 --> 00:02:04.000
Let's look at an example
of a second order reaction.
00:02:04.000 --> 00:02:09.000
C5H6 is cyclopentadiene, and two molecules
00:02:09.570 --> 00:02:12.960
of cyclopentadiene will
react with each other
00:02:12.960 --> 00:02:14.913
to form dicyclopentadiene.
00:02:16.120 --> 00:02:19.200
Our goal is to use the
data from this data table
00:02:19.200 --> 00:02:22.083
to prove that this
reaction is second order.
00:02:23.150 --> 00:02:24.530
However, we have to be careful
00:02:24.530 --> 00:02:26.140
because in our balanced equation,
00:02:26.140 --> 00:02:28.870
we have a two as a coefficient in front
00:02:28.870 --> 00:02:29.893
of cyclopentadiene.
00:02:31.660 --> 00:02:34.100
Going back to our hypothetical reaction
00:02:34.100 --> 00:02:36.730
where reactant A turned into products,
00:02:36.730 --> 00:02:40.020
there's also one as a
coefficient in front of the A.
00:02:40.020 --> 00:02:42.450
And if there's a one as a
coefficient in front of the A,
00:02:42.450 --> 00:02:45.250
we can use this form of
the integrated rate law
00:02:45.250 --> 00:02:47.370
for a second order reaction.
00:02:47.370 --> 00:02:50.110
However, for our problem, we have a two
00:02:50.110 --> 00:02:54.180
as a coefficient in
front of cyclopentadiene.
00:02:54.180 --> 00:02:55.740
And that means we need to have
00:02:55.740 --> 00:03:00.000
a stoichiometric
coefficient of 1/2 in here,
00:03:00.000 --> 00:03:01.590
and that changes the math.
00:03:01.590 --> 00:03:05.140
Now when we set these two
rates of reactions equal
00:03:05.140 --> 00:03:08.990
to each other, and we use
calculus and we integrate
00:03:08.990 --> 00:03:10.770
to get our integrated rate law,
00:03:10.770 --> 00:03:13.100
because of this one half,
00:03:13.100 --> 00:03:17.500
we end up with a two in front of the K.
00:03:17.500 --> 00:03:22.500
So thinking about y is equal to mx plus b,
00:03:23.320 --> 00:03:28.103
now the slope of the
line is equal to two K.
00:03:29.490 --> 00:03:30.940
So now for our reaction,
00:03:30.940 --> 00:03:32.660
we can write our integrated rate law
00:03:32.660 --> 00:03:36.240
as one over the concentration
of cyclopentadiene
00:03:36.240 --> 00:03:40.470
at some time t, is
equal to two kt plus one
00:03:40.470 --> 00:03:43.913
over the initial concentration
of cyclopentadiene.
00:03:45.340 --> 00:03:46.720
So if we look at our data table,
00:03:46.720 --> 00:03:50.750
we have time in seconds and
we have the concentration
00:03:50.750 --> 00:03:54.450
of cyclopentadiene,
but we need to have one
00:03:54.450 --> 00:03:57.430
over the concentration of cyclopentadiene
00:03:57.430 --> 00:03:59.900
so we need a new column.
00:03:59.900 --> 00:04:04.420
So we're going to calculate
one over the concentration
00:04:04.420 --> 00:04:06.513
of cyclopentadiene.
00:04:08.900 --> 00:04:11.790
So if the concentration of cyclopentadiene
00:04:11.790 --> 00:04:16.790
when time is equal to zero
seconds is 0.0400 molar,
00:04:16.930 --> 00:04:19.980
if we take one divided by 0.0400,
00:04:23.260 --> 00:04:24.830
we would get 25.0.
00:04:29.810 --> 00:04:31.450
To save some time I've gone ahead
00:04:31.450 --> 00:04:34.200
and filled in the rest of this column.
00:04:34.200 --> 00:04:37.480
Notice as time increases so
as we go from zero seconds
00:04:37.480 --> 00:04:40.610
to 50 to 100 to 150 to 200,
00:04:40.610 --> 00:04:43.640
the concentration of
cyclopentadiene decreases
00:04:43.640 --> 00:04:47.983
because cyclopentadiene is
turning into dicyclopentadiene.
00:04:49.290 --> 00:04:50.760
Next, we need to graph our data.
00:04:50.760 --> 00:04:52.840
So we're gonna have one
over the concentration
00:04:52.840 --> 00:04:55.110
of cyclopentadiene on the y axis
00:04:55.110 --> 00:04:57.890
and time on the x axis.
00:04:57.890 --> 00:05:00.840
Our first point, so when
time is equal to zero,
00:05:00.840 --> 00:05:04.770
one over the concentration
of cyclopentadiene is 25.0.
00:05:04.770 --> 00:05:08.113
So if we go down to our graph,
00:05:09.880 --> 00:05:12.210
we can see that when
time is equal to zero,
00:05:12.210 --> 00:05:15.570
our first point here is 25.0.
00:05:15.570 --> 00:05:20.403
And plotting the other points
gives us a straight line.
00:05:21.860 --> 00:05:26.860
Next, we need to find the
slope of this straight line.
00:05:26.860 --> 00:05:28.730
And there are many ways to do that.
00:05:28.730 --> 00:05:32.440
One way to do it is to
use a graphing calculator.
00:05:32.440 --> 00:05:34.890
And when I used a graphing calculator
00:05:34.890 --> 00:05:36.670
to find the slope of this line,
00:05:36.670 --> 00:05:41.207
I found that the slope is equal to 0.1634.
00:05:46.350 --> 00:05:51.090
Thinking about y is equal to mx plus b,
00:05:52.090 --> 00:05:56.163
our slope should be equal to two k.
00:05:57.280 --> 00:05:59.140
So to find the rate constant k,
00:05:59.140 --> 00:06:03.230
we need to divide the slope by two,
00:06:03.230 --> 00:06:06.890
which gives us 0.0817.
00:06:12.480 --> 00:06:15.320
To find the units for
K, remember that slope
00:06:15.320 --> 00:06:20.320
is equal to change in y over change in x,
00:06:20.740 --> 00:06:24.000
and on our Y axis, our
units are one over molar,
00:06:24.000 --> 00:06:27.180
and the x axis the units are seconds.
00:06:27.180 --> 00:06:29.740
So therefore, we can
write the rate constant k
00:06:29.740 --> 00:06:32.443
is equal to 0.0817.
00:06:34.786 --> 00:06:37.270
It's to be one over
molar divided by seconds
00:06:37.270 --> 00:06:42.270
which is the same thing as
one over molar times seconds.
00:06:43.370 --> 00:06:45.630
It's important to point
out that most textbooks
00:06:45.630 --> 00:06:50.360
don't cover how the two
as a coefficient changes
00:06:50.360 --> 00:06:53.050
the integrated rate law.
00:06:53.050 --> 00:06:55.800
And so a lot of textbooks will simply say
00:06:55.800 --> 00:06:57.970
that the slope of the line
00:06:57.970 --> 00:07:00.970
for the second order integrated rate law,
00:07:00.970 --> 00:07:02.100
is equal to K.
00:07:02.100 --> 00:07:04.590
So a lot of books would
just say the final answer
00:07:04.590 --> 00:07:07.570
for the rate constant is 0.163.
00:07:07.570 --> 00:07:10.000
So you'll see you'll see
a lot of textbooks say
00:07:10.000 --> 00:07:13.290
that the rate constant would be 0.163,
00:07:13.290 --> 00:07:17.743
one over molar times seconds.
00:07:18.820 --> 00:07:20.800
However, since the coefficient
00:07:20.800 --> 00:07:23.570
in front of cyclopentadiene is a two,
00:07:23.570 --> 00:07:28.063
technically this rate
constant is the correct one.
00:07:29.390 --> 00:07:32.700
Finally, since we got a straight line,
00:07:32.700 --> 00:07:36.140
when we graphed one over the concentration
00:07:36.140 --> 00:07:38.830
of cyclopentadiene versus time,
00:07:38.830 --> 00:07:42.403
we know that this reaction
has second order kinetics.
|
First-order reactions | https://www.youtube.com/watch?v=PVqWOehVTOg | vtt | https://www.youtube.com/api/timedtext?v=PVqWOehVTOg&ei=6VWUZY_GN-6fp-oPpuCOmAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245337&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D7508BF6A810E7CC157BBEED47304459364A4F4C.94264279A90F9C1FD63D82F8C06EAF84A5EC0CC7&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.750 --> 00:00:03.010
- [Instructor] Let's say we
have a hypothetical reaction
00:00:03.010 --> 00:00:06.210
where reactant A turns into products
00:00:06.210 --> 00:00:10.423
and that the reaction is
first-order with respect to A.
00:00:11.500 --> 00:00:15.300
If the reaction is first-order
with respect to reactant A,
00:00:15.300 --> 00:00:17.850
for the rate law we can write
the rate of the reaction
00:00:17.850 --> 00:00:19.650
is equal to the rate constant K
00:00:19.650 --> 00:00:23.410
times the concentration
of A to the first power.
00:00:23.410 --> 00:00:25.700
We can also write that
the rate of the reaction
00:00:25.700 --> 00:00:29.240
is equal to the negative of
the change in the concentration
00:00:29.240 --> 00:00:31.463
of A over the change in time.
00:00:32.530 --> 00:00:35.200
By setting both of these
equal to each other,
00:00:35.200 --> 00:00:36.900
and by doing some calculus,
00:00:36.900 --> 00:00:39.230
including the concept of integration,
00:00:39.230 --> 00:00:41.200
we arrive at the integrated rate law
00:00:41.200 --> 00:00:43.200
for a first-order reaction,
00:00:43.200 --> 00:00:46.020
which says that the natural
log of the concentration of A
00:00:46.020 --> 00:00:49.780
at some time T, is equal to negative KT,
00:00:49.780 --> 00:00:51.530
where K is the rate constant
00:00:51.530 --> 00:00:55.130
plus the natural log of the
initial concentration of A.
00:00:56.890 --> 00:00:58.450
Notice how the integrated rate law
00:00:58.450 --> 00:01:03.450
has the form of Y is equal to mx plus b,
00:01:03.630 --> 00:01:07.180
which is the equation for a straight line.
00:01:07.180 --> 00:01:10.980
So if we were to graph the
natural log of the concentration
00:01:10.980 --> 00:01:15.040
of A on the Y axis, so let's
go ahead and put that in here,
00:01:15.040 --> 00:01:19.130
the natural log of the concentration of A,
00:01:19.130 --> 00:01:23.660
and on the X axis we put the time,
00:01:23.660 --> 00:01:26.330
we would get a straight line
00:01:26.330 --> 00:01:28.900
and the slope of that straight line
00:01:28.900 --> 00:01:31.680
would be equal to negative K.
00:01:31.680 --> 00:01:33.593
So the slope of this line,
00:01:34.520 --> 00:01:36.670
the slope would be equal to the negative
00:01:36.670 --> 00:01:39.170
of the rate constant K,
00:01:39.170 --> 00:01:43.200
and the Y intercept would
be equal to the natural log
00:01:43.200 --> 00:01:45.110
of the initial concentration of A.
00:01:45.110 --> 00:01:49.150
So right where this line meets the Y axis,
00:01:49.150 --> 00:01:51.560
that point is equal to the natural log
00:01:51.560 --> 00:01:54.740
of the initial concentration of A.
00:01:56.250 --> 00:01:59.970
The conversion of methyl
isonitrile to acetonitrile
00:01:59.970 --> 00:02:02.150
is a first-order reaction.
00:02:02.150 --> 00:02:05.340
And these two molecules
are isomers of each other.
00:02:05.340 --> 00:02:08.220
Let's use the data that's
provided to us in this data table
00:02:08.220 --> 00:02:12.680
to show that this conversion
is a first-order reaction.
00:02:12.680 --> 00:02:15.720
Since the coefficient in
front of methyl isonitrile
00:02:15.720 --> 00:02:19.870
is a one, we can use this form
of the integrated rate law
00:02:19.870 --> 00:02:21.870
where the slope is equal to the negative
00:02:21.870 --> 00:02:23.563
of the rate constant K.
00:02:24.820 --> 00:02:28.100
If our balanced equation
had a two as a coefficient
00:02:28.100 --> 00:02:31.130
in front of our reactant, we
would have had to include 1/2
00:02:32.070 --> 00:02:35.570
as a stoichiometric coefficient.
00:02:35.570 --> 00:02:38.540
And when we set our two
rates equal to each other now
00:02:38.540 --> 00:02:42.610
and go through the calculus,
instead of getting negative KT,
00:02:42.610 --> 00:02:45.513
we have gotten negative two KT.
00:02:46.400 --> 00:02:51.100
However for our reaction we
don't have a coefficient of two.
00:02:51.100 --> 00:02:54.340
We have a coefficient of one and therefore
00:02:54.340 --> 00:02:58.113
we can use this form of
the integrated rate law.
00:02:59.660 --> 00:03:02.070
Also notice that this form
of the integrated rate law
00:03:02.070 --> 00:03:05.760
is in terms of the concentration of A
00:03:05.760 --> 00:03:08.930
but we don't have the
concentration of methyl isonitrile
00:03:08.930 --> 00:03:10.090
in our data table,
00:03:10.090 --> 00:03:13.350
we have the pressure of methyl isonitrile.
00:03:13.350 --> 00:03:16.080
But pressure is related to concentration
00:03:16.080 --> 00:03:21.080
from the ideal gas law,
so PV is equal to nRT.
00:03:21.360 --> 00:03:25.470
If we divide both sides by V,
00:03:25.470 --> 00:03:28.630
then we can see that pressure is equal to,
00:03:28.630 --> 00:03:30.730
n is moles and V is volumes,
00:03:30.730 --> 00:03:34.020
so moles divided by
volume would be molarity,
00:03:34.020 --> 00:03:38.210
so molarity times R times T.
00:03:38.210 --> 00:03:41.340
And therefore pressure
is directly proportional
00:03:41.340 --> 00:03:45.520
to concentration, and for a
gas it's easier to measure
00:03:45.520 --> 00:03:48.390
the pressure than to
get the concentration.
00:03:48.390 --> 00:03:50.310
And so you'll often see data
00:03:50.310 --> 00:03:53.670
for gases in terms of the pressure.
00:03:53.670 --> 00:03:55.780
Therefore, we can imagine this form of the
00:03:55.780 --> 00:04:00.290
integrated rate law as the
natural log of the pressure
00:04:00.290 --> 00:04:03.530
of our gas at time T
is equal to negative KT
00:04:03.530 --> 00:04:08.160
plus the natural log of the
initial pressure of the gas.
00:04:08.160 --> 00:04:10.350
Therefore, to show that this reaction
00:04:10.350 --> 00:04:14.060
is a first-order reaction we
need to graph the natural log
00:04:14.060 --> 00:04:18.380
of the pressure of methyl
isonitrile on the Y axis
00:04:18.380 --> 00:04:20.960
and time on the X axis.
00:04:20.960 --> 00:04:24.283
So we need a new column in our data table.
00:04:25.184 --> 00:04:27.950
We need to put in the natural log
00:04:27.950 --> 00:04:32.950
of the pressure of methyl isonitrile.
00:04:33.690 --> 00:04:36.460
So for example, when time is equal to zero
00:04:36.460 --> 00:04:41.460
the pressure of methyl
isonitrile is 502 torrs.
00:04:41.670 --> 00:04:45.350
So we need to take the natural log of 502.
00:04:45.350 --> 00:04:49.313
And the natural log of
502 is equal to 6.219.
00:04:55.480 --> 00:04:56.730
To save time, I've gone ahead
00:04:56.730 --> 00:04:58.600
and filled in this last column here,
00:04:58.600 --> 00:05:01.840
the natural log of the
pressure methyl isonitrile.
00:05:01.840 --> 00:05:04.790
Notice what happens as
time increases, right,
00:05:04.790 --> 00:05:09.230
as time increases the
pressure of methyl isonitrile
00:05:09.230 --> 00:05:13.900
decreases since it's being
turned into acetonitrile.
00:05:13.900 --> 00:05:16.690
So for our graph, we're
gonna have the natural log
00:05:16.690 --> 00:05:20.370
of the pressure of methyl
isonitrile on the y-axis.
00:05:20.370 --> 00:05:23.930
And we're gonna have time on the X axis.
00:05:23.930 --> 00:05:25.540
So notice our first point here
00:05:25.540 --> 00:05:28.460
when time is equal to zero seconds,
00:05:28.460 --> 00:05:33.460
the natural log of the
pressure as equal to 6.219.
00:05:33.800 --> 00:05:37.050
So let's go down and
let's look at the graph.
00:05:37.050 --> 00:05:39.560
All right, so I've
already graphed it here.
00:05:39.560 --> 00:05:43.490
And we just saw when time
is equal to zero seconds,
00:05:43.490 --> 00:05:47.560
the first point is equal to 6.219.
00:05:47.560 --> 00:05:52.560
And here I have the other data
points already on the graph.
00:05:52.810 --> 00:05:55.820
Here's the integrated rate
law for a first-order reaction
00:05:55.820 --> 00:06:00.720
and I put pressures in there
instead of concentrations.
00:06:00.720 --> 00:06:03.890
And so we have the natural
log of the pressure
00:06:03.890 --> 00:06:06.850
of methyl isonitrile on the y-axis
00:06:06.850 --> 00:06:10.300
and we have time on the X axis,
00:06:10.300 --> 00:06:12.700
and the slope of this line should be equal
00:06:12.700 --> 00:06:15.950
to the negative of the rate constant K.
00:06:15.950 --> 00:06:18.870
So there are many ways to
find the slope of this line,
00:06:18.870 --> 00:06:22.900
one way would be to use
a graphing calculator.
00:06:22.900 --> 00:06:25.210
So I used a graphing calculator
00:06:25.210 --> 00:06:28.030
and I put in the data from the data table
00:06:28.030 --> 00:06:30.700
and I found that the slope of this line
00:06:30.700 --> 00:06:33.850
is equal to negative 2.08
00:06:37.230 --> 00:06:42.130
times 10 to the negative fourth.
00:06:42.130 --> 00:06:46.360
And since if I go ahead and
write y is equal to mx plus b,
00:06:46.360 --> 00:06:49.900
I need to remember to take
the negative of that slope
00:06:49.900 --> 00:06:52.430
to find the rate constant K.
00:06:52.430 --> 00:06:56.350
Therefore K is equal to positive 2.08
00:06:58.230 --> 00:07:02.150
times 10 to the negative fourth.
00:07:02.150 --> 00:07:03.800
To get the units for the rate constant,
00:07:03.800 --> 00:07:06.040
we can remember that slope is equal to
00:07:06.040 --> 00:07:10.460
change in Y over change in X.
00:07:10.460 --> 00:07:14.100
So change in Y would be the
natural log of the pressure,
00:07:14.100 --> 00:07:19.070
which has no unit, and X
the unit is in seconds.
00:07:19.070 --> 00:07:24.070
So we would have one over
seconds for the units for K.
00:07:24.950 --> 00:07:27.640
And finally, since we got a straight line
00:07:27.640 --> 00:07:32.640
when we graphed the natural log
of the pressure versus time,
00:07:33.130 --> 00:07:36.770
we know that this data is
for a first-order reaction.
00:07:36.770 --> 00:07:39.070
And therefore we've proved
that the transformation
00:07:39.070 --> 00:07:41.400
of methyl isonitrile to acetonitrile
00:07:41.400 --> 00:07:43.283
is a first-order reaction.
|
Factors affecting reaction rates | https://www.youtube.com/watch?v=CoNHV7786Hg | vtt | https://www.youtube.com/api/timedtext?v=CoNHV7786Hg&ei=6lWUZbSFKIWDp-oP-IOOuAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245338&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=34BBCCF5616A64DD2A43DFE89043959BF5EDCAD9.F0D44F097F0B3BE2D9F8A11C1E3C6187F96DA888&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.380 --> 00:00:01.610
- [Instructor] There are several factors
00:00:01.610 --> 00:00:04.140
that can affect the rate of a reaction.
00:00:04.140 --> 00:00:08.640
One factor is the
concentration of a reactant.
00:00:08.640 --> 00:00:10.400
Most chemical reactions proceed faster
00:00:10.400 --> 00:00:14.290
when the concentration of one
of the reactants is increased.
00:00:14.290 --> 00:00:17.100
For example, let's look at
the reaction of solid zinc
00:00:17.100 --> 00:00:19.810
with hydrochloric acid to
form an aqueous solution
00:00:19.810 --> 00:00:23.430
of zinc chloride and hydrogen gas.
00:00:23.430 --> 00:00:25.860
Let's say we put a piece of zinc metal.
00:00:25.860 --> 00:00:29.970
So go ahead and draw in the
piece of zinc metal in here
00:00:29.970 --> 00:00:34.970
in a flask that contains
three molar hydrochloric acid.
00:00:36.130 --> 00:00:39.090
So in our flask here, we have three molar,
00:00:39.090 --> 00:00:41.363
a solution of three
molar hydrochloric acid.
00:00:42.500 --> 00:00:45.670
As the reaction proceeds,
hydrogen gas is formed.
00:00:45.670 --> 00:00:47.890
So we could monitor the
rate of this reaction
00:00:47.890 --> 00:00:51.250
by observing the amount
of hydrogen gas bubbles
00:00:51.250 --> 00:00:53.280
that are coming out of the flask.
00:00:53.280 --> 00:00:54.954
Let's say that we repeat the experiment.
00:00:54.954 --> 00:00:58.400
This time instead of using
three molar hydrochloric acid
00:00:58.400 --> 00:01:01.050
we're gonna use six
molar hydrochloric acid.
00:01:01.050 --> 00:01:04.471
So we've increased the concentration
00:01:04.471 --> 00:01:08.520
of our hydrochloric acid solution.
00:01:08.520 --> 00:01:11.510
This time, when we add
our piece of solid zinc
00:01:11.510 --> 00:01:14.973
to our six molar
hydrochloric acid solution,
00:01:14.973 --> 00:01:18.620
we would observe more hydrogen gas bubbles
00:01:18.620 --> 00:01:21.753
coming out of our flask.
00:01:22.670 --> 00:01:24.770
So we have increased the concentration
00:01:24.770 --> 00:01:27.620
of one of our reactants hydrochloric acid.
00:01:27.620 --> 00:01:32.620
And we've observed an increase
in the rate of the reaction.
00:01:33.840 --> 00:01:36.943
As the concentration of
hydrochloric acid increases,
00:01:36.943 --> 00:01:39.278
there are more acid particles to collide
00:01:39.278 --> 00:01:41.210
with the piece of zinc.
00:01:41.210 --> 00:01:43.049
And therefore, as the concentration
00:01:43.049 --> 00:01:45.810
of hydrochloric acid goes up,
00:01:45.810 --> 00:01:48.391
the frequency of collisions increase
00:01:48.391 --> 00:01:51.700
and the rate of the reaction increases.
00:01:51.700 --> 00:01:52.808
Let's use the same reaction
00:01:52.808 --> 00:01:54.373
to talk about another factor
00:01:54.373 --> 00:01:56.800
that affects the rate of reaction.
00:01:56.800 --> 00:01:59.620
And that factor is surface area.
00:01:59.620 --> 00:02:01.704
You've already reacted
a piece of solid zinc
00:02:01.704 --> 00:02:03.050
with hydrochloric acid.
00:02:03.050 --> 00:02:05.973
We could use three molar
hydrochloric acid again.
00:02:05.973 --> 00:02:09.029
And we saw some bubbles come
off of the piece of zinc
00:02:09.029 --> 00:02:11.880
indicating that hydrogen gas was produced.
00:02:11.880 --> 00:02:14.120
This time let's try
breaking the piece of zinc
00:02:14.120 --> 00:02:15.784
into smaller pieces.
00:02:15.784 --> 00:02:19.200
So instead of using one
large piece of zinc,
00:02:19.200 --> 00:02:22.323
here we have a bunch of
small pieces of zinc.
00:02:22.323 --> 00:02:25.730
And if we were to do the experiment again,
00:02:25.730 --> 00:02:28.480
with three molar hydrochloric acid,
00:02:28.480 --> 00:02:33.280
this time we would see more
bubbles of hydrogen gas
00:02:33.280 --> 00:02:37.090
coming off of those small pieces of zinc.
00:02:37.090 --> 00:02:41.308
So we have increased the
surface area of the solid
00:02:41.308 --> 00:02:46.308
and we observed an increase
in the rate of the reaction.
00:02:47.244 --> 00:02:49.519
When we had only one piece of zinc,
00:02:49.519 --> 00:02:52.153
the rate of the reaction was limited
00:02:52.153 --> 00:02:54.628
by the surface area of this one piece.
00:02:54.628 --> 00:02:57.388
Therefore by breaking it
up into smaller pieces,
00:02:57.388 --> 00:03:01.700
we were able to the rate of the reaction.
00:03:01.700 --> 00:03:03.460
Temperature is another factor
00:03:03.460 --> 00:03:05.910
that can affect the rate of a reaction.
00:03:05.910 --> 00:03:09.330
So let's say on the left,
we have a glow stick
00:03:09.330 --> 00:03:12.796
in a flask that contains some cold water.
00:03:12.796 --> 00:03:14.380
And the glow stick,
00:03:14.380 --> 00:03:16.440
let's say the glow stick
is already glowing here.
00:03:16.440 --> 00:03:21.210
So let's draw in this color
here for our glow stick.
00:03:21.210 --> 00:03:22.043
The glow from a glow stick
00:03:22.043 --> 00:03:24.580
comes from a chemical reaction.
00:03:24.580 --> 00:03:27.390
And if we were to
increase the temperature,
00:03:27.390 --> 00:03:29.835
so let's say we heated
this flask on the left.
00:03:29.835 --> 00:03:32.170
So we increase the temperature.
00:03:32.170 --> 00:03:35.200
We would observe the glow to get stronger.
00:03:35.200 --> 00:03:37.517
So let's go ahead and draw in here,
00:03:37.517 --> 00:03:41.490
a more vibrant glow coming
from our glow stick.
00:03:41.490 --> 00:03:43.482
So increasing the temperature
00:03:43.482 --> 00:03:47.536
must have increased the
rate of the reaction.
00:03:47.536 --> 00:03:49.670
The reason increasing the temperature
00:03:49.670 --> 00:03:52.090
increases the rate of
the reaction in general,
00:03:52.090 --> 00:03:53.423
is because increase in temperature means
00:03:53.423 --> 00:03:55.410
the molecules are moving faster.
00:03:55.410 --> 00:03:57.591
And therefore the molecules
are colliding with each other
00:03:57.591 --> 00:04:00.900
with greater frequency
and with greater force
00:04:00.900 --> 00:04:03.410
which increases the rate of the reaction.
00:04:03.410 --> 00:04:05.314
The catalyst is another factor
00:04:05.314 --> 00:04:08.278
that can affect the rate of a reaction.
00:04:08.278 --> 00:04:10.886
Let's look at the balanced
equation for the decomposition
00:04:10.886 --> 00:04:15.440
of hydrogen peroxide, which
turns into water and oxygen.
00:04:15.440 --> 00:04:17.630
And let's say in our flask on the left,
00:04:17.630 --> 00:04:20.887
we have a solution of hydrogen peroxide.
00:04:20.887 --> 00:04:24.902
The hydrogen peroxide is
decomposing at room temperature,
00:04:24.902 --> 00:04:27.172
but the reaction proceeds so slowly
00:04:27.172 --> 00:04:30.517
that we don't see it even happening.
00:04:30.517 --> 00:04:33.720
We can speed up the reaction
by adding a catalyst.
00:04:33.720 --> 00:04:38.720
Let's say we have an aqueous
solution of potassium iodide
00:04:39.660 --> 00:04:41.376
in our beaker here.
00:04:41.376 --> 00:04:45.261
And we pour the solution
of potassium iodide
00:04:45.261 --> 00:04:50.058
into our flask containing
the hydrogen peroxide.
00:04:50.058 --> 00:04:53.843
The addition of the
iodide ion as a catalyst,
00:04:53.843 --> 00:04:56.389
causes the decomposition
of hydrogen peroxide
00:04:56.389 --> 00:04:58.480
to occur very quickly.
00:04:58.480 --> 00:05:02.280
And we would see a huge plume of gas
00:05:02.280 --> 00:05:05.180
come out of the reaction flask.
00:05:05.180 --> 00:05:07.030
So the addition of a catalyst,
00:05:07.030 --> 00:05:10.095
in this case it was the iodide, an ion,
00:05:10.095 --> 00:05:14.483
increased the rate of the reaction.
00:05:15.500 --> 00:05:18.080
A catalyst increases the rate of reaction
00:05:18.080 --> 00:05:20.037
by effecting the kinds of collisions
00:05:20.037 --> 00:05:23.180
that occur between particles.
00:05:23.180 --> 00:05:25.770
And a catalyst increases
the rate of reaction
00:05:25.770 --> 00:05:27.783
without being used up.
|
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00:00:00.392 --> 00:00:03.445
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00:00:15.107 --> 00:00:17.700
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00:02:07.046 --> 00:02:08.837
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|
Human impacts on ecosystems | https://www.youtube.com/watch?v=K10qnzCYH54 | vtt | https://www.youtube.com/api/timedtext?v=K10qnzCYH54&ei=7lWUZb3xFJezvdIPyJaFyAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=37DFA0D9F9778697AC021887E400B66F97077D79.5F9B92488B2F2F5028D82BDB97E0645FBF869D15&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.570 --> 00:00:01.750
- [Instructor] What
we're going to talk about
00:00:01.750 --> 00:00:04.030
in this video is how human activity
00:00:04.030 --> 00:00:06.260
creates changes in the environment.
00:00:06.260 --> 00:00:07.800
And not just any changes,
00:00:07.800 --> 00:00:10.420
but changes that can disrupt an ecosystem.
00:00:10.420 --> 00:00:14.730
And it can threaten the very
existence of some species.
00:00:14.730 --> 00:00:16.240
And for the sake of this video,
00:00:16.240 --> 00:00:19.070
we'll think about it in
five different dimensions.
00:00:19.070 --> 00:00:21.900
The first is habitat destruction.
00:00:21.900 --> 00:00:24.940
So this over here is a
picture of some trees
00:00:24.940 --> 00:00:26.590
that have clearly been cut down.
00:00:26.590 --> 00:00:28.040
And there's many reasons why trees
00:00:28.040 --> 00:00:29.670
could be cut down like this.
00:00:29.670 --> 00:00:32.120
One could be maybe
there's some logging here,
00:00:32.120 --> 00:00:34.550
and we human beings, we do need wood.
00:00:34.550 --> 00:00:37.370
Maybe it's being cleared for agriculture,
00:00:37.370 --> 00:00:39.300
which we also need.
00:00:39.300 --> 00:00:42.960
But when you do that, it's
clearly eliminating the trees
00:00:42.960 --> 00:00:45.840
and many animals, many
different types of species,
00:00:45.840 --> 00:00:49.950
were probably living in or
amongst or on those trees.
00:00:49.950 --> 00:00:51.640
And if you do too much of that
00:00:51.640 --> 00:00:53.150
they might not have anywhere to live,
00:00:53.150 --> 00:00:55.230
or they might not have
enough places to live
00:00:55.230 --> 00:00:57.430
to really thrive.
00:00:57.430 --> 00:01:01.510
Now, another form of anthropogenic changes
00:01:01.510 --> 00:01:06.510
or changes induced by human
activity would be pollution.
00:01:06.710 --> 00:01:09.620
This right over here,
you can see the exhaust,
00:01:09.620 --> 00:01:12.070
so to speak, from a
coal-fired power plant.
00:01:12.070 --> 00:01:14.513
And that is polluting the air.
00:01:15.610 --> 00:01:17.310
harmful chemicals are being released,
00:01:17.310 --> 00:01:18.880
including greenhouse gases.
00:01:18.880 --> 00:01:20.700
And that's going to have other effects
00:01:20.700 --> 00:01:23.730
above and beyond just making
the air less pleasant.
00:01:23.730 --> 00:01:25.440
But pollution isn't just about
00:01:25.440 --> 00:01:27.180
harmful chemicals going into the air.
00:01:27.180 --> 00:01:30.330
It could be about harmful
chemicals going into the water,
00:01:30.330 --> 00:01:32.170
could be runoff from irrigation,
00:01:32.170 --> 00:01:34.160
or some other type of chemical.
00:01:34.160 --> 00:01:35.890
You could even have noise pollution.
00:01:35.890 --> 00:01:37.550
And you might think of
that as an annoyance,
00:01:37.550 --> 00:01:40.420
but it can actually disrupt
how certain animals behave.
00:01:40.420 --> 00:01:42.230
In fact, it could raise the stress level,
00:01:42.230 --> 00:01:45.280
which can change the biology
of animals in subtle,
00:01:45.280 --> 00:01:47.400
but important ways.
00:01:47.400 --> 00:01:49.830
Another dimension in which we humans
00:01:49.830 --> 00:01:54.150
are affecting ecosystems
is by introducing species
00:01:54.150 --> 00:01:56.870
to places where they might
not have been before,
00:01:56.870 --> 00:02:00.350
especially what's often
called invasive species.
00:02:00.350 --> 00:02:03.460
So this is a picture here of nutria,
00:02:03.460 --> 00:02:05.870
oftentimes referred to as nutria rats.
00:02:05.870 --> 00:02:07.560
I was born and raised in Louisiana,
00:02:07.560 --> 00:02:10.230
and there are many nutria in Louisiana,
00:02:10.230 --> 00:02:11.850
and they did not come from Louisiana.
00:02:11.850 --> 00:02:14.180
They came originally from South America.
00:02:14.180 --> 00:02:15.900
They were brought to the Gulf Coast,
00:02:15.900 --> 00:02:18.520
to the Southern United
States, for their firs.
00:02:18.520 --> 00:02:20.490
The demand for their firs did not keep up,
00:02:20.490 --> 00:02:25.000
and these nutria escaped
and now they are everywhere.
00:02:25.000 --> 00:02:27.686
And you might just, once again,
view that as an annoyance,
00:02:27.686 --> 00:02:30.855
but they start overpowering other species.
00:02:30.855 --> 00:02:34.310
They are competing with other
animals for the same food,
00:02:34.310 --> 00:02:36.640
for the same niche in the ecosystem.
00:02:36.640 --> 00:02:39.580
Nutria are also infamous
for eating the plants
00:02:39.580 --> 00:02:43.120
that hold together the
soil and the wetlands.
00:02:43.120 --> 00:02:45.080
And so the more that they do that
00:02:45.080 --> 00:02:47.280
the more that that soil gets eroded.
00:02:47.280 --> 00:02:50.820
And then you have issues
like habitat destruction.
00:02:50.820 --> 00:02:54.530
You have fewer wetlands for other species.
00:02:54.530 --> 00:02:59.500
Now another dimension
is over-exploitation.
00:02:59.500 --> 00:03:02.220
So this is a picture here
of what's known as trawling,
00:03:02.220 --> 00:03:06.190
where you take a big boat
and you have this huge net,
00:03:06.190 --> 00:03:08.670
and you just, the boat goes while the net
00:03:08.670 --> 00:03:10.790
is just grabbing all
the fish in the water.
00:03:10.790 --> 00:03:13.300
And these dots here are all fish.
00:03:13.300 --> 00:03:15.130
And actually it goes, extends out here,
00:03:15.130 --> 00:03:18.460
'cause the net is bulging
outward like that.
00:03:18.460 --> 00:03:21.050
And you can see it's a
very efficient method
00:03:21.050 --> 00:03:25.080
of getting fish, but you could over fish.
00:03:25.080 --> 00:03:27.430
If you take too many
fish out of the ocean,
00:03:27.430 --> 00:03:29.500
you're not going to
have enough to reproduce
00:03:29.500 --> 00:03:31.240
and keep the population going.
00:03:31.240 --> 00:03:33.770
And even though you might
get a lot of cheap fish
00:03:33.770 --> 00:03:35.850
very efficiently in the short-term,
00:03:35.850 --> 00:03:38.370
in the long-term the fish might go away.
00:03:38.370 --> 00:03:39.630
All of these, as you can imagine,
00:03:39.630 --> 00:03:40.810
connect in many ways.
00:03:40.810 --> 00:03:43.210
And a fifth dimension we could talk about,
00:03:43.210 --> 00:03:45.740
although it's very related to pollution
00:03:45.740 --> 00:03:49.600
and even deforestation, is climate change.
00:03:49.600 --> 00:03:51.110
And the climate change that we are
00:03:51.110 --> 00:03:52.810
most familiar with right now
00:03:52.810 --> 00:03:55.840
is this notion of global warming,
00:03:55.840 --> 00:03:59.150
which is occurring as
we have rising levels
00:03:59.150 --> 00:04:01.930
of greenhouse gases, like CO2.
00:04:01.930 --> 00:04:04.250
And those could be
released from things like
00:04:04.250 --> 00:04:07.890
this coal-fired power plant
that we saw a few minutes ago.
00:04:07.890 --> 00:04:10.410
But there's many other
sources of things like CO2
00:04:10.410 --> 00:04:12.520
and there's other greenhouse gases.
00:04:12.520 --> 00:04:15.130
But as we human beings
release more and more of this
00:04:15.130 --> 00:04:18.090
into the atmosphere,
these greenhouse gases
00:04:18.090 --> 00:04:20.700
trap more and more heat, and that,
00:04:20.700 --> 00:04:24.600
over the longterm, increases
average global temperatures.
00:04:24.600 --> 00:04:26.570
And that doesn't just affect temperature.
00:04:26.570 --> 00:04:28.910
When you affect temperature,
it can affect rainfall.
00:04:28.910 --> 00:04:30.410
It can affect wind patterns.
00:04:30.410 --> 00:04:32.980
And as we see in this picture over here,
00:04:32.980 --> 00:04:36.280
it can affect things like the
amount of sea ice we have.
00:04:36.280 --> 00:04:39.930
Because if, on average, global
temperatures are increasing,
00:04:39.930 --> 00:04:42.200
then water temperatures
could be increasing,
00:04:42.200 --> 00:04:44.080
then you have more melting sea ice
00:04:44.080 --> 00:04:46.140
in both the Arctic and Antarctic.
00:04:46.140 --> 00:04:47.490
And then, for example,
00:04:47.490 --> 00:04:50.020
in the Arctic where you have polar bears,
00:04:50.020 --> 00:04:53.020
they would have less ice to
be on when they're hunting
00:04:53.020 --> 00:04:54.450
the walruses or the seals,
00:04:54.450 --> 00:04:56.880
or frankly just ice to be on to rest
00:04:56.880 --> 00:04:59.310
from swimming in the water.
00:04:59.310 --> 00:05:01.270
And that melting ice also can contribute
00:05:01.270 --> 00:05:02.700
to rising sea levels.
00:05:02.700 --> 00:05:04.100
And it's not just the melting ice
00:05:04.100 --> 00:05:06.070
that's contributing to rising sea levels.
00:05:06.070 --> 00:05:08.240
It's also that water has different density
00:05:08.240 --> 00:05:09.460
at different temperatures.
00:05:09.460 --> 00:05:12.430
And so as you have that rising sea levels,
00:05:12.430 --> 00:05:15.220
that affects ecosystems around the planet,
00:05:15.220 --> 00:05:17.480
especially ecosystems close to the water.
00:05:17.480 --> 00:05:18.960
And one of the species that is
00:05:18.960 --> 00:05:21.070
most impacted by that is human beings.
00:05:21.070 --> 00:05:23.800
Most human beings actually live very close
00:05:23.800 --> 00:05:26.720
to sea level near a body of water.
00:05:26.720 --> 00:05:28.940
So as those sea levels rise
00:05:28.940 --> 00:05:30.980
they will have a very profound impact
00:05:30.980 --> 00:05:34.363
on a lot of animals, but
especially human beings.
|
K selected and r selected population growth strategies | https://www.youtube.com/watch?v=ey4FTyYjiPw | vtt | https://www.youtube.com/api/timedtext?v=ey4FTyYjiPw&ei=7lWUZdLqI5W-mLAPz_OJ4As&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=734B9EF91E21678BAFFA6420517CA94CCD2EE093.2921103367E4FAE86C520AA89391DC940742B3DB&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.220 --> 00:00:01.460
- [Narrator] What we're
going to do in this video
00:00:01.460 --> 00:00:04.290
is talk about different
population growth strategies
00:00:04.290 --> 00:00:05.410
for different species.
00:00:05.410 --> 00:00:06.570
And think about if we can come up
00:00:06.570 --> 00:00:08.820
with a broad categorization
00:00:08.820 --> 00:00:10.990
or if there's a broad
categorization already
00:00:10.990 --> 00:00:12.630
out there for us.
00:00:12.630 --> 00:00:15.530
So, we see that there are
species like elephants
00:00:15.530 --> 00:00:17.203
that are long lived,
00:00:18.730 --> 00:00:19.820
in the wild.
00:00:19.820 --> 00:00:22.800
An African elephant can
live roughly as long
00:00:22.800 --> 00:00:26.900
as a human being can 50, 60,
70, in some cases, 80 years.
00:00:26.900 --> 00:00:29.130
You also have things like killer whales
00:00:29.130 --> 00:00:30.920
that are also long lived.
00:00:30.920 --> 00:00:32.560
You have things like human beings that
00:00:32.560 --> 00:00:34.630
live a pretty good long time compared
00:00:34.630 --> 00:00:36.500
to other things in nature.
00:00:36.500 --> 00:00:39.190
You have things like gorillas
that are also reasonably long
00:00:39.190 --> 00:00:41.600
lived, live many, many, many decades.
00:00:41.600 --> 00:00:44.120
Now there's also other
patterns that you see
00:00:44.120 --> 00:00:45.793
on these large mammals.
00:00:46.974 --> 00:00:48.423
They tend to be large.
00:00:49.290 --> 00:00:50.940
Especially, if you think about compared
00:00:50.940 --> 00:00:53.740
to very small things
in the animal kingdom.
00:00:53.740 --> 00:00:57.330
They tend to not have a lot of children
00:00:57.330 --> 00:00:59.760
every reproductive event,
I guess you could say
00:00:59.760 --> 00:01:00.900
at every time they give birth.
00:01:00.900 --> 00:01:04.683
So few few children,
00:01:05.630 --> 00:01:07.110
children
00:01:07.110 --> 00:01:10.810
at a time
00:01:10.810 --> 00:01:13.480
And it takes them a while to
give birth to those children.
00:01:13.480 --> 00:01:16.040
And then they take care
of them for a while.
00:01:16.040 --> 00:01:18.500
Now, the other end of the
spectrum, you have some
00:01:18.500 --> 00:01:19.910
of the things that we have here.
00:01:19.910 --> 00:01:24.310
You have amphibians like
frogs, you have insects.
00:01:24.310 --> 00:01:28.170
You could imagine small
fish, bacteria, mosquitoes
00:01:28.170 --> 00:01:30.210
that are more short-lived.
00:01:30.210 --> 00:01:31.090
Short
00:01:32.600 --> 00:01:33.433
lived.
00:01:34.766 --> 00:01:36.823
They tend to be smaller.
00:01:39.080 --> 00:01:42.180
And they tend to have a
lot of children at a time.
00:01:42.180 --> 00:01:45.850
So lots of children
00:01:47.610 --> 00:01:49.890
at a time.
00:01:49.890 --> 00:01:53.000
Just an example, a frog
or what do you see here
00:01:53.000 --> 00:01:56.390
is this is a spiders
coming out of an egg sack.
00:01:56.390 --> 00:01:58.430
Frogs or spiders,
00:01:58.430 --> 00:02:02.660
they can lay in many cases,
thousands of eggs at a time.
00:02:02.660 --> 00:02:05.510
And they're not really dependent
on any one of those eggs,
00:02:05.510 --> 00:02:06.870
necessarily surviving.
00:02:06.870 --> 00:02:08.990
Many of them will be
killed off by predators
00:02:08.990 --> 00:02:12.130
but as long as a few survive
then the next generation,
00:02:12.130 --> 00:02:14.110
you can imagine, they get to reproduction
00:02:14.110 --> 00:02:16.250
and then they'll lay thousands of eggs.
00:02:16.250 --> 00:02:18.070
And they're shorter lived.
00:02:18.070 --> 00:02:20.430
A frog could live a few years.
00:02:20.430 --> 00:02:23.650
Some insects might live
anywhere from a few days
00:02:23.650 --> 00:02:25.290
to a few years.
00:02:25.290 --> 00:02:27.040
You have things like
bacteria that can have
00:02:27.040 --> 00:02:29.460
an even shorter life span.
00:02:29.460 --> 00:02:32.690
So, when biologists or
ecologists look at this, they say
00:02:32.690 --> 00:02:35.920
it looks like there is
a spectrum over here.
00:02:35.920 --> 00:02:39.410
You have these large long-lived animals
00:02:39.410 --> 00:02:41.380
that have a few children at a time.
00:02:41.380 --> 00:02:44.900
And really the limiting
factor on their population
00:02:44.900 --> 00:02:47.610
is how dense their population is.
00:02:47.610 --> 00:02:49.810
At some point, these
animals are going to compete
00:02:49.810 --> 00:02:51.720
for resources with each other.
00:02:51.720 --> 00:02:53.630
And that's true of
things like human beings.
00:02:53.630 --> 00:02:55.720
And the other end, you have these things
00:02:55.720 --> 00:03:00.150
like spiders or frogs,
instead might be limited
00:03:00.150 --> 00:03:02.620
on their reproduction
by environmental factors
00:03:02.620 --> 00:03:07.490
like how moist or dry it
is, how hot or cold it is.
00:03:07.490 --> 00:03:10.970
And so generally speaking
folks have attempted
00:03:10.970 --> 00:03:14.100
to classify these types of species.
00:03:14.100 --> 00:03:15.780
They call them K selected.
00:03:15.780 --> 00:03:18.950
I'll talk about where the
K comes from in a second.
00:03:18.950 --> 00:03:23.633
And they talk about these
types of species as R selected.
00:03:24.530 --> 00:03:26.810
And where these letters come from,
00:03:26.810 --> 00:03:29.490
is there, there's a general idea that
00:03:29.490 --> 00:03:32.390
if we draw a little axis here, time
00:03:32.390 --> 00:03:35.750
and then draw up axis here, population
00:03:35.750 --> 00:03:38.650
on the vertical axis, most species that
00:03:38.650 --> 00:03:40.790
when there's not a lot of
them, and they're not limited
00:03:40.790 --> 00:03:45.610
by resources they will grow
exponentially like this.
00:03:45.610 --> 00:03:46.960
Now, when you go into the math of it,
00:03:46.960 --> 00:03:50.080
that rate of growth is usually
denoted by the letter R,
00:03:50.080 --> 00:03:52.550
and you could see where this
R selected is coming from.
00:03:52.550 --> 00:03:56.110
And what that R is how
large it is is determined
00:03:56.110 --> 00:03:59.480
by a species biotic potential.
00:03:59.480 --> 00:04:04.070
And biotic potential just
means in a given environment,
00:04:04.070 --> 00:04:05.630
how quickly can they reproduce?
00:04:05.630 --> 00:04:08.510
What percentage of those
are able to get to maturity
00:04:08.510 --> 00:04:11.010
so that they can reproduce,
et cetera, et cetera.
00:04:11.010 --> 00:04:13.500
And so you could imagine the higher the R,
00:04:13.500 --> 00:04:17.190
the faster this
exponential growth goes up.
00:04:17.190 --> 00:04:21.040
Now, at some point you're going
to be resource constrained.
00:04:21.040 --> 00:04:23.860
And some there's some carrying capacity.
00:04:23.860 --> 00:04:26.310
And so let's say this is
the carrying capacity here,
00:04:26.310 --> 00:04:27.620
and let's call that K.
00:04:27.620 --> 00:04:30.780
And the reason why we use
K instead of C is K comes
00:04:30.780 --> 00:04:33.860
from a word for capacity in German.
00:04:33.860 --> 00:04:37.300
So, at some point you're
gonna have so many things
00:04:37.300 --> 00:04:39.100
that you're not gonna
have enough resources
00:04:39.100 --> 00:04:39.970
to support more.
00:04:39.970 --> 00:04:42.510
And so your population would flatten out
00:04:42.510 --> 00:04:44.180
something like this.
00:04:44.180 --> 00:04:48.520
And so, generally speaking
biologists have categorized
00:04:48.520 --> 00:04:52.644
these left categories of
species as K selected.
00:04:52.644 --> 00:04:55.920
The amount that you have,
the amount of population
00:04:55.920 --> 00:04:58.920
is going to be determined by
the resources that are there,
00:04:58.920 --> 00:05:01.250
the carrying capacity in the environment,
00:05:01.250 --> 00:05:04.430
while things like frogs
and mosquitoes and bacteria
00:05:04.430 --> 00:05:07.370
and spiders, you view more as R selected.
00:05:07.370 --> 00:05:11.450
They're gonna grow exponentially
at their biotic potential,
00:05:11.450 --> 00:05:14.030
but that biotic potential
is gonna be determined
00:05:14.030 --> 00:05:16.180
by how hot or cold or wet or dry
00:05:16.180 --> 00:05:17.700
or other environmental factors.
00:05:17.700 --> 00:05:20.060
They're not gonna get
to such a high density,
00:05:20.060 --> 00:05:23.040
that they're really
competing with each other.
00:05:23.040 --> 00:05:26.120
Now, as you can imagine
with most categorizations,
00:05:26.120 --> 00:05:29.420
nature is not that clean
that things are always going
00:05:29.420 --> 00:05:31.180
to be on the left side, or always gonna
00:05:31.180 --> 00:05:32.370
be on the right side.
00:05:32.370 --> 00:05:35.100
For example, things like
turtles, lay a lot of eggs
00:05:35.100 --> 00:05:37.740
but they live a very long time.
00:05:37.740 --> 00:05:41.210
It's also worth noting that
there's no value judgment
00:05:41.210 --> 00:05:43.860
that one strategy is
better than the other.
00:05:43.860 --> 00:05:45.230
They've both been successful.
00:05:45.230 --> 00:05:47.120
The fact that these species exist today,
00:05:47.120 --> 00:05:49.210
show that they have worked well.
00:05:49.210 --> 00:05:52.030
It is worth noting that
invasive species tend
00:05:52.030 --> 00:05:53.810
to be more R selected.
00:05:53.810 --> 00:05:55.540
They will just grow and grow and grow,
00:05:55.540 --> 00:05:58.430
and gonna be limited by the
environment and not as much
00:05:58.430 --> 00:05:59.730
by each other.
00:05:59.730 --> 00:06:02.570
While K selected species
are often the ones
00:06:02.570 --> 00:06:06.270
that are most effected
by invasive species.
00:06:06.270 --> 00:06:08.600
Now, the last thing I wanna highlight is,
00:06:08.600 --> 00:06:12.110
what we just talked about as
population growth strategies.
00:06:12.110 --> 00:06:16.150
And that can sometimes be
confused with niche strategies
00:06:16.150 --> 00:06:18.530
where are there certain
species that are generalists,
00:06:18.530 --> 00:06:20.310
that can occupy many different niches
00:06:20.310 --> 00:06:23.540
while there's certain species
that are more specialists.
00:06:23.540 --> 00:06:26.060
Here, we're just talking
about generally speaking,
00:06:26.060 --> 00:06:28.750
how do species tend to grow in population?
00:06:28.750 --> 00:06:31.010
While when we talk about niche strategies,
00:06:31.010 --> 00:06:34.160
we're gonna talk about the
types of niches they feel
00:06:34.160 --> 00:06:36.450
in order to get their resources.
00:06:36.450 --> 00:06:39.353
And we'll talk more about
all of that in future videos.
|
Official SAT Practice Tips for Students | https://www.youtube.com/watch?v=Jw38WchbD-4 | vtt | https://www.youtube.com/api/timedtext?v=Jw38WchbD-4&ei=7lWUZZ71LbaLvdIPvo-WoAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C8D3426F7D54FDEE70F3DF90DCCEC784604D7B3D.E05E3C505FB601B1799E7C0F06A9D2B8A85F164B&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.600 --> 00:00:04.170
- [Shannon] Hi, I'm
Shannon from Khan Academy.
00:00:04.170 --> 00:00:06.330
And I want to show you
how to make the most
00:00:06.330 --> 00:00:10.490
of your learning time on
Official SAT Practice.
00:00:10.490 --> 00:00:12.800
Research has shown that more time spent
00:00:12.800 --> 00:00:15.810
on Official SAT Practice is associated
00:00:15.810 --> 00:00:18.360
with greater SAT scores,
00:00:18.360 --> 00:00:21.850
but how you spend that
time really matters.
00:00:21.850 --> 00:00:24.990
Before we begin, let's make
sure you know how to access
00:00:24.990 --> 00:00:26.823
Official SAT Practice.
00:00:27.670 --> 00:00:30.290
Make sure you're signed into
your Khan Academy account
00:00:30.290 --> 00:00:33.363
by checking for your name in
the upper right-hand corner.
00:00:34.600 --> 00:00:37.890
If you're using Official
SAT Practice in a class,
00:00:37.890 --> 00:00:40.570
you should see a tab that says SAT
00:00:40.570 --> 00:00:42.393
on the left side navigation.
00:00:43.240 --> 00:00:47.900
Select the SAT tab and
from there select Practice
00:00:47.900 --> 00:00:50.113
to be taken to your student dashboard.
00:00:51.230 --> 00:00:54.620
If you aren't using SAT
practice in a class,
00:00:54.620 --> 00:00:58.460
you can select Edit
Courses to add the SAT tab
00:00:58.460 --> 00:01:00.133
to your Khan Academy account.
00:01:04.890 --> 00:01:08.123
Number one. Link your
account to CollegeBoard.
00:01:09.710 --> 00:01:12.410
To receive a personalized practice plan,
00:01:12.410 --> 00:01:14.580
you have two options.
00:01:14.580 --> 00:01:18.600
Number one, take a series
of diagnostic quizzes.
00:01:18.600 --> 00:01:21.310
Or number two, link your
CollegeBoard account
00:01:21.310 --> 00:01:22.423
to Khan Academy.
00:01:23.440 --> 00:01:25.450
The easiest way to get a study plan
00:01:25.450 --> 00:01:28.280
that is personalized to
your results is to link
00:01:28.280 --> 00:01:30.980
your Khan and CollegeBoard accounts.
00:01:30.980 --> 00:01:32.600
Once your accounts are linked,
00:01:32.600 --> 00:01:34.710
we'll automatically recommend skills
00:01:34.710 --> 00:01:36.890
where you have room to improve,
00:01:36.890 --> 00:01:39.643
especially ones that show
up frequently on the SAT.
00:01:40.890 --> 00:01:42.423
We recommend that you link your accounts
00:01:42.423 --> 00:01:46.093
so that you can waste no time
improving the right skills.
00:01:47.800 --> 00:01:49.280
Number two.
00:01:49.280 --> 00:01:52.833
Follow your personalized
practice recommendations.
00:01:54.140 --> 00:01:56.800
If you already linked your Khan Academy
00:01:56.800 --> 00:01:58.530
and CollegeBoard accounts,
00:01:58.530 --> 00:02:02.263
you will see your skill
recommendations on the Practice tab.
00:02:03.260 --> 00:02:06.290
At the top of the page,
you should see a set
00:02:06.290 --> 00:02:10.570
of recommended practice for
math and reading and writing
00:02:10.570 --> 00:02:14.380
that always end in a timed mini section.
00:02:14.380 --> 00:02:17.913
Now, let's take a deeper look
at how skills are recommended.
00:02:18.770 --> 00:02:22.450
Let's say there are two skills
at two different levels.
00:02:22.450 --> 00:02:27.450
Skill A is at level two,
skill B is that level three.
00:02:28.650 --> 00:02:30.670
You might think it would be more important
00:02:30.670 --> 00:02:32.900
to improve skill A.
00:02:32.900 --> 00:02:36.030
However, in some cases, we may recommend
00:02:36.030 --> 00:02:37.680
that you practice skill B
00:02:37.680 --> 00:02:40.400
because it shows up more
frequently on the SAT
00:02:41.340 --> 00:02:43.538
and improving it to
level four would do more
00:02:43.538 --> 00:02:45.163
to raise your score.
00:02:48.070 --> 00:02:50.833
Number three. Level up skills.
00:02:51.890 --> 00:02:56.110
In official SAT practice, you
have a specific skill level
00:02:56.110 --> 00:02:58.280
for the 41 skills in math
00:02:58.280 --> 00:03:01.610
and the 28 skills in reading and writing.
00:03:01.610 --> 00:03:06.420
As you answer questions, your
skill levels move up or down
00:03:06.420 --> 00:03:07.923
depending on how you do.
00:03:08.790 --> 00:03:10.610
Leveling up your skills shows you
00:03:10.610 --> 00:03:12.720
that you are consistently advancing
00:03:12.720 --> 00:03:15.050
in the content on the SAT.
00:03:15.050 --> 00:03:18.510
And it's a great way to
monitor your progress.
00:03:18.510 --> 00:03:20.167
You might be wondering,
00:03:20.167 --> 00:03:22.997
"But what if I do if I
get stuck on a skill?"
00:03:23.930 --> 00:03:25.650
It's normal to feel stuck at times
00:03:25.650 --> 00:03:27.580
when studying for the SAT.
00:03:27.580 --> 00:03:29.340
We've all been there.
00:03:29.340 --> 00:03:31.988
But those moments of
confusion are also the times
00:03:31.988 --> 00:03:33.550
when you have the opportunity
00:03:33.550 --> 00:03:36.220
to improve your score the most.
00:03:36.220 --> 00:03:40.120
Push through by using the
hints, instructional videos
00:03:40.120 --> 00:03:42.803
or ask for help when you're
learning a new skill.
00:03:43.750 --> 00:03:47.010
As you answer questions
on Official SAT Practice,
00:03:47.010 --> 00:03:50.540
you have access to text
explanations and videos
00:03:50.540 --> 00:03:53.470
to deepen your understanding
of the content.
00:03:53.470 --> 00:03:56.910
You can also use the Review
tab to review your answers
00:03:56.910 --> 00:03:59.030
from completed practice.
00:03:59.030 --> 00:04:02.570
If you're still stuck, reach
out to one of your classmates,
00:04:02.570 --> 00:04:05.403
a teacher or a family member for support.
00:04:08.680 --> 00:04:12.413
Number four. Take a
full-length practice test.
00:04:14.890 --> 00:04:17.410
Select the Full Tests tab at the top
00:04:17.410 --> 00:04:20.593
to access the full-length
SAT practice tests.
00:04:21.610 --> 00:04:24.250
Taking a practice test is a crucial step
00:04:24.250 --> 00:04:27.090
to ensure you're prepared for a test day
00:04:27.090 --> 00:04:30.510
by simulating the real test experience.
00:04:30.510 --> 00:04:32.910
Eight full-length practice
tests are available
00:04:32.910 --> 00:04:35.020
on Official SAT Practice,
00:04:35.020 --> 00:04:36.910
which can be taken in one sitting
00:04:36.910 --> 00:04:39.023
or section by section over time.
00:04:39.890 --> 00:04:42.030
The information from your full-length test
00:04:42.030 --> 00:04:45.093
will also result in even
more personalized practice.
00:04:46.910 --> 00:04:49.200
Now that you know the
top four tips to using
00:04:49.200 --> 00:04:53.320
Official SAT Practice,
you're ready to get started.
00:04:53.320 --> 00:04:56.060
Log into your Khan Academy account today.
00:04:56.060 --> 00:04:57.123
Happy studying!
|
Khan Kickoff Pep Talk: Akbar Gbajabiamila | https://www.youtube.com/watch?v=Bue8hgXgoWc | vtt | https://www.youtube.com/api/timedtext?v=Bue8hgXgoWc&ei=7lWUZdyzLq-Dp-oP5MqtgAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=92D8F047930AB2ACE638A9933BDC95B6512D3709.E8C969FC388A295EB1297A8FBF29EF01B6A8B20E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.560 --> 00:00:02.730
- Khan Academy students, what's goin' on?
00:00:02.730 --> 00:00:07.340
It's Akbar Gbaja-Biamila, host
of American Ninja Warrior.
00:00:07.340 --> 00:00:09.330
I just wanted to check in with you guys,
00:00:09.330 --> 00:00:12.400
but also to wish you a happy New Year.
00:00:12.400 --> 00:00:14.390
It's 2021.
00:00:14.390 --> 00:00:15.990
Things are gonna be a lot different.
00:00:15.990 --> 00:00:19.010
And I know in 2020
things got crazy, right?
00:00:19.010 --> 00:00:21.610
We had the isolation and a
lot of us were struggling,
00:00:21.610 --> 00:00:23.240
going through the ups and the downs
00:00:23.240 --> 00:00:25.880
and things at home were
starting the change
00:00:25.880 --> 00:00:27.480
because of COVID-19.
00:00:27.480 --> 00:00:30.510
Well, this is a new year, a new mindset.
00:00:30.510 --> 00:00:32.950
And, as you can see,
I'm inside of my office
00:00:32.950 --> 00:00:35.230
and you can see some
of my football jerseys.
00:00:35.230 --> 00:00:37.050
And what I love about football,
00:00:37.050 --> 00:00:39.550
what I love about American Ninja Warrior,
00:00:39.550 --> 00:00:41.410
is that you constantly have obstacles
00:00:41.410 --> 00:00:42.870
that you have to overcome.
00:00:42.870 --> 00:00:46.790
That is going to happen
regardless of it's a good year
00:00:46.790 --> 00:00:49.040
or a bad year that we saw,
00:00:49.040 --> 00:00:51.550
and I put it in quote
because that's all relative,
00:00:51.550 --> 00:00:53.610
that we saw in 2020.
00:00:53.610 --> 00:00:56.010
So my coach used to tell me this,
00:00:56.010 --> 00:00:57.950
and I truly do believe this,
00:00:57.950 --> 00:01:01.390
is that tough times don't
last, but tough people do.
00:01:01.390 --> 00:01:03.280
And to be tough, what does that mean?
00:01:03.280 --> 00:01:04.700
Does that mean you have to growl, like
00:01:04.700 --> 00:01:05.690
(Akbar growls)
00:01:05.690 --> 00:01:08.470
No, what it means is that
you're willing to accept
00:01:08.470 --> 00:01:10.890
the challenges that are in front of you.
00:01:10.890 --> 00:01:14.210
You're willing to go with
the ups and the downs,
00:01:14.210 --> 00:01:17.670
but you're also knowing that
you have this trajectory,
00:01:17.670 --> 00:01:18.600
you're going up.
00:01:18.600 --> 00:01:22.260
So to the Khan Academy
students, I say this to you:
00:01:22.260 --> 00:01:25.800
be an American Ninja
Warrior in the classroom,
00:01:25.800 --> 00:01:28.330
at home, doing your personal life.
00:01:28.330 --> 00:01:30.755
Whatever it is that you're
going, have that mindset
00:01:30.755 --> 00:01:33.120
that I will overcome.
00:01:33.120 --> 00:01:35.370
You're overcome whatever those obstacles.
00:01:35.370 --> 00:01:37.140
And then when I see you at that buzzer,
00:01:37.140 --> 00:01:39.110
when you get up that warp wall in life,
00:01:39.110 --> 00:01:41.260
in school, in your personal life,
00:01:41.260 --> 00:01:43.400
and you hit that buzzer, I'm gonna say,
00:01:43.400 --> 00:01:46.130
I see you, I see you hitting that buzzer!
00:01:46.130 --> 00:01:50.970
So, take on 2021 with a new
mindset, a new attitude.
00:01:50.970 --> 00:01:52.300
Don't look in the past.
00:01:52.300 --> 00:01:55.640
It's just something for you
to reflect and move forward.
00:01:55.640 --> 00:01:57.170
I'll leave you with this:
00:01:57.170 --> 00:02:01.960
take every stumbling block
in school, in life, whatever,
00:02:01.960 --> 00:02:04.890
and turn it into a stepping stone.
00:02:04.890 --> 00:02:06.270
You got that?
00:02:06.270 --> 00:02:08.810
Stumbling block into a stepping stone,
00:02:08.810 --> 00:02:12.040
that's your challenge for 2021, all right?
00:02:12.040 --> 00:02:16.110
You guys are Khan Academy ninja warriors!
00:02:16.110 --> 00:02:18.613
Have a great school year
and we'll talk soon.
|
Khan Kickoff Overview | https://www.youtube.com/watch?v=aGAzB633b4U | vtt | https://www.youtube.com/api/timedtext?v=aGAzB633b4U&ei=7lWUZdTKMOunp-oPxue78AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5EF2664D1D989ABE3BB597DF5E6DB7F1A64B4A45.3C7C3D65371234170C3A191EAC4726A9FA64FC68&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.810 --> 00:00:01.890
- [Narrator] Here's a quick overview
00:00:01.890 --> 00:00:04.810
of our free motivation
program, Khan Kickoff.
00:00:04.810 --> 00:00:06.500
Let's start with a challenge,
00:00:06.500 --> 00:00:08.430
which is that motivating
students right now
00:00:08.430 --> 00:00:09.950
is just super hard.
00:00:09.950 --> 00:00:11.740
With everything going on in the world,
00:00:11.740 --> 00:00:13.950
getting students to show
up and engage day-after-day
00:00:13.950 --> 00:00:15.610
is no easy feat,
00:00:15.610 --> 00:00:18.530
but teachers did report one
bright spot from the fall,
00:00:18.530 --> 00:00:20.610
which was the power of teamwork.
00:00:20.610 --> 00:00:23.110
Specifically, hundreds
of educators told us
00:00:23.110 --> 00:00:25.140
that having students work
together to make progress
00:00:25.140 --> 00:00:28.730
and learn storm, got their
classes to show up and work hard
00:00:28.730 --> 00:00:30.900
even during incredibly tough times.
00:00:30.900 --> 00:00:32.870
So, Khan kickoff builds on that same sense
00:00:32.870 --> 00:00:35.990
of camaraderie to get your
students energized this winter.
00:00:35.990 --> 00:00:37.073
Here's how it works.
00:00:37.970 --> 00:00:41.510
So, all you have to do is
go to your activity overview
00:00:41.510 --> 00:00:42.900
and then on a weekly basis
00:00:42.900 --> 00:00:44.570
copying your student's progress
00:00:44.570 --> 00:00:46.270
right into your progress tracker.
00:00:46.270 --> 00:00:47.470
And then you set up your teams,
00:00:47.470 --> 00:00:50.250
either within your classroom
breaking into groups,
00:00:50.250 --> 00:00:53.270
competing against other periods
or even other classrooms.
00:00:53.270 --> 00:00:55.890
And then you celebrate your
progress with the big reveal,
00:00:55.890 --> 00:00:59.310
the scoreboard, and a chance to celebrate.
00:00:59.310 --> 00:01:03.060
And that celebration
includes custom certificates
00:01:03.060 --> 00:01:05.770
with each student being acknowledged
00:01:05.770 --> 00:01:08.320
on their own personalized certificate,
00:01:08.320 --> 00:01:09.690
as well as the ability for you
00:01:09.690 --> 00:01:12.640
as the teacher to take
your own little victory lap
00:01:12.640 --> 00:01:16.100
and show off with your certificate
to your fellow educators.
00:01:16.100 --> 00:01:17.600
And when you do that
00:01:17.600 --> 00:01:20.620
you're gonna be automatically
entered into our giveaway,
00:01:20.620 --> 00:01:22.980
which features 10 prize packs
00:01:22.980 --> 00:01:24.870
that include a Wacom drawing tablet,
00:01:24.870 --> 00:01:29.000
just like the one that Sal Khan
uses and the $100 gift card.
00:01:29.000 --> 00:01:31.400
So, you can commission
your own celebration videos
00:01:31.400 --> 00:01:33.570
from top athletes and performers.
00:01:33.570 --> 00:01:35.970
And best of all Khan kickoff is free
00:01:35.970 --> 00:01:37.520
and open to all educators.
00:01:37.520 --> 00:01:39.313
So, feel free to dive in today.
|
Primary productivity in ecosystems | https://www.youtube.com/watch?v=8zO0algdgNM | vtt | https://www.youtube.com/api/timedtext?v=8zO0algdgNM&ei=7lWUZdHQIJefp-oP5qGb0AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9C9D1309677CE458C9AC016B452E36959FCB1371.E00AA81B8D19A3B8B4FE90E8B5FFC388F30A2312&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.130 --> 00:00:01.963
- [Instructor] In this video,
00:00:01.963 --> 00:00:03.950
we're going to talk about energy,
00:00:03.950 --> 00:00:05.330
and in particular, we're gonna talk about
00:00:05.330 --> 00:00:08.190
the energy of life, the
energy that I need to live
00:00:08.190 --> 00:00:09.240
and all of us need to live,
00:00:09.240 --> 00:00:10.430
the energy you need to think,
00:00:10.430 --> 00:00:13.610
the energy I'm using to
make this video right now.
00:00:13.610 --> 00:00:15.570
And some of you might already guess
00:00:15.570 --> 00:00:17.930
where this energy is coming from,
00:00:17.930 --> 00:00:21.080
the surface of our planet is
constantly being bombarded
00:00:21.080 --> 00:00:24.740
with light energy from the Sun,
00:00:24.740 --> 00:00:27.670
and you might know that
there is certain organisms
00:00:27.670 --> 00:00:31.320
on our planet that are capable
of taking that light energy
00:00:31.320 --> 00:00:35.390
and then storing it as chemical energy.
00:00:35.390 --> 00:00:37.470
And those things, and there's many types,
00:00:37.470 --> 00:00:39.420
but the ones that we see most often
00:00:39.420 --> 00:00:42.050
in our day-to-day life, are plants.
00:00:42.050 --> 00:00:44.600
And so let's imagine a plant here.
00:00:44.600 --> 00:00:46.440
And what it's doing is,
00:00:46.440 --> 00:00:48.280
it's using that light energy
00:00:48.280 --> 00:00:50.770
in conjunction with water,
00:00:50.770 --> 00:00:52.890
typically from the soil,
00:00:52.890 --> 00:00:55.610
that maybe it's getting through its roots,
00:00:55.610 --> 00:00:59.100
and carbon dioxide in the air.
00:00:59.100 --> 00:01:01.160
And it's using that light energy
00:01:01.160 --> 00:01:04.830
to actually stick, or you could say fix,
00:01:04.830 --> 00:01:07.450
the carbon to construct itself.
00:01:07.450 --> 00:01:11.440
And in its own tissue,
it's storing that energy,
00:01:11.440 --> 00:01:13.560
and then if it were to
break down that tissue,
00:01:13.560 --> 00:01:17.610
it can release that
energy in various forms.
00:01:17.610 --> 00:01:19.230
Now, as it does this,
00:01:19.230 --> 00:01:22.580
you might also be familiar
that these photosynthesizers,
00:01:22.580 --> 00:01:26.230
or these primary producers,
or these autotrophs,
00:01:26.230 --> 00:01:30.320
they're also releasing molecular oxygen.
00:01:30.320 --> 00:01:31.700
Now, if we were to describe this
00:01:31.700 --> 00:01:34.790
in chemical terms, or chemistry terms,
00:01:34.790 --> 00:01:38.480
we would describe this
process of photosynthesis
00:01:38.480 --> 00:01:42.940
as taking carbon dioxide from the air,
00:01:42.940 --> 00:01:47.780
in conjunction with water from the soil,
00:01:47.780 --> 00:01:51.200
and what's, I guess you could
say, fueling all of this
00:01:51.200 --> 00:01:56.193
is light energy, usually from the Sun,
00:01:57.080 --> 00:02:00.730
and what that is yielding is
00:02:00.730 --> 00:02:02.260
the tissue of the plant
00:02:02.260 --> 00:02:05.340
that is actually storing that
energy is chemical energy
00:02:05.340 --> 00:02:07.010
in an organic form,
00:02:07.010 --> 00:02:12.010
and the primary way that this
is done is through glucose,
00:02:12.370 --> 00:02:16.880
which is C6H12O6.
00:02:16.880 --> 00:02:17.757
I know what you're thinking,
00:02:17.757 --> 00:02:19.260
"All plants don't taste sweet."
00:02:19.260 --> 00:02:21.210
Well, if you take chains of sugars
00:02:21.210 --> 00:02:23.410
and put them together,
you get carbohydrates,
00:02:23.410 --> 00:02:24.860
and you adapt 'em a little bit,
00:02:24.860 --> 00:02:26.450
you get things like starches,
00:02:26.450 --> 00:02:28.840
and that's what most
of the plant tissue is.
00:02:28.840 --> 00:02:30.420
So some variations of this,
00:02:30.420 --> 00:02:33.480
or variations of this linked together,
00:02:33.480 --> 00:02:35.830
but this is where the energy is stored,
00:02:35.830 --> 00:02:38.400
so energy stored,
00:02:38.400 --> 00:02:40.700
in the actual plant tissue,
00:02:40.700 --> 00:02:45.580
and then of course, it
releases that molecular oxygen.
00:02:45.580 --> 00:02:50.510
And this is the process of photosynthesis.
00:02:50.510 --> 00:02:53.820
And even if you look at
the word photosynthesis,
00:02:53.820 --> 00:02:55.140
and what the parts of it mean,
00:02:55.140 --> 00:02:57.040
photo is referring to light,
00:02:57.040 --> 00:03:00.050
and synthesis is referring to
putting something together,
00:03:00.050 --> 00:03:01.570
synthesizing something.
00:03:01.570 --> 00:03:04.070
So photosynthesis, you're using light
00:03:04.070 --> 00:03:06.980
to put together these,
00:03:06.980 --> 00:03:11.540
essentially, fix the carbon
together, to store energy.
00:03:11.540 --> 00:03:13.297
Now, you might say,
"All right, that's nice.
00:03:13.297 --> 00:03:15.297
"I'm storing the energy this way,
00:03:15.297 --> 00:03:17.680
"how do I actually use the energy?"
00:03:17.680 --> 00:03:19.530
And that's something
that all of us are doing,
00:03:19.530 --> 00:03:21.260
all living systems have to do,
00:03:21.260 --> 00:03:24.023
and that process is respiration.
00:03:25.190 --> 00:03:27.430
And you could already guess
00:03:27.430 --> 00:03:32.000
what at least the chemical reaction
00:03:32.000 --> 00:03:33.950
for respiration will look like,
00:03:33.950 --> 00:03:36.480
you're going to start
with our stored energy,
00:03:36.480 --> 00:03:38.933
our glucose C6H12O6,
00:03:43.170 --> 00:03:45.270
in the presence of oxygen.
00:03:45.270 --> 00:03:47.210
And since we're respiring all the time,
00:03:47.210 --> 00:03:50.360
this is why we need to breathe oxygen,
00:03:50.360 --> 00:03:54.580
and this is going to yield carbon dioxide,
00:03:54.580 --> 00:03:59.050
and that's why we exhale more
carbon dioxide than we inhale,
00:03:59.050 --> 00:04:02.610
it's also going to release water,
00:04:02.610 --> 00:04:03.930
and it's going to release,
00:04:03.930 --> 00:04:08.230
and this is the whole point
of it, cellular energy.
00:04:08.230 --> 00:04:10.660
And in other videos that
you'll see in a biology class
00:04:10.660 --> 00:04:14.470
will talk about how this
form of stored energy
00:04:14.470 --> 00:04:15.800
gets converted to other forms
00:04:15.800 --> 00:04:18.930
and then how that's used by
the various machinery and cells
00:04:18.930 --> 00:04:21.870
to actually live, to reproduce,
00:04:21.870 --> 00:04:24.760
to move, in many cases.
00:04:24.760 --> 00:04:26.090
Now, an interesting question is,
00:04:26.090 --> 00:04:30.730
how do you measure how much
photosynthesis is going on,
00:04:30.730 --> 00:04:34.410
how much primary productivity is going on?
00:04:34.410 --> 00:04:36.340
Well, one way to think about it is,
00:04:36.340 --> 00:04:40.500
find an ecosystem and take a certain area
00:04:40.500 --> 00:04:42.510
of the surface of that ecosystem,
00:04:42.510 --> 00:04:45.240
and it could be a terrestrial
ecosystem, on land,
00:04:45.240 --> 00:04:47.230
it could be a marine ecosystem,
00:04:47.230 --> 00:04:50.050
and then say, for this area,
00:04:50.050 --> 00:04:51.460
in a given period of time,
00:04:51.460 --> 00:04:52.790
oftentimes, a year,
00:04:52.790 --> 00:04:54.590
how much stuff is growing?
00:04:54.590 --> 00:04:56.490
So this is the stuff that grows,
00:04:56.490 --> 00:04:58.870
and obviously it would seem
00:04:58.870 --> 00:05:00.963
that the more stuff that is growing,
00:05:01.850 --> 00:05:05.510
that the more photosynthesis
that is taking place.
00:05:05.510 --> 00:05:08.430
And the way that they measure how much,
00:05:08.430 --> 00:05:11.070
how much, is growing,
00:05:11.070 --> 00:05:14.530
you could either measure it
in terms of grams of biomass,
00:05:14.530 --> 00:05:17.310
so grams of biomass,
00:05:17.310 --> 00:05:19.970
and biomass is just a fancy way of saying
00:05:19.970 --> 00:05:21.870
that the mass of biological stuff
00:05:21.870 --> 00:05:24.500
that's just growing on this area,
00:05:24.500 --> 00:05:26.360
and usually they'll take the water out
00:05:26.360 --> 00:05:27.960
so they get a consistent measurement,
00:05:27.960 --> 00:05:30.830
or you can convert this to calories,
00:05:30.830 --> 00:05:31.740
and it's usually measured
00:05:31.740 --> 00:05:34.100
in thousands of calories, kilocalories.
00:05:34.100 --> 00:05:36.950
And when you see calories
on a packaging food label,
00:05:36.950 --> 00:05:38.730
what most of us think of calories,
00:05:38.730 --> 00:05:40.110
those are actually kilocalories
00:05:40.110 --> 00:05:42.800
when we think about it
in scientific terms.
00:05:42.800 --> 00:05:44.190
And I know what you're thinking,
00:05:44.190 --> 00:05:46.627
you're like, "Wait, mass and kilocalories,
00:05:46.627 --> 00:05:48.700
"calories, that's just a form of energy."
00:05:48.700 --> 00:05:50.520
Well, those two things you can go between,
00:05:50.520 --> 00:05:52.930
because usually a certain type of biomass,
00:05:52.930 --> 00:05:54.760
a gram of a certain type of biomass,
00:05:54.760 --> 00:05:58.210
will have a certain amount
of energy stored in it,
00:05:58.210 --> 00:06:00.990
not energy that necessarily
all animals could use
00:06:00.990 --> 00:06:02.160
or that we could use,
00:06:02.160 --> 00:06:04.133
but it does have energy in it.
00:06:04.980 --> 00:06:09.000
Now, when we talk about
this primary productivity,
00:06:09.000 --> 00:06:11.147
you might already be thinking about,
00:06:11.147 --> 00:06:16.147
"Well, don't the plants need
to use some of the energy
00:06:16.197 --> 00:06:18.930
"that they are producing
themselves to live?"
00:06:18.930 --> 00:06:21.550
And my answer to you is
of course they need it.
00:06:21.550 --> 00:06:23.960
In fact, that's probably
the most important reason
00:06:23.960 --> 00:06:25.770
why they need to photosynthesize,
00:06:25.770 --> 00:06:28.380
is because they need to do respiration
00:06:28.380 --> 00:06:31.280
in order for them to grow and metabolize
00:06:31.280 --> 00:06:33.670
and live and reproduce.
00:06:33.670 --> 00:06:37.200
And so when you see how
much has been produced
00:06:37.200 --> 00:06:39.080
in a given area in given year,
00:06:39.080 --> 00:06:43.540
you're actually seeing the
net primary productivity.
00:06:43.540 --> 00:06:45.580
This is the, you could think about it,
00:06:45.580 --> 00:06:48.190
how much photosynthesis they did
00:06:48.190 --> 00:06:51.660
minus how much respiration they did.
00:06:51.660 --> 00:06:55.020
So if you think of how much
photosynthesis they did
00:06:55.020 --> 00:06:58.040
as gross primary productivity,
00:06:58.040 --> 00:07:00.460
so that's the total
amount of photosynthesis,
00:07:00.460 --> 00:07:05.460
and then you subtract
out the amount of energy,
00:07:06.090 --> 00:07:08.500
chemical energy or cellular energy
00:07:08.500 --> 00:07:10.600
they needed for respiration,
00:07:10.600 --> 00:07:15.600
that would then give you the
net primary productivity.
00:07:18.460 --> 00:07:20.040
And as I mentioned,
00:07:20.040 --> 00:07:22.800
just to make things a little bit tangible,
00:07:22.800 --> 00:07:25.400
if you took a very productive ecosystem,
00:07:25.400 --> 00:07:27.440
let's say something like a rainforest
00:07:27.440 --> 00:07:30.100
that I have here in the background,
00:07:30.100 --> 00:07:33.200
a very productive ecosystem like this,
00:07:33.200 --> 00:07:35.680
if you were to take, on average,
00:07:35.680 --> 00:07:40.340
a square meter of this,
00:07:40.340 --> 00:07:45.340
it produces in a year about
2,000 grams of biomass.
00:07:47.990 --> 00:07:51.210
So here, we would say that
the net primary productivity
00:07:51.210 --> 00:07:54.010
of this rainforest that you
see in the background here
00:07:54.010 --> 00:07:58.800
would be approximately 2,000 grams
00:07:58.800 --> 00:08:02.640
per square meter per year,
00:08:02.640 --> 00:08:04.010
and if you wanted to think about this
00:08:04.010 --> 00:08:05.030
in terms of kilocalories,
00:08:05.030 --> 00:08:05.863
you just have to say,
00:08:05.863 --> 00:08:09.850
well, if each gram of biomass
is how many kilocalories,
00:08:09.850 --> 00:08:12.370
and it depends on the type of biomass,
00:08:12.370 --> 00:08:14.520
but let's say that we have
00:08:14.520 --> 00:08:19.370
four kilocalories per gram of biomass.
00:08:19.370 --> 00:08:20.780
So then we could also say
00:08:20.780 --> 00:08:22.920
that this net primary productivity
00:08:22.920 --> 00:08:27.920
is equal to 2,000 grams
per square meter per year
00:08:29.240 --> 00:08:34.083
times four kilocalories per gram,
00:08:35.280 --> 00:08:36.710
the grams cancel out,
00:08:36.710 --> 00:08:39.000
and then you multiply four times 2,000,
00:08:39.000 --> 00:08:43.140
that's going to be 8,000 kilocalories,
00:08:43.140 --> 00:08:48.140
kilocalories per square meter per year.
00:08:48.230 --> 00:08:49.890
That would be the net
primary productivity,
00:08:49.890 --> 00:08:51.240
because that's after the plants
00:08:51.240 --> 00:08:52.910
have been doing respiration.
00:08:52.910 --> 00:08:55.830
Now, how would you figure out
gross primary productivity?
00:08:55.830 --> 00:08:58.180
Well, you're not going to
be able to do it directly,
00:08:58.180 --> 00:08:59.240
but you can figure that out
00:08:59.240 --> 00:09:01.360
by figuring out the rate of respiration.
00:09:01.360 --> 00:09:04.180
If you took some plants in that ecosystem,
00:09:04.180 --> 00:09:07.710
and then you put them in
a dark room with no light,
00:09:07.710 --> 00:09:12.110
and then you if you saw how
much oxygen they are absorbing,
00:09:12.110 --> 00:09:13.760
or they're having to use,
00:09:13.760 --> 00:09:15.480
then that gives you a sense
00:09:15.480 --> 00:09:18.880
of how much respiration they are doing.
00:09:18.880 --> 00:09:20.630
And there's ways that you
could look at the ratios
00:09:20.630 --> 00:09:22.030
of the oxygens and the carbons
00:09:22.030 --> 00:09:25.690
to figure out exactly how
much respiration is going on.
00:09:25.690 --> 00:09:27.920
And then if you know the
net primary productivity
00:09:27.920 --> 00:09:29.560
and the rate of respiration,
00:09:29.560 --> 00:09:33.010
then you could figure out the
gross primary productivity.
00:09:33.010 --> 00:09:34.310
But I will leave you there,
00:09:34.310 --> 00:09:36.520
because these are really
useful measurements.
00:09:36.520 --> 00:09:37.470
Well, one, it's really useful
00:09:37.470 --> 00:09:38.870
to think about where all of the energy
00:09:38.870 --> 00:09:40.790
that allows us to live comes from,
00:09:40.790 --> 00:09:42.950
but it's also useful for ecologists
00:09:42.950 --> 00:09:44.800
to think about how productive a system is,
00:09:44.800 --> 00:09:47.540
or what's making it more
productive, or less productive.
00:09:47.540 --> 00:09:49.580
And as we'll see, these numbers here,
00:09:49.580 --> 00:09:52.070
these are for sure on the high end
00:09:52.070 --> 00:09:54.360
of net primary productivity.
00:09:54.360 --> 00:09:56.850
If we were in a desert type of ecosystem,
00:09:56.850 --> 00:09:59.620
this number might be in the low hundreds
00:09:59.620 --> 00:10:02.513
and not in the 8,000 range.
|
Elon Musk $5 million donation to Khan Academy thank you | https://www.youtube.com/watch?v=id_MB2RClG4 | vtt | https://www.youtube.com/api/timedtext?v=id_MB2RClG4&ei=7lWUZYnRHM6Ip-oPie6hIA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=BCB2A00BEB52831590F4C0C7F7127CE57AC4ADAA.ECEB9B1FF5F62CE6850066FBC4E2273ABD5D0AEC&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.780 --> 00:00:03.410
- Hi everyone, Sal Khan
here from Khan Academy.
00:00:03.410 --> 00:00:06.080
And I just wanted to give a
huge shout out and thank you
00:00:06.080 --> 00:00:09.370
to Elon Musk and everyone
at the Musk Foundation
00:00:09.370 --> 00:00:12.280
for their incredibly generous
support for Khan Academy,
00:00:12.280 --> 00:00:16.250
they just recently gave
a $5 million donation
00:00:16.250 --> 00:00:18.200
to Khan Academy.
00:00:18.200 --> 00:00:21.570
Elon I hope you really
feel good about this.
00:00:21.570 --> 00:00:22.840
This is going to allow us
00:00:22.840 --> 00:00:25.670
to accelerate all sorts of content.
00:00:25.670 --> 00:00:27.690
Our aspirations are all subjects
00:00:27.690 --> 00:00:30.370
from K through the
early stages of college.
00:00:30.370 --> 00:00:32.150
This will accelerate our science content,
00:00:32.150 --> 00:00:33.980
allow us to do more on early learning,
00:00:33.980 --> 00:00:36.560
allow us to make the
software and the practice
00:00:36.560 --> 00:00:39.420
that much more engaging
for millions of students
00:00:39.420 --> 00:00:42.210
around the world, for
teachers around the world.
00:00:42.210 --> 00:00:44.650
And as far as Khan Academy has come,
00:00:44.650 --> 00:00:47.250
we have 120 million registered users,
00:00:47.250 --> 00:00:50.770
20 or 30 million students
using the platform every month.
00:00:50.770 --> 00:00:54.880
We have about 200 million
hours of learning a year,
00:00:54.880 --> 00:00:56.550
which any way you want to evaluate that
00:00:56.550 --> 00:00:59.440
that's worth a lot to the world.
00:00:59.440 --> 00:01:00.880
And when you look at our efficacy studies
00:01:00.880 --> 00:01:03.740
and how we've been able to
move the dial in classrooms
00:01:03.740 --> 00:01:06.930
just that social return
to investment ratio
00:01:06.930 --> 00:01:09.720
is 400 to 500 to one.
00:01:09.720 --> 00:01:11.960
A good return in the philanthropic sector
00:01:11.960 --> 00:01:15.440
is considered a five to one
ratio or 10 to one ratio.
00:01:15.440 --> 00:01:17.810
So as much as progress has been made,
00:01:17.810 --> 00:01:19.080
I think you appreciate,
00:01:19.080 --> 00:01:21.550
and hopefully everyone
watching appreciates
00:01:21.550 --> 00:01:23.760
that there's many billions who need this
00:01:23.760 --> 00:01:25.510
there's people throughout the planet
00:01:25.510 --> 00:01:29.070
who need a way to tap
into their potential.
00:01:29.070 --> 00:01:32.690
And I view this type of
investment in what we're doing
00:01:32.690 --> 00:01:35.530
as really foundational
for us to be able to build
00:01:35.530 --> 00:01:38.000
a multi-generational institution.
00:01:38.000 --> 00:01:40.970
So that future Elon Musk's of the world
00:01:40.970 --> 00:01:43.940
are also able to tap into their potential
00:01:43.940 --> 00:01:48.940
and help all of us up-level
who we are as a civilization,
00:01:49.060 --> 00:01:51.740
for everyone listening
I wanna remind folks
00:01:51.740 --> 00:01:54.050
that as incredible as this donation is,
00:01:54.050 --> 00:01:57.360
and it really is incredible,
that we do need more help
00:01:57.360 --> 00:02:01.520
we continue to be running
at a deficit for 2021.
00:02:01.520 --> 00:02:03.970
So every donation of every size helps
00:02:03.970 --> 00:02:06.030
and we're able to take
every one of those dollars
00:02:06.030 --> 00:02:07.910
and it helps us accelerate learning
00:02:07.910 --> 00:02:09.970
in a whole bunch of dimensions.
00:02:09.970 --> 00:02:12.890
The world as a whole spends $5 trillion
00:02:12.890 --> 00:02:15.950
on education annually
Khan Academy's budget
00:02:15.950 --> 00:02:18.860
is one, 100,000th of that.
00:02:18.860 --> 00:02:20.690
We are the budget of a large high school,
00:02:20.690 --> 00:02:23.030
but our aspirations
are to serve the globe.
00:02:23.030 --> 00:02:27.940
So hopefully, more folks
listening at all scales,
00:02:27.940 --> 00:02:30.420
can help support what we're trying to do.
00:02:30.420 --> 00:02:31.930
And the last thing I'll mention,
00:02:31.930 --> 00:02:34.000
and it's especially powerful to get
00:02:34.000 --> 00:02:35.380
a donation from you Elon.
00:02:35.380 --> 00:02:38.100
I had the privilege of
interviewing you back in 2013,
00:02:38.100 --> 00:02:39.240
when you visited our office
00:02:39.240 --> 00:02:41.070
and someone on YouTube commented.
00:02:41.070 --> 00:02:43.210
I wanna find someone who looks at me
00:02:43.210 --> 00:02:45.240
the same way that Sal looks at Elon
00:02:45.240 --> 00:02:47.260
and they were catching onto something.
00:02:47.260 --> 00:02:49.330
I do look up to you and incredible way
00:02:49.330 --> 00:02:52.340
any time that I questioned even myself
00:02:52.340 --> 00:02:54.870
and I say, is this mission too big
00:02:54.870 --> 00:02:57.470
to actually try to
educate all of humanity?
00:02:57.470 --> 00:03:00.400
I think of the incredible
work that you've done.
00:03:00.400 --> 00:03:04.480
I remember back in 2013
when I interviewed you
00:03:04.480 --> 00:03:06.310
pretty much everything you
said you were going to do,
00:03:06.310 --> 00:03:08.940
and you made some pretty large statements
00:03:08.940 --> 00:03:12.180
you have either done or your
very close to doing right now.
00:03:12.180 --> 00:03:14.140
And I take incredible inspiration
00:03:14.140 --> 00:03:16.040
that it is not too big of a mission
00:03:16.040 --> 00:03:19.150
that if anything, we
cannot shy away right now
00:03:19.150 --> 00:03:20.310
from this goal,
00:03:20.310 --> 00:03:22.960
just as we shouldn't shy
away from solving climate,
00:03:22.960 --> 00:03:24.440
solving transportation,
00:03:24.440 --> 00:03:26.930
being able to colonize other planets,
00:03:26.930 --> 00:03:29.620
we can't shy away from
educating the planet
00:03:29.620 --> 00:03:31.990
and other planets, going forward.
00:03:31.990 --> 00:03:33.990
So thank you so much and I look forward
00:03:33.990 --> 00:03:36.103
to going on this journey
with all of y'all.
|
Energy flow in a marine ecosystem | https://www.youtube.com/watch?v=fL0W_boPHLs | vtt | https://www.youtube.com/api/timedtext?v=fL0W_boPHLs&ei=7lWUZZTNI7uJp-oPrp6j8AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B2189102B75BD89E3584E4758FFCA79C9EEE9F8A.8576BF528DA292234DDE76079B134CB3EAA73B&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.370 --> 00:00:02.130
- [Instructor] In this video
we're gonna take a deeper look
00:00:02.130 --> 00:00:05.560
at the various producers and
consumers in an ecosystem.
00:00:05.560 --> 00:00:08.930
And for the sake of
diversity, no pun intended,
00:00:08.930 --> 00:00:10.870
we're gonna look at a marine ecosystem,
00:00:10.870 --> 00:00:12.300
let's say an estuary.
00:00:12.300 --> 00:00:16.010
And an estuary generally refers to a place
00:00:16.010 --> 00:00:20.940
where you have a river coming
to where the tide comes.
00:00:20.940 --> 00:00:23.350
So it's a mixture of both the
fresh water from the river
00:00:23.350 --> 00:00:25.240
and the saltwater from the sea.
00:00:25.240 --> 00:00:29.670
And they tend to be very
productive from an energetic,
00:00:29.670 --> 00:00:33.040
or a biomass point of view.
00:00:33.040 --> 00:00:35.470
So if I were to make an
energy pyramid for, let's say,
00:00:35.470 --> 00:00:38.140
this estuary that we're
looking at right over here,
00:00:38.140 --> 00:00:40.670
it might look something like this,
00:00:40.670 --> 00:00:45.100
where at the bottom layer,
these are the primary producers,
00:00:45.100 --> 00:00:47.470
and we've studied this in other videos.
00:00:47.470 --> 00:00:50.710
Primary producers in a marine environment.
00:00:50.710 --> 00:00:53.380
These would be things like phytoplankton.
00:00:53.380 --> 00:00:56.240
Phyto, they're doing photosynthesis,
00:00:56.240 --> 00:00:57.073
and they're plankton.
00:00:57.073 --> 00:00:58.490
Plankton is a general term.
00:00:58.490 --> 00:01:01.130
It comes from the Greek for drifter.
00:01:01.130 --> 00:01:03.820
This right over here is sea grass.
00:01:03.820 --> 00:01:06.300
Also something that can photosynthesize,
00:01:06.300 --> 00:01:08.220
and this right over here is algae,
00:01:08.220 --> 00:01:11.230
which I'm sure you have seen
when you've gone to the sea
00:01:11.230 --> 00:01:13.640
or you've gone to a pond of some sort.
00:01:13.640 --> 00:01:16.500
And when we think of photosynthesis,
00:01:16.500 --> 00:01:18.360
we often talk about terrestrial things.
00:01:18.360 --> 00:01:22.910
Things like trees, but a lot
of us don't realize that 50%,
00:01:22.910 --> 00:01:25.920
that's a big number, of
Earth's photosynthesis,
00:01:25.920 --> 00:01:30.920
or net primary production,
or organic energy compounds,
00:01:31.270 --> 00:01:34.700
is produced by floating photosynthesizers,
00:01:34.700 --> 00:01:36.960
like phytoplankton and ultraplankton.
00:01:36.960 --> 00:01:40.280
So things like this, things
that you oftentimes don't see.
00:01:40.280 --> 00:01:43.730
And as I mentioned, estuaries
tend to be quite productive.
00:01:43.730 --> 00:01:46.640
They actually are comparable
to things like rainforests.
00:01:46.640 --> 00:01:48.810
Now, for the sake of
making things tangible,
00:01:48.810 --> 00:01:51.550
this being an estuary,
which is very productive,
00:01:51.550 --> 00:01:54.520
let's imagine that the net
primary production from
00:01:54.520 --> 00:01:57.920
this first layer, we can think
about it in terms of biomass,
00:01:57.920 --> 00:02:02.920
maybe it's about 2,000 grams
per square meter per year.
00:02:05.240 --> 00:02:07.990
Or we could think about
it in terms of calories.
00:02:07.990 --> 00:02:10.320
This would be approximately equal to it.
00:02:10.320 --> 00:02:12.970
It depends on the type of
biomass you're talking about,
00:02:12.970 --> 00:02:17.380
but you have roughly four
kilocalories per gram.
00:02:17.380 --> 00:02:21.780
So that would be roughly
8,000 kilocalories
00:02:22.670 --> 00:02:26.100
per square meter per year.
00:02:26.100 --> 00:02:29.290
That's the net primary
production of this first layer
00:02:29.290 --> 00:02:31.490
of the primary producers.
00:02:31.490 --> 00:02:33.620
Then what would we see at the next layer?
00:02:33.620 --> 00:02:36.840
Well, we know that not all
of that energy can be used
00:02:36.840 --> 00:02:41.840
by that next layer, which
would be the primary consumers.
00:02:41.850 --> 00:02:45.360
And there's some examples here
and it's much more complex
00:02:45.360 --> 00:02:47.860
than what this pyramid
depicts, but what we see here,
00:02:47.860 --> 00:02:50.180
these are zooplankton, which are really,
00:02:50.180 --> 00:02:51.560
you could view it as animal plankton.
00:02:51.560 --> 00:02:53.480
It's a large category of things.
00:02:53.480 --> 00:02:54.660
They have the word plankton in it.
00:02:54.660 --> 00:02:56.070
So they kinda have to go with the flow
00:02:56.070 --> 00:02:57.380
of whatever the tide is doing,
00:02:57.380 --> 00:02:58.780
whatever the currents are doing.
00:02:58.780 --> 00:03:01.230
Another primary consumer could be a fish
00:03:01.230 --> 00:03:05.290
like this royal blue tang
that might be eating plankton,
00:03:05.290 --> 00:03:09.270
and the net energy that's
available to the layer above that
00:03:09.270 --> 00:03:12.400
is gonna be a small fraction
of the net primary productivity
00:03:12.400 --> 00:03:13.750
of that first layer.
00:03:13.750 --> 00:03:15.870
Typically it's about 10%.
00:03:15.870 --> 00:03:16.750
So there might be,
00:03:16.750 --> 00:03:19.650
instead of 8,000
kilocalories, 10% of that,
00:03:19.650 --> 00:03:21.293
we'd be talking about approximately
00:03:21.293 --> 00:03:26.293
800 potential kilocalories
per square meter per year
00:03:27.350 --> 00:03:29.610
that'd be available for the next layer.
00:03:29.610 --> 00:03:31.150
Now you might be saying, "Hey,
00:03:31.150 --> 00:03:34.060
where are all of the
other calories going?"
00:03:34.060 --> 00:03:36.170
Well, remember, even in this first layer,
00:03:36.170 --> 00:03:38.940
we said this is net primary production.
00:03:38.940 --> 00:03:40.590
The gross would be even higher.
00:03:40.590 --> 00:03:44.530
These photosynthesizers had
to use that energy for things
00:03:44.530 --> 00:03:47.510
like respiration, and
even on the net basis,
00:03:47.510 --> 00:03:49.230
the reason why so much
gets lost when you go
00:03:49.230 --> 00:03:51.970
to the next layer, is these animals here.
00:03:51.970 --> 00:03:54.360
They have to use that energy to live,
00:03:54.360 --> 00:03:58.550
to do things like respiration
and a lot of this energy is
00:03:58.550 --> 00:04:00.610
just not consumable by the next layer.
00:04:00.610 --> 00:04:02.270
So it can become detritus, which is,
00:04:02.270 --> 00:04:04.210
you can just think of this biomass
00:04:04.210 --> 00:04:06.090
that is just laying around.
00:04:06.090 --> 00:04:08.610
Energy at every level can be lost to heat,
00:04:08.610 --> 00:04:11.100
can be used for movement, for growth.
00:04:11.100 --> 00:04:13.170
So you can imagine you
get to a level above that,
00:04:13.170 --> 00:04:17.310
we could call this secondary consumer.
00:04:17.310 --> 00:04:19.960
And this is just a picture of a grouper.
00:04:19.960 --> 00:04:22.900
Marine ecosystems would be
much more complex than this,
00:04:22.900 --> 00:04:26.540
but the net calories after
the groupers lived their life,
00:04:26.540 --> 00:04:28.580
et cetera, et cetera, that
is available to the level
00:04:28.580 --> 00:04:30.990
above that would be roughly, again, 10%.
00:04:30.990 --> 00:04:35.990
So maybe 80 kilocalories
per square meter per year.
00:04:36.720 --> 00:04:38.300
And that at least in this example,
00:04:38.300 --> 00:04:39.840
at the top of this pyramid,
00:04:39.840 --> 00:04:43.920
we have an apex predator, that is a shark.
00:04:43.920 --> 00:04:47.020
What is available after
the shark's done all
00:04:47.020 --> 00:04:49.410
of its business is roughly 10% of that.
00:04:49.410 --> 00:04:52.140
So approximately eight kilocalories
00:04:53.310 --> 00:04:57.750
per square meter per year.
00:04:57.750 --> 00:05:00.910
And so the important
thing to think about is,
00:05:00.910 --> 00:05:02.330
whether we're talking about terrestrial
00:05:02.330 --> 00:05:04.220
or marine environments,
00:05:04.220 --> 00:05:07.060
you have this significant
loss of energy as we go
00:05:07.060 --> 00:05:10.540
from one layer of the pyramid to another,
00:05:10.540 --> 00:05:13.030
but at the same time, everyone
has to be using energy.
00:05:13.030 --> 00:05:15.030
And the energy has to come from someplace
00:05:15.030 --> 00:05:16.820
and we've covered in other videos,
00:05:16.820 --> 00:05:19.060
it's coming from sunlight.
00:05:19.060 --> 00:05:21.890
And there has to be this continual process
00:05:21.890 --> 00:05:25.220
of taking light energy and
through photosynthesis converting
00:05:25.220 --> 00:05:27.790
it into a form of energy
that can be used by life.
00:05:27.790 --> 00:05:30.120
And then you have significant energy loss,
00:05:30.120 --> 00:05:32.820
but that energy keeps
flowing up this pyramid.
00:05:32.820 --> 00:05:35.390
And we're not even done because
even the apex predators,
00:05:35.390 --> 00:05:36.950
at some point they're going to die
00:05:36.950 --> 00:05:39.450
and then they have tissue
and in that biomass
00:05:39.450 --> 00:05:42.340
there's energy that could
be consumed by others.
00:05:42.340 --> 00:05:44.340
Also to release nutrients
that could be used
00:05:44.340 --> 00:05:46.340
by these initial primary producers.
00:05:46.340 --> 00:05:49.950
And that's where things like detritivores,
00:05:49.950 --> 00:05:51.880
and this is a starfish,
which is a detritivore,
00:05:51.880 --> 00:05:54.770
things that can actually
consume dead matter.
00:05:54.770 --> 00:05:57.730
They are really useful because
then they can bring nutrients
00:05:57.730 --> 00:06:01.270
back to primary producers, and to others.
00:06:01.270 --> 00:06:03.170
And when we're talking
about an aquatic environment
00:06:03.170 --> 00:06:05.500
like this and we're talking
about photosynthesis,
00:06:05.500 --> 00:06:06.897
one question you might be asking is,
00:06:06.897 --> 00:06:09.570
"Wait, where can photosynthesis occur?
00:06:09.570 --> 00:06:12.080
If you go deep enough it's
going to get quite dark."
00:06:12.080 --> 00:06:14.670
And you'd be right if you
were asking that question.
00:06:14.670 --> 00:06:16.570
When you think about marine environments,
00:06:16.570 --> 00:06:19.930
there's something known
as a euphotic zone,
00:06:19.930 --> 00:06:22.710
which is the zone where
it's shallow enough
00:06:22.710 --> 00:06:24.050
to get enough light
00:06:24.050 --> 00:06:26.490
so that you can actually
do photosynthesis.
00:06:26.490 --> 00:06:29.850
And so it's no coincidence
that things like estuaries,
00:06:29.850 --> 00:06:31.850
things where the water is shallower,
00:06:31.850 --> 00:06:33.400
where there's going to be more nutrients
00:06:33.400 --> 00:06:35.030
and where there's going to be more light,
00:06:35.030 --> 00:06:38.500
that you actually have
more primary production.
|
Reminder: Support Khan Academy today! | https://www.youtube.com/watch?v=jTIwEYeDCf8 | vtt | https://www.youtube.com/api/timedtext?v=jTIwEYeDCf8&ei=7lWUZZ7QLfmdvdIPopOJmA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EFA0592415333187A114181CD242A73517EE7F20.BCA49FD9FA57F84A540A32580C88C29046635D30&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.290 --> 00:00:02.450
- Hi, Sal Khan here from Khan Academy.
00:00:02.450 --> 00:00:03.620
And I just wanna remind you
00:00:03.620 --> 00:00:06.170
that as we get to the
final few days of 2020,
00:00:06.170 --> 00:00:09.080
which has been a tough year,
I think for most of us,
00:00:09.080 --> 00:00:11.550
there's also the final few days of our
00:00:11.550 --> 00:00:13.200
end-of-year giving campaign.
00:00:13.200 --> 00:00:14.960
And as we go through those final few days,
00:00:14.960 --> 00:00:17.410
I wanna remind you that Khan
Academy is a not-for-profit
00:00:17.410 --> 00:00:19.590
with the mission of providing
a free world-class education
00:00:19.590 --> 00:00:22.400
for anyone anywhere, we
can only do that work
00:00:22.400 --> 00:00:25.530
through philanthropic donations
from folks like yourself.
00:00:25.530 --> 00:00:27.200
And any way you slice it,
00:00:27.200 --> 00:00:30.450
the social return on every dollar you give
00:00:30.450 --> 00:00:32.460
is really off the charts for Khan Academy.
00:00:32.460 --> 00:00:33.850
Think of the scale,
00:00:33.850 --> 00:00:36.530
think of the tens or
hundreds of millions of folks
00:00:36.530 --> 00:00:40.180
that Khan Academy reaches
in over 46 languages
00:00:40.180 --> 00:00:41.590
around the world.
00:00:41.590 --> 00:00:44.610
And if that by itself
isn't convincing enough,
00:00:44.610 --> 00:00:46.560
I'll give you some of my
favorite recent research
00:00:46.560 --> 00:00:47.420
that I've been looking at,
00:00:47.420 --> 00:00:49.910
which is how do you
become a happier person.
00:00:49.910 --> 00:00:52.320
And there's some things like
you should sleep enough,
00:00:52.320 --> 00:00:57.060
you should meditate, you
should have gratitude,
00:00:57.060 --> 00:00:59.280
but also do random acts of kindness,
00:00:59.280 --> 00:01:02.610
and a very powerful random act of kindness
00:01:02.610 --> 00:01:04.300
would be to donate to Khan Academy.
00:01:04.300 --> 00:01:06.840
So not only will it help
others tap into their potential
00:01:06.840 --> 00:01:09.760
around the world, millions
and millions of people,
00:01:09.760 --> 00:01:14.000
I think it actually might
make all of us happy
00:01:14.000 --> 00:01:17.420
by giving to it as well
and make you feel good
00:01:17.420 --> 00:01:21.970
about strong way of ending
another wise tough year
00:01:21.970 --> 00:01:26.080
and going into 2021 on a
very very positive footing.
00:01:26.080 --> 00:01:27.860
So if you're in a position to do so,
00:01:27.860 --> 00:01:30.290
please think about making
a donation to Khan Academy,
00:01:30.290 --> 00:01:32.940
we wouldn't be able to do
the work we do without you.
|
Khan Lab School | https://www.youtube.com/watch?v=OSLITlRlEuQ | vtt | https://www.youtube.com/api/timedtext?v=OSLITlRlEuQ&ei=7lWUZcbJMIK5mLAPtLWl2AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=78F25A80E025D636D31E107C7E29F6F6296E05C0.7E5233C7AE4D03B381F093703802510033D52E5D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.230 --> 00:00:01.990
- Hi, everyone, Sal Khan here.
00:00:01.990 --> 00:00:04.010
And I just wanted to tell you all
00:00:04.010 --> 00:00:07.420
that we've reached kind of
several really cool milestones
00:00:07.420 --> 00:00:09.300
at Khan Lab School,
which you can learn more
00:00:09.300 --> 00:00:13.550
about at khanlabschool.org or kls.org.
00:00:13.550 --> 00:00:15.940
A lot of folks are surprised to hear
00:00:15.940 --> 00:00:20.410
that I started a physical
school back in 2014
00:00:20.410 --> 00:00:22.250
when I'm so associated
with online learning.
00:00:22.250 --> 00:00:23.840
But I've never viewed online
00:00:23.840 --> 00:00:26.770
as somehow a replacement
for an in-person experience.
00:00:26.770 --> 00:00:28.030
The dream has always been
00:00:28.030 --> 00:00:31.230
that online can unlock
the physical experience.
00:00:31.230 --> 00:00:33.350
It can allow students to learn
00:00:33.350 --> 00:00:35.640
at a pace that is appropriate for them.
00:00:35.640 --> 00:00:38.910
It could allow for mastery-based learning
00:00:38.910 --> 00:00:41.470
where if you get an 80% on something,
00:00:41.470 --> 00:00:43.400
you don't just get a C on your forehead
00:00:43.400 --> 00:00:44.670
and your permanent transcript
00:00:44.670 --> 00:00:46.870
and then you're expected
to learn the next concept
00:00:46.870 --> 00:00:49.060
that builds on that 20% gap.
00:00:49.060 --> 00:00:51.190
Instead, you're expected
to master the concept.
00:00:51.190 --> 00:00:53.500
So you always have a strong foundation.
00:00:53.500 --> 00:00:56.470
That we can unlock a situation when
00:00:56.470 --> 00:00:58.980
human beings get to a classroom together,
00:00:58.980 --> 00:01:00.530
both the students and the teachers,
00:01:00.530 --> 00:01:02.160
they're able to interact with each other,
00:01:02.160 --> 00:01:03.910
they're able to collaborate
with each other,
00:01:03.910 --> 00:01:07.300
they're able to have Socratic
dialogues, have games.
00:01:07.300 --> 00:01:10.970
They're able to do projects together.
00:01:10.970 --> 00:01:13.210
We wanted to create a
reality where students
00:01:13.210 --> 00:01:15.920
aren't just accountable
for their own gains
00:01:15.920 --> 00:01:18.900
or their own progress
but also for each other,
00:01:18.900 --> 00:01:20.210
that they're invested in each other,
00:01:20.210 --> 00:01:22.610
that they are unusually collaborative.
00:01:22.610 --> 00:01:24.970
We wanted to explore blurring the lines
00:01:24.970 --> 00:01:26.900
between high school and college.
00:01:26.900 --> 00:01:28.370
If kids are able to learn more,
00:01:28.370 --> 00:01:30.890
be truly curious, be truly engaged.
00:01:30.890 --> 00:01:34.330
Why can't they learn faster
than you would normally expect?
00:01:34.330 --> 00:01:36.970
The middle schoolers can
learn high school concepts,
00:01:36.970 --> 00:01:39.090
high school students can
learn college concepts
00:01:39.090 --> 00:01:40.520
and get credit for it.
00:01:40.520 --> 00:01:42.760
So that by the time they graduate,
00:01:42.760 --> 00:01:45.050
they're already operating at a junior
00:01:45.050 --> 00:01:46.710
or a senior level in college
00:01:46.710 --> 00:01:48.410
and actually getting credit for it.
00:01:48.410 --> 00:01:50.630
And so the milestone that we're at
00:01:50.630 --> 00:01:52.950
is that we're actually now at
a full K through 12 school,
00:01:52.950 --> 00:01:56.380
over 200 students, we have
our first graduates this year.
00:01:56.380 --> 00:01:58.660
And you could imagine in the early days
00:01:58.660 --> 00:01:59.493
a lot of people went,
00:01:59.493 --> 00:02:01.920
well, these are all
interesting ideas, Sal,
00:02:01.920 --> 00:02:03.670
but will this work?
00:02:03.670 --> 00:02:05.320
And it's a lab school,
00:02:05.320 --> 00:02:07.970
there's all sorts of stuff
that we're constantly trying.
00:02:07.970 --> 00:02:10.520
But you know, when I look at
this year's graduating cohort,
00:02:10.520 --> 00:02:12.860
I'm incredibly proud of them,
00:02:12.860 --> 00:02:16.150
mainly for who they have
become as human beings,
00:02:16.150 --> 00:02:18.450
but some of the traditional metrics
00:02:18.450 --> 00:02:22.750
by which we measure students,
they're also crushing it,
00:02:22.750 --> 00:02:24.490
I guess is the best way to say it,
00:02:24.490 --> 00:02:27.550
which is really powerful to show that
00:02:27.550 --> 00:02:29.500
you can create a learning experience
00:02:29.500 --> 00:02:32.360
where kids are intrinsically curious.
00:02:32.360 --> 00:02:35.470
They're intrinsically wanna
collaborate with each other
00:02:35.470 --> 00:02:37.250
and just wanna learn more.
00:02:37.250 --> 00:02:40.000
But as a by-product of
it, not as a goal of it,
00:02:40.000 --> 00:02:42.700
they're able to do incredibly
well on standardized tests.
00:02:42.700 --> 00:02:45.450
Our students are scoring on average
00:02:45.450 --> 00:02:46.670
better on standardized tests
00:02:46.670 --> 00:02:49.900
than some of the very top
universities in the country
00:02:49.900 --> 00:02:51.270
or in the world.
00:02:51.270 --> 00:02:52.280
They are getting in to
00:02:52.280 --> 00:02:55.360
some of the top universities in the world
00:02:55.360 --> 00:02:57.350
even though they don't have
traditional letter grades
00:02:57.350 --> 00:02:59.980
because the universities
are seeing that the grades
00:02:59.980 --> 00:03:02.230
of mastery based learning
are even more powerful
00:03:02.230 --> 00:03:03.640
because it's a higher standards,
00:03:03.640 --> 00:03:07.430
it's expecting that all students
really master the concepts.
00:03:07.430 --> 00:03:09.790
We're deepening our partnership
with Foothill College
00:03:09.790 --> 00:03:12.360
which is a local college in the area
00:03:12.360 --> 00:03:14.540
to get the best of both worlds,
00:03:14.540 --> 00:03:18.280
the high school experience
and the college experience.
00:03:18.280 --> 00:03:20.590
And so they have some exciting things
00:03:20.590 --> 00:03:23.620
that I can't announce it just
yet also on the capacity side.
00:03:23.620 --> 00:03:25.530
And so that's why I'm
out here telling folks
00:03:25.530 --> 00:03:28.900
normally we can only admit
a few folks every year,
00:03:28.900 --> 00:03:31.400
but this year there might
be an opportunity for more.
00:03:31.400 --> 00:03:32.370
So, if you're interested,
00:03:32.370 --> 00:03:35.420
if you live in the San
Francisco Bay area in particular
00:03:35.420 --> 00:03:37.310
within driving distance to Mountain View,
00:03:37.310 --> 00:03:41.070
Palo Alto Los Altos, encourage
you to take a look at it.
00:03:41.070 --> 00:03:42.940
And I'm happy to answer any questions
00:03:42.940 --> 00:03:44.200
in the message board below
00:03:44.200 --> 00:03:46.780
that you might have about Khan Lab School.
00:03:46.780 --> 00:03:50.530
My kids go there, I teach
there, I work very closely
00:03:50.530 --> 00:03:53.000
with the faculty and the
administration there.
00:03:53.000 --> 00:03:54.690
And what's exciting about it for me,
00:03:54.690 --> 00:03:57.110
is that not just creating a really
00:03:57.110 --> 00:03:58.710
unique learning experience
00:03:58.710 --> 00:04:01.130
for the students who attend,
00:04:01.130 --> 00:04:05.360
but as a lab school, creating
a model that can be replicated
00:04:05.360 --> 00:04:06.310
throughout the world.
00:04:06.310 --> 00:04:07.143
So once again,
00:04:07.143 --> 00:04:09.710
happy to answer any questions
that anyone might have.
|
Sampling distribution of the difference in sample means | https://www.youtube.com/watch?v=p24UTvbKZog | vtt | https://www.youtube.com/api/timedtext?v=p24UTvbKZog&ei=7lWUZfeELpW3mLAPubyJ6A4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0F7E5B5404DE160CE9F6E5C0E5259C5C77B75E83.01E804EB2D5DE8F149BD7F7F5409559B1802A6DF&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.270 --> 00:00:01.590
- [Teacher] What we're
going to do in this video
00:00:01.590 --> 00:00:05.440
is explore the sampling
distribution for a difference
00:00:05.440 --> 00:00:10.100
in sample means, and we'll use
this example right over here.
00:00:10.100 --> 00:00:12.030
So it tells us a large bakery
00:00:12.030 --> 00:00:15.620
makes thousands of cupcakes
daily in two shifts:
00:00:15.620 --> 00:00:18.300
shift A and shift B.
00:00:18.300 --> 00:00:23.010
Suppose that, on average,
cupcakes from shift A
00:00:23.010 --> 00:00:27.270
weigh 130 grams with a
standard deviation of 4 grams.
00:00:27.270 --> 00:00:30.320
For shift B, the mean
and standard deviation
00:00:30.320 --> 00:00:34.510
are 125 grams and 3 grams, respectively.
00:00:34.510 --> 00:00:37.970
Assume independence between shifts.
00:00:37.970 --> 00:00:41.700
Every day, the bakery takes
a simple random sample
00:00:41.700 --> 00:00:44.940
of 40 cupcakes from each shift.
00:00:44.940 --> 00:00:48.490
They calculate the mean
weight for each sample,
00:00:48.490 --> 00:00:51.100
then look at the difference, A minus B,
00:00:51.100 --> 00:00:53.710
between the sample means.
00:00:53.710 --> 00:00:57.970
Find the probability that the
mean weights from the samples
00:00:57.970 --> 00:01:02.260
are more than 6 grams
apart from each other.
00:01:02.260 --> 00:01:03.930
So I'm actually not gonna
tell you immediately
00:01:03.930 --> 00:01:04.763
to pause this video
00:01:04.763 --> 00:01:06.340
and try to work through this on your own.
00:01:06.340 --> 00:01:08.550
First I'm gonna think about
how we could break this down,
00:01:08.550 --> 00:01:10.390
and then I'll ask you to pause
00:01:10.390 --> 00:01:13.260
and try to tackle each
of those parts by itself.
00:01:13.260 --> 00:01:15.810
So in order to tackle
this eventual question,
00:01:15.810 --> 00:01:17.640
we're going to have to
think about the mean
00:01:17.640 --> 00:01:19.460
of the sampling distribution
00:01:19.460 --> 00:01:22.130
for the difference in sample means.
00:01:22.130 --> 00:01:27.130
So sample mean from group A
minus sample mean for group B.
00:01:27.380 --> 00:01:30.350
We're gonna have to think
about the standard deviation
00:01:30.350 --> 00:01:32.320
of the sampling distribution
00:01:32.320 --> 00:01:36.140
for the difference in sample means.
00:01:36.140 --> 00:01:37.110
And we're going to have to think
00:01:37.110 --> 00:01:40.690
about is this distribution normal?
00:01:40.690 --> 00:01:43.090
If we're able to figure
out these three things,
00:01:43.090 --> 00:01:44.210
then we just have to figure out,
00:01:44.210 --> 00:01:46.910
well, how many standard
deviations away from the mean
00:01:46.910 --> 00:01:47.743
is this?
00:01:47.743 --> 00:01:49.700
And we could use your standard z-table
00:01:49.700 --> 00:01:51.950
to figure out the probability.
00:01:51.950 --> 00:01:54.750
So now I encourage you to pause this video
00:01:54.750 --> 00:01:56.720
and try to tackle this first part.
00:01:56.720 --> 00:01:59.880
What is the mean of the
sampling distribution
00:01:59.880 --> 00:02:02.523
for the difference in sample means?
00:02:03.930 --> 00:02:05.750
All right, now let's work
through this together.
00:02:05.750 --> 00:02:08.330
So the mean of the sampling distribution
00:02:08.330 --> 00:02:11.370
for the difference in sample means,
00:02:11.370 --> 00:02:13.550
and we have seen this before,
00:02:13.550 --> 00:02:16.850
this is going to be
equal to the difference
00:02:16.850 --> 00:02:20.220
between the means of the
sampling distribution
00:02:20.220 --> 00:02:22.370
for each of the sample means.
00:02:22.370 --> 00:02:26.330
So that mean minus this mean.
00:02:26.330 --> 00:02:29.910
And we also know that the mean
of the sampling distribution
00:02:29.910 --> 00:02:31.620
for each of these sample means,
00:02:31.620 --> 00:02:33.830
that's just going to be
the mean of the population
00:02:33.830 --> 00:02:35.420
that we are sampling from.
00:02:35.420 --> 00:02:37.400
So this mean right over here
00:02:37.400 --> 00:02:40.220
is just going to be the
mean, the population mean,
00:02:40.220 --> 00:02:44.410
for shift A, which is gonna be 130 grams.
00:02:44.410 --> 00:02:46.120
I'll just write that there.
00:02:46.120 --> 00:02:49.190
And then the mean of the
sampling distribution
00:02:49.190 --> 00:02:52.000
for the sample means from shift B,
00:02:52.000 --> 00:02:55.260
we can see that that's just
going to be the population mean
00:02:55.260 --> 00:02:58.990
for shift B, which is right over here.
00:02:58.990 --> 00:03:01.820
So minus 125 grams.
00:03:01.820 --> 00:03:05.920
And of course, this is just
going to be equal to 5 grams.
00:03:05.920 --> 00:03:08.240
So we have answered the first part.
00:03:08.240 --> 00:03:10.760
We know the mean of the
sampling distribution
00:03:10.760 --> 00:03:12.750
of the difference in sample means.
00:03:12.750 --> 00:03:15.710
Now what about the standard deviation?
00:03:15.710 --> 00:03:18.150
So for that, let's think
actually about variances
00:03:18.150 --> 00:03:19.940
'cause the math's a little
bit easier with variances.
00:03:19.940 --> 00:03:23.120
And then from that, we can
derive standard deviations.
00:03:23.120 --> 00:03:27.480
So we know that the variance
of the sampling distribution
00:03:27.480 --> 00:03:30.630
for the difference in sample means,
00:03:30.630 --> 00:03:34.090
assuming that your two
samples are independent
00:03:34.090 --> 00:03:36.560
and you're sampling with replacement,
00:03:36.560 --> 00:03:38.490
if you're sampling with replacement,
00:03:38.490 --> 00:03:41.650
it's actually going to be
the sum of the variances
00:03:41.650 --> 00:03:44.930
of the sampling distribution
for each of the sample means.
00:03:44.930 --> 00:03:49.930
So it's going to be that
plus this right over here.
00:03:50.010 --> 00:03:50.843
Now you might be saying,
00:03:50.843 --> 00:03:53.960
"Wait, we're not sampling
with replacement."
00:03:53.960 --> 00:03:57.360
Well, we also know that if
each of the sample sizes
00:03:57.360 --> 00:04:00.610
are less than 10% of the population,
00:04:00.610 --> 00:04:02.720
then the difference is negligible,
00:04:02.720 --> 00:04:05.000
and so we could still use this formula.
00:04:05.000 --> 00:04:07.580
And so you could see that
the simple random sample here
00:04:07.580 --> 00:04:09.290
is 40 from each shift.
00:04:09.290 --> 00:04:11.070
And they say that a large bakery
00:04:11.070 --> 00:04:14.830
makes thousands of cupcakes
daily in two shifts.
00:04:14.830 --> 00:04:18.120
So even if it was a thousand,
10% of that would be 100,
00:04:18.120 --> 00:04:20.190
this is less than 10%.
00:04:20.190 --> 00:04:23.020
So we meet that condition, so
we can use this same formula
00:04:23.020 --> 00:04:26.440
that you would use if you were
sampling with replacement.
00:04:26.440 --> 00:04:29.340
So this first variance right over here
00:04:29.340 --> 00:04:31.210
of the sampling distribution
00:04:31.210 --> 00:04:33.960
for the sample means from shift A,
00:04:33.960 --> 00:04:38.610
this is going to be equal
to the variance of shift A,
00:04:38.610 --> 00:04:40.870
the population variance of shift A
00:04:40.870 --> 00:04:44.510
divided by your sample size.
00:04:44.510 --> 00:04:46.950
And then this over here,
00:04:46.950 --> 00:04:49.460
it's gonna be the same thing for shift B.
00:04:49.460 --> 00:04:53.420
It's going to be the variance of shift B
00:04:53.420 --> 00:04:56.120
divided by your sample size.
00:04:56.120 --> 00:04:59.680
And so this is going to be equal to what?
00:04:59.680 --> 00:05:01.960
Well, the variance from shift A
00:05:01.960 --> 00:05:05.440
is going to be the square of
the the standard deviation
00:05:05.440 --> 00:05:06.800
from shift A.
00:05:06.800 --> 00:05:09.180
The standard deviation's right over there.
00:05:09.180 --> 00:05:12.630
And so that's going to be 16.
00:05:12.630 --> 00:05:14.560
We could write grams squared
00:05:14.560 --> 00:05:16.210
if we wanna keep the units there.
00:05:16.210 --> 00:05:19.530
And then we're going to
divide by the sample size.
00:05:19.530 --> 00:05:21.550
We know that the sample size in each case,
00:05:21.550 --> 00:05:25.090
40 cupcakes at a time for each sample.
00:05:25.090 --> 00:05:30.090
And then for shift B, we know
that the standard deviation,
00:05:30.400 --> 00:05:35.120
the population standard
deviation for shift B is 3 grams.
00:05:35.120 --> 00:05:40.120
You square that, and
you get 9 grams squared.
00:05:40.540 --> 00:05:42.710
A gram squared is kind
of an interesting idea,
00:05:42.710 --> 00:05:45.630
but that's what the units are
working out to be right now.
00:05:45.630 --> 00:05:49.170
And our sample size is still equal to 40.
00:05:49.170 --> 00:05:50.956
And so this is going to be equal to,
00:05:50.956 --> 00:05:54.090
let's see, 16 plus 9 is 25.
00:05:54.090 --> 00:05:55.580
Common denominator, 40.
00:05:55.580 --> 00:06:00.153
So it's 25 over 40, which
is the same thing as 5/8,
00:06:01.000 --> 00:06:06.000
5/8 of a gram squared, which
is a little bit strange unit,
00:06:06.850 --> 00:06:08.340
but this now tells us
00:06:08.340 --> 00:06:09.884
what the standard deviation is going to be
00:06:09.884 --> 00:06:11.080
because it's going to be the square root
00:06:11.080 --> 00:06:12.590
of all of this business.
00:06:12.590 --> 00:06:16.390
So the standard deviation
of the sampling distribution
00:06:16.390 --> 00:06:20.660
for the difference in
sample means over here
00:06:20.660 --> 00:06:24.790
is going to be the square root of 5/8.
00:06:24.790 --> 00:06:27.400
And now of course, the
units are back to grams,
00:06:27.400 --> 00:06:28.570
which makes sense.
00:06:28.570 --> 00:06:31.140
And this is approximately
going to be equal to,
00:06:31.140 --> 00:06:35.370
get my calculator out,
5 divided by 8 equals,
00:06:35.370 --> 00:06:37.970
and then we take the square root of that,
00:06:37.970 --> 00:06:41.413
and it's going to be approximately 0.79.
00:06:42.600 --> 00:06:44.233
0.79.
00:06:47.090 --> 00:06:48.210
So the next question,
00:06:48.210 --> 00:06:51.150
before we try to figure
out the probability is,
00:06:51.150 --> 00:06:53.930
is are we dealing with a
normal distribution here
00:06:53.930 --> 00:06:55.880
when we think about the
sampling distribution
00:06:55.880 --> 00:06:58.220
for the difference in sample means?
00:06:58.220 --> 00:06:59.950
And so I encourage you
to pause the video again
00:06:59.950 --> 00:07:01.403
and think about that.
00:07:02.310 --> 00:07:04.010
So there's two ways that we can assume
00:07:04.010 --> 00:07:06.120
that the sampling distribution
for the difference
00:07:06.120 --> 00:07:08.100
in sampling means is normal.
00:07:08.100 --> 00:07:11.450
If the original populations
that each of the sample means
00:07:11.450 --> 00:07:14.470
are being calculated from are normal,
00:07:14.470 --> 00:07:16.760
then that means that the
sampling distribution
00:07:16.760 --> 00:07:18.860
for each of the sample
means is gonna be normal.
00:07:18.860 --> 00:07:20.170
And that means that the difference
00:07:20.170 --> 00:07:23.400
of the sampling distributions
are going to be normal.
00:07:23.400 --> 00:07:24.600
Now we don't know for a fact
00:07:24.600 --> 00:07:26.240
that the weights of the cupcakes
00:07:26.240 --> 00:07:29.840
from each shift are normal distributions,
00:07:29.840 --> 00:07:32.570
but we also know that
the sampling distribution
00:07:32.570 --> 00:07:34.080
of the sampling means
00:07:34.080 --> 00:07:37.410
can be modeled as being
approximately normal
00:07:37.410 --> 00:07:41.480
if the two sample sizes are
greater than or equal to 30.
00:07:41.480 --> 00:07:43.600
And we know that each of these samples
00:07:43.600 --> 00:07:46.780
are definitely greater than
or equal to 30, they are 40.
00:07:46.780 --> 00:07:49.390
So that tells us that
the sampling distribution
00:07:49.390 --> 00:07:53.470
of the difference in sample
means is also normal.
00:07:53.470 --> 00:07:55.590
So we've established
the things that we need
00:07:55.590 --> 00:07:58.000
to then calculate the probability.
00:07:58.000 --> 00:07:59.750
So I encourage you, pause the video,
00:07:59.750 --> 00:08:01.420
and see if you can use that information
00:08:01.420 --> 00:08:02.990
to calculate that probability,
00:08:02.990 --> 00:08:05.763
and we will then do
that in the next video.
|
Be Like Sal: 3 Ways a Tablet Can Energize Your Digital Teaching! | https://www.youtube.com/watch?v=ITsSBEkEo0c | vtt | https://www.youtube.com/api/timedtext?v=ITsSBEkEo0c&ei=7lWUZYDTLNqPp-oPmueosAM&caps=asr&opi=112496729&xoaf=4&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=60E8CE2FD55FAC13A35825B26A3DA8D3805F63A8.27A2C5CEC9350544A252ABDEE5DA3909BC52FB01&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:03.300 --> 00:00:06.210
- Thank you so much for
joining today or this evening,
00:00:06.210 --> 00:00:07.430
depending on where you're calling from.
00:00:07.430 --> 00:00:09.620
This is Jeremy Shi at Khan Academy
00:00:09.620 --> 00:00:11.285
and I'm so excited you're joining with us
00:00:11.285 --> 00:00:14.760
because if anything, at Khan Academy,
00:00:14.760 --> 00:00:17.210
2020 has been the year of the tablet.
00:00:17.210 --> 00:00:20.439
We've given away by my
calculation, at least 50 tablets
00:00:20.439 --> 00:00:23.600
over the course of the year
in response to questions like,
00:00:23.600 --> 00:00:25.310
how does Sal Khan make those videos?
00:00:25.310 --> 00:00:27.320
How can I make my own videos?
00:00:27.320 --> 00:00:29.559
And that's why I'm so excited
about tonight's session
00:00:29.559 --> 00:00:30.910
because now you're going to learn
00:00:30.910 --> 00:00:32.690
from the experts themselves.
00:00:32.690 --> 00:00:35.610
First of all, we are so
lucky to have Stacey with us.
00:00:35.610 --> 00:00:37.970
Stacey is a math teacher
and director of innovation
00:00:37.970 --> 00:00:41.290
educational technology at the
Bullet School in Maryland.
00:00:41.290 --> 00:00:42.957
And one of the things
that really impresses me
00:00:42.957 --> 00:00:45.467
is not only does she wear
multiple hats at school
00:00:45.467 --> 00:00:48.230
but she's also the
author of Tech with Heart
00:00:48.230 --> 00:00:49.140
which is an amazing book
00:00:49.140 --> 00:00:50.837
on how to use tech in your classroom
00:00:50.837 --> 00:00:53.830
not just to break your
students down to bits and bytes
00:00:53.830 --> 00:00:56.350
but to actually empower
them, to lift them up.
00:00:56.350 --> 00:00:59.150
And I think in 2020, I can't
imagine a better lesson
00:00:59.150 --> 00:01:01.330
than how to use technology
in a more holistic way.
00:01:01.330 --> 00:01:02.960
So check out Tech with Heart,
00:01:02.960 --> 00:01:04.920
would make a great stocking stuffer.
00:01:04.920 --> 00:01:07.040
And then also I have to
give a huge shout out
00:01:07.040 --> 00:01:08.590
to the Wacom team.
00:01:08.590 --> 00:01:10.660
If you're familiar with Wacom, the brand,
00:01:10.660 --> 00:01:13.860
they're the world's leader
in handwriting tablets.
00:01:13.860 --> 00:01:16.295
So whether you use it for
design or for teaching,
00:01:16.295 --> 00:01:18.269
there's just these really powerful tools
00:01:18.269 --> 00:01:21.100
to bring your teaching
style and your pedagogy
00:01:21.100 --> 00:01:22.510
into the digital world.
00:01:22.510 --> 00:01:25.450
And in fact, Sal Khan himself
has been using their tablets
00:01:25.450 --> 00:01:27.000
for a decade at this point
00:01:27.000 --> 00:01:29.550
and is still using them to make
videos at this very moment.
00:01:29.550 --> 00:01:31.960
So a huge shout out to the Wacom team
00:01:31.960 --> 00:01:33.960
and especially because Wacom
has been generous enough
00:01:33.960 --> 00:01:38.320
to give away five more tablets,
to lucky attendees tonight
00:01:38.320 --> 00:01:40.090
and you will be notified automatically
00:01:40.090 --> 00:01:41.620
just for being in attendance.
00:01:41.620 --> 00:01:43.420
If you're one of those lucky five.
00:01:43.420 --> 00:01:45.470
And then in addition, even
if you're not selected
00:01:45.470 --> 00:01:46.790
to win a tablet
00:01:46.790 --> 00:01:48.855
walk is giving an exclusive discount code
00:01:48.855 --> 00:01:51.030
just to attendees of the session
00:01:51.030 --> 00:01:54.110
that Stacey will unveil at the
very end of the presentation.
00:01:54.110 --> 00:01:55.480
Now, all that being said,
00:01:55.480 --> 00:01:58.150
I would be remiss in 2020 on a webinar
00:01:58.150 --> 00:02:00.900
not to mention that number
one, this is being recorded.
00:02:00.900 --> 00:02:03.080
So you'll get all those
goodies in your email
00:02:03.080 --> 00:02:06.117
right afterwards, including
a PDF of the handouts
00:02:06.117 --> 00:02:08.350
and all the links that we talked about.
00:02:08.350 --> 00:02:11.700
And then of course, because
we're educators, all in all
00:02:11.700 --> 00:02:14.080
we want to make sure that the
session is really interactive.
00:02:14.080 --> 00:02:16.980
So ask questions at any
point using the questions tab
00:02:16.980 --> 00:02:17.980
and Stacey will take a ton
00:02:17.980 --> 00:02:20.420
of those questions at
the end of the session.
00:02:20.420 --> 00:02:23.300
So without further ado, let
me turn it over to Stacey
00:02:23.300 --> 00:02:25.184
to tell you all about
how you can use tablets
00:02:25.184 --> 00:02:29.190
in your own classroom to make
2021 even more effective.
00:02:29.190 --> 00:02:30.190
Over to you, Stacey.
00:02:31.130 --> 00:02:32.570
- Thank you so much.
00:02:32.570 --> 00:02:36.570
I'm so excited to be
with you all this evening
00:02:36.570 --> 00:02:39.900
or whatever time it is over on your end.
00:02:39.900 --> 00:02:44.540
So I'm going to be sharing some ways
00:02:44.540 --> 00:02:47.351
that you can use the tablet.
00:02:47.351 --> 00:02:52.351
I have been using a Wacom
tablet myself for years now.
00:02:53.560 --> 00:02:56.460
I think I got my first one in 2013.
00:02:56.460 --> 00:03:00.030
And what I love about
these tablets is that
00:03:00.030 --> 00:03:02.820
it's the same tablet
that I was using in 2013.
00:03:02.820 --> 00:03:04.830
I'm still able to use today,
00:03:04.830 --> 00:03:08.210
though I'm going to showcase
some of their newer products.
00:03:08.210 --> 00:03:10.200
It has worked for me over the years
00:03:10.200 --> 00:03:14.740
and it's a way of allowing
me to handwrite on anything.
00:03:14.740 --> 00:03:18.184
And as a math teacher, I need that.
00:03:18.184 --> 00:03:22.526
So in addition to my role
in really working as a coach
00:03:22.526 --> 00:03:25.058
with teachers at my school
00:03:25.058 --> 00:03:28.970
and helping them onboard
the tech that will work best
00:03:28.970 --> 00:03:32.430
for their classroom, I'm
also an AP calculus teacher.
00:03:32.430 --> 00:03:34.930
So I've taught a number
of classes over the year
00:03:34.930 --> 00:03:36.710
but in the past several years,
00:03:36.710 --> 00:03:38.930
I've taught AP calculus AB.
00:03:38.930 --> 00:03:42.930
I also taught a purely online
version of AP calculus AB
00:03:42.930 --> 00:03:44.126
for a number of years
00:03:44.126 --> 00:03:46.960
and I am a flip classroom teacher.
00:03:46.960 --> 00:03:48.840
So I'll get into a lot
00:03:48.840 --> 00:03:51.650
of how I started exploring the tablets
00:03:51.650 --> 00:03:54.000
and how I'm using them now.
00:03:54.000 --> 00:03:58.250
And hopefully some easy ways
to help you get started.
00:03:58.250 --> 00:04:01.540
If you are on Twitter, I would
love to connect with you.
00:04:01.540 --> 00:04:06.233
My Twitter hashtag is, or my
Twitter handle is @buddyXO.
00:04:07.590 --> 00:04:09.620
So if you are there,
please connect with me.
00:04:09.620 --> 00:04:11.270
And if you have any questions at all,
00:04:11.270 --> 00:04:16.270
I'm so happy to follow up
and answer as many as I can.
00:04:16.506 --> 00:04:18.985
I do have a contact form on my blog.
00:04:18.985 --> 00:04:21.830
So now that we're done
with that little intro,
00:04:21.830 --> 00:04:26.830
let's go ahead and let me start
off with some of the things
00:04:27.390 --> 00:04:29.440
I hope to achieve today.
00:04:29.440 --> 00:04:30.273
First of all,
00:04:30.273 --> 00:04:34.070
how to get started with
a whiteboard application.
00:04:34.070 --> 00:04:39.070
Then how to use a scratch
pad in Khan Academy?
00:04:39.170 --> 00:04:42.100
Then we'll talk more
about how to ink up slides
00:04:42.100 --> 00:04:44.080
and make screencasts of your own.
00:04:44.080 --> 00:04:49.080
And then as Jeremy said, we
will have some time for Q&A.
00:04:49.090 --> 00:04:50.880
So before we get started,
00:04:50.880 --> 00:04:53.440
I'm gonna just put a question out to you.
00:04:53.440 --> 00:04:54.744
What subject do you teach
00:04:54.744 --> 00:04:58.113
and what grade levels do you teach?
00:04:59.730 --> 00:05:02.233
Go ahead and type that in.
00:05:04.750 --> 00:05:06.250
- [Jeremy] Okay. We've got
the poll on your screen.
00:05:06.250 --> 00:05:09.150
So feel free to start
answering right there.
00:05:09.150 --> 00:05:12.500
About a third of the 500 or so educators
00:05:12.500 --> 00:05:14.000
across the country have answered.
00:05:14.000 --> 00:05:15.980
We're up to about two thirds now.
00:05:15.980 --> 00:05:17.900
And it looks like there
are a lot of educators
00:05:17.900 --> 00:05:20.300
who are following in
your footsteps, Stacey,
00:05:20.300 --> 00:05:22.850
because as we close the
poll and share the results,
00:05:22.850 --> 00:05:25.250
you can see that a plurality
are math educators.
00:05:27.880 --> 00:05:29.420
- Awesome.
00:05:29.420 --> 00:05:31.920
- [Jeremy] And now we'll
do the same, that's right,
00:05:31.920 --> 00:05:34.290
but also a nice diversity of educators
00:05:34.290 --> 00:05:36.010
across the content spectrum.
00:05:36.010 --> 00:05:37.720
Let's do the same for grade level now.
00:05:37.720 --> 00:05:40.140
So elementary, all the way to high,
00:05:40.140 --> 00:05:41.883
maybe even beyond or before.
00:05:43.510 --> 00:05:45.270
It's looking like a
little bit of a horse race
00:05:45.270 --> 00:05:46.820
between middle and high school.
00:05:51.350 --> 00:05:52.890
And we'll go ahead and share that.
00:05:52.890 --> 00:05:54.540
And it looks like a lot
of high school educators.
00:05:54.540 --> 00:05:58.170
Again, your tribe is here
in force tonight, Stacey.
00:05:58.170 --> 00:06:00.870
So a lot of high school math
educators have joined us.
00:06:02.300 --> 00:06:03.133
- All right.
00:06:04.775 --> 00:06:06.543
Well, we'll have some fun tonight.
00:06:11.855 --> 00:06:16.170
So this is me back in the day.
00:06:16.170 --> 00:06:18.280
Let me go back into present.
00:06:18.280 --> 00:06:19.620
This is me back in the day
00:06:19.620 --> 00:06:21.500
when I started flipping my classroom.
00:06:21.500 --> 00:06:24.820
This was back in 2010.
00:06:24.820 --> 00:06:28.610
And what I had here was
a tablet PC, actually.
00:06:28.610 --> 00:06:31.030
So this is how I got
started making my videos.
00:06:31.030 --> 00:06:34.820
I had a microphone that I got
and I was using my tablet PC,
00:06:34.820 --> 00:06:37.260
which is what we have through our school.
00:06:37.260 --> 00:06:39.720
That was kind of how I got
interested in the first place.
00:06:39.720 --> 00:06:42.140
I said, Hey, I got this
technology in my hands.
00:06:42.140 --> 00:06:45.160
Let me start making some
screencasts for my students.
00:06:45.160 --> 00:06:48.250
Especially when I started
AP calculus teaching,
00:06:48.250 --> 00:06:50.350
you know how much content
there is to get through,
00:06:50.350 --> 00:06:52.040
not enough time to get through it.
00:06:52.040 --> 00:06:53.960
So wanted a way to offload
00:06:53.960 --> 00:06:57.730
that very teacher
directed lecture to video,
00:06:57.730 --> 00:07:01.050
and I started using my
tablet PC to do that.
00:07:01.050 --> 00:07:02.916
However, I am a Mac user
00:07:02.916 --> 00:07:07.760
and this tablet PC wasn't my preference.
00:07:07.760 --> 00:07:10.990
So when I learned about Wacom,
00:07:10.990 --> 00:07:15.510
then I had my solution because
I could plug the tablet
00:07:15.510 --> 00:07:19.497
into my Mac and I still had
the pen and the handwriting.
00:07:19.497 --> 00:07:24.497
And I've been happily using
that solution ever since.
00:07:24.940 --> 00:07:29.370
So there are two main
types of Wacom devices.
00:07:29.370 --> 00:07:33.340
There is the slate style
like this one in the left.
00:07:33.340 --> 00:07:35.370
So this is a blank slate.
00:07:35.370 --> 00:07:39.880
And you can write just
looking up at the screen
00:07:39.880 --> 00:07:41.470
is what you would have to do there
00:07:41.470 --> 00:07:44.390
so that you're not seeing
what you're writing.
00:07:44.390 --> 00:07:46.000
Actually, you're looking up at the screen
00:07:46.000 --> 00:07:47.580
to see what you're writing.
00:07:47.580 --> 00:07:50.820
And then there's also the
display style tablets,
00:07:50.820 --> 00:07:55.010
like this one where you actually
either mirror your screen
00:07:55.010 --> 00:07:57.201
or you use it as a second display,
00:07:57.201 --> 00:08:00.834
just like if you had
another monitor attached.
00:08:00.834 --> 00:08:05.600
So that is really amazing,
especially remote learning.
00:08:05.600 --> 00:08:08.578
I think we've all learned
that we need two monitors.
00:08:08.578 --> 00:08:11.960
And so this can be a simple
way to have two monitors
00:08:11.960 --> 00:08:15.490
available to you or two
screens available to you.
00:08:15.490 --> 00:08:19.650
So I really recommend the Wacom Intuos.
00:08:19.650 --> 00:08:23.520
There are different styles
of it, but I like the one.
00:08:23.520 --> 00:08:24.940
This is the small one that I have.
00:08:24.940 --> 00:08:27.000
It's a small style, but it is Bluetooth.
00:08:27.000 --> 00:08:28.540
And I love that because it's wireless
00:08:28.540 --> 00:08:31.659
and I can move it around,
easy to carry with me
00:08:31.659 --> 00:08:34.410
when we are in the actual classroom
00:08:34.410 --> 00:08:35.690
and we're able to move around.
00:08:35.690 --> 00:08:38.820
This is a great device to
have, throw it in your bag.
00:08:38.820 --> 00:08:42.056
And then the Wacom One
is what I actually make
00:08:42.056 --> 00:08:47.020
flip classroom videos with nowadays.
00:08:47.020 --> 00:08:48.710
You do have to plug it in.
00:08:48.710 --> 00:08:50.750
So it is much larger.
I have it right here.
00:08:50.750 --> 00:08:52.000
I don't have it plugged in
00:08:52.000 --> 00:08:55.020
'cause I didn't want another
screen going right now
00:08:55.020 --> 00:08:59.230
but this is really great
because I can have it
00:08:59.230 --> 00:09:03.030
to write out all of my lessons,
00:09:03.030 --> 00:09:06.690
make my screen recordings,
and it feels so natural.
00:09:06.690 --> 00:09:08.670
It really feels like writing on paper.
00:09:08.670 --> 00:09:11.278
The quality of this tablet is amazing,
00:09:11.278 --> 00:09:13.180
and I recommend the Wacom One
00:09:13.180 --> 00:09:15.410
because it's the lowest price point
00:09:15.410 --> 00:09:20.120
for a screen display style
tablet that Wacom offers.
00:09:20.120 --> 00:09:22.910
And it's met all of my
needs as a math teacher
00:09:22.910 --> 00:09:27.910
a hundred percent, and it
feels so, so nice to write on.
00:09:28.100 --> 00:09:30.680
So those are the two style of tablets.
00:09:30.680 --> 00:09:34.660
Just wanted to throw those
out there for some background.
00:09:34.660 --> 00:09:38.100
And then I'm gonna pose one
more question to you right now.
00:09:38.100 --> 00:09:40.623
Do you currently have a writing tablet?
00:09:48.750 --> 00:09:51.620
So I think there's a poll that
you can answer on this one
00:09:59.650 --> 00:10:01.320
- [Jeremy] And it looks like
we're up to about almost 90%
00:10:01.320 --> 00:10:03.430
of the votes here, Stacey.
00:10:03.430 --> 00:10:06.530
It looks like about, as you
can see here on the screen,
00:10:06.530 --> 00:10:10.290
about a third of teachers had
that writing tablet already
00:10:10.290 --> 00:10:11.600
but the majority do not.
00:10:11.600 --> 00:10:14.130
So just a little good background to go on.
00:10:14.130 --> 00:10:18.060
- Awesome, so hopefully
that some of that background
00:10:18.060 --> 00:10:21.500
was helpful in helping you
understand the different styles
00:10:21.500 --> 00:10:22.890
of tablets that are available
00:10:22.890 --> 00:10:26.260
and which one you might want
to purchase going forward.
00:10:26.260 --> 00:10:28.781
If you really just are
looking to just get started
00:10:28.781 --> 00:10:31.460
with the most affordable option
00:10:31.460 --> 00:10:33.060
and the most portable option,
00:10:33.060 --> 00:10:35.781
that is the Intuos style tablet.
00:10:35.781 --> 00:10:38.530
And again, there's a
Bluetooth version of that,
00:10:38.530 --> 00:10:41.120
which is what I really like
because I can just be using it,
00:10:41.120 --> 00:10:43.061
just click a button, no wires needed,
00:10:43.061 --> 00:10:46.360
and I can move around and it's wireless.
00:10:46.360 --> 00:10:48.610
Again. The Wacom one.
00:10:48.610 --> 00:10:52.050
I love it for making my
flip classroom videos.
00:10:52.050 --> 00:10:53.100
It does need to be plugged in.
00:10:53.100 --> 00:10:54.470
So I just like to mention that
00:10:54.470 --> 00:10:56.930
because I think it's important
to weigh the options.
00:10:56.930 --> 00:10:58.110
Do you need portability
00:10:58.110 --> 00:11:01.479
or are you going to be
making videos all the time?
00:11:01.479 --> 00:11:04.910
In which case, I think the Wacom One
00:11:04.910 --> 00:11:06.870
is really worth the investment.
00:11:06.870 --> 00:11:10.853
That's what I use most of
my time and I just love it.
00:11:12.640 --> 00:11:17.640
All right, so let's continue on
00:11:18.870 --> 00:11:22.750
and start with some of the basics.
00:11:22.750 --> 00:11:26.970
So I wish that I could just tell you, Hey,
00:11:26.970 --> 00:11:28.500
this is what I recommend.
00:11:28.500 --> 00:11:30.140
This is what you should do.
00:11:30.140 --> 00:11:34.860
But the reality is we are
all at different schools
00:11:34.860 --> 00:11:36.810
that use different technologies,
00:11:36.810 --> 00:11:38.400
that have different subscriptions
00:11:38.400 --> 00:11:40.010
but also we're at Google Schools.
00:11:40.010 --> 00:11:41.430
We are at Microsoft schools.
00:11:41.430 --> 00:11:43.050
We are at Google Meet schools.
00:11:43.050 --> 00:11:45.720
We are at Zoom schools right now.
00:11:45.720 --> 00:11:50.720
And so I am going to present,
again, a variety of options,
00:11:50.720 --> 00:11:54.590
ones that I would most
recommend depending on
00:11:54.590 --> 00:11:57.000
which of those camps you fall into.
00:11:57.000 --> 00:12:01.410
So if you are using
Google everything already,
00:12:01.410 --> 00:12:03.023
if you're using Google Meet,
00:12:03.930 --> 00:12:07.450
even if you're using Zoom and
your school is a Google school
00:12:07.450 --> 00:12:11.300
I think Google Jamboard is the
simplest whiteboarding option
00:12:11.300 --> 00:12:13.890
that I can possibly offer you.
00:12:13.890 --> 00:12:16.910
There is a video of how
the Google Meet integration
00:12:16.910 --> 00:12:19.550
with the Jamboard whiteboard works
00:12:19.550 --> 00:12:22.341
if you haven't used that before and again,
00:12:22.341 --> 00:12:24.510
these resources are available after
00:12:24.510 --> 00:12:26.563
and I put a little play
button so that you can know
00:12:26.563 --> 00:12:29.850
that you can watch this video afterwards
00:12:29.850 --> 00:12:30.880
if you want to review it.
00:12:30.880 --> 00:12:33.260
I'm trying to load you
up with some resources
00:12:33.260 --> 00:12:34.770
to really help you out.
00:12:34.770 --> 00:12:37.490
But I'm going to show
you just a basic demo
00:12:37.490 --> 00:12:41.250
and you can get started by just
going to your Google Drive,
00:12:41.250 --> 00:12:42.445
pressing the new button,
00:12:42.445 --> 00:12:46.210
go into more and then
using a Google Jamboard.
00:12:46.210 --> 00:12:48.170
And that's how you start
up a new whiteboard.
00:12:48.170 --> 00:12:50.950
Or if you're in a Google
Meet, you'll see that option
00:12:50.950 --> 00:12:52.660
right when you click the three dots.
00:12:52.660 --> 00:12:54.770
So let me show you what
a Jamboard looks like.
00:12:54.770 --> 00:12:59.420
It is super simple, super
basic, but it is collaborative,
00:12:59.420 --> 00:13:01.780
or it can be just more instructional.
00:13:01.780 --> 00:13:04.230
So like anything else in Google,
00:13:04.230 --> 00:13:08.060
you can share this and make
everybody else an editor,
00:13:08.060 --> 00:13:10.410
or you can share it with
view only permissions.
00:13:10.410 --> 00:13:12.619
If everybody else has an editor,
00:13:12.619 --> 00:13:13.750
it's real-time collaboration.
00:13:13.750 --> 00:13:15.080
Amazing. Right?
00:13:15.080 --> 00:13:18.910
So there is a pen tool right here.
00:13:18.910 --> 00:13:21.810
And again, the options with
this one are very, very simple.
00:13:21.810 --> 00:13:25.140
You only have a couple
pallets of color here.
00:13:25.140 --> 00:13:27.610
You do have different pen thicknesses.
00:13:27.610 --> 00:13:30.060
You have a marker, you have a highlighter,
00:13:30.060 --> 00:13:31.810
you have more of a brush tool.
00:13:31.810 --> 00:13:36.410
And so, you know, you can just
very simply get to writing.
00:13:36.410 --> 00:13:39.300
If you want to write, you
can also pull in an image.
00:13:39.300 --> 00:13:42.110
So sometimes I like to
use this to say, you know,
00:13:42.110 --> 00:13:44.240
you have a question that you want,
00:13:44.240 --> 00:13:47.510
take a snapshot of the
question, pull it into here
00:13:47.510 --> 00:13:50.630
and then just use your tablet and write.
00:13:50.630 --> 00:13:52.497
That's basically it.
00:13:52.497 --> 00:13:54.940
And you can present during
class with this also.
00:13:54.940 --> 00:13:56.530
There's this nice laser pointer.
00:13:56.530 --> 00:14:00.220
So it's easier for students
to follow what you are writing
00:14:00.220 --> 00:14:02.730
and you can more easily point.
00:14:02.730 --> 00:14:04.610
There's a sticky note that you can have.
00:14:04.610 --> 00:14:09.610
And then for my people
who need some shapes,
00:14:09.706 --> 00:14:11.580
there's some basic shapes
here available too.
00:14:11.580 --> 00:14:15.350
So this I think is one of the
simplest options available.
00:14:15.350 --> 00:14:18.380
It is automatically built into Google Meet
00:14:18.380 --> 00:14:19.213
if you're using that
00:14:19.213 --> 00:14:21.770
or if you're using
Google Drive, I'm sorry.
00:14:21.770 --> 00:14:22.730
If you're a Google school,
00:14:22.730 --> 00:14:25.030
then this will save to your Google Drive.
00:14:25.030 --> 00:14:27.270
So that's the nice ability there too.
00:14:27.270 --> 00:14:32.220
And you can share, lastly,
you can always export this,
00:14:32.220 --> 00:14:34.400
save this as a PDF afterwards,
00:14:34.400 --> 00:14:37.210
so that you can share
these as lesson notes.
00:14:37.210 --> 00:14:39.240
If you can't get everything on one slide,
00:14:39.240 --> 00:14:43.003
you can make multiple
pages just like that.
00:14:44.950 --> 00:14:48.480
And so those are the very very basics
00:14:48.480 --> 00:14:50.260
of getting started with this.
00:14:50.260 --> 00:14:51.690
And there's also the ability
00:14:51.690 --> 00:14:55.133
to have some grid paper background also.
00:14:57.270 --> 00:15:01.730
So, let me go ahead and
move into the next option,
00:15:01.730 --> 00:15:04.960
which since I was on Google schools,
00:15:04.960 --> 00:15:08.890
this one is really, I feel
like if you are a Google school
00:15:08.890 --> 00:15:11.060
that is already a Kami user,
00:15:11.060 --> 00:15:13.570
if you are using Kami or if your school
00:15:13.570 --> 00:15:15.480
has a site license to Kami,
00:15:15.480 --> 00:15:18.940
I really recommend checking that tool out.
00:15:18.940 --> 00:15:20.978
If you've not heard about it before,
00:15:20.978 --> 00:15:24.580
it's not the absolute thing
that you need right now.
00:15:24.580 --> 00:15:26.140
I want you to pick which one
00:15:26.140 --> 00:15:30.463
is going to fit your needs
the best, but what Kami is,
00:15:31.316 --> 00:15:32.920
it's integrated again with Google Drive,
00:15:32.920 --> 00:15:36.080
but it also can be kind of
just a white boarding tool
00:15:36.080 --> 00:15:39.240
because there are these amazing pen tools
00:15:39.240 --> 00:15:41.850
built right into Kami.
00:15:41.850 --> 00:15:44.620
This is a Chrome extension,
by the way, you can get it
00:15:44.620 --> 00:15:49.340
so you can open any of your
Google Drive files with Kami.
00:15:49.340 --> 00:15:53.100
You can also just go to Kami
on the web and you can write.
00:15:53.100 --> 00:15:56.798
So again, I can just write and talk.
00:15:56.798 --> 00:16:00.060
There's so many more
features available into Kami.
00:16:00.060 --> 00:16:03.044
I could do a whole webinar
on Kami, to be honest.
00:16:03.044 --> 00:16:06.530
There is even the ability to
make your whole screen capture
00:16:06.530 --> 00:16:09.185
right here in Kami, if
you have a paid version.
00:16:09.185 --> 00:16:13.342
But what I like to show here
is just like this, for example,
00:16:13.342 --> 00:16:18.342
was I was just showing how
students can kind of upload work
00:16:18.720 --> 00:16:20.300
that they were stuck on
00:16:20.300 --> 00:16:23.430
and then they can pull
it all into a document.
00:16:23.430 --> 00:16:26.943
And then I can use the pen
tools like I used right here
00:16:26.943 --> 00:16:31.260
to guide to say where they
went wrong for example.
00:16:31.260 --> 00:16:34.806
We can discuss errors as a class.
00:16:34.806 --> 00:16:37.040
So again, this is one of
00:16:37.040 --> 00:16:39.830
the really nice white boarding tool.
00:16:39.830 --> 00:16:42.560
You can add extra pages as you go.
00:16:42.560 --> 00:16:44.130
When you want to add more pages.
00:16:44.130 --> 00:16:47.670
Again, if you need lined
paper, you can have that.
00:16:47.670 --> 00:16:50.470
If you need grid paper, you can have that.
00:16:50.470 --> 00:16:53.802
If you want a music sheet,
you can even add that.
00:16:53.802 --> 00:16:56.910
So if you are using Kami already
00:16:56.910 --> 00:16:58.550
and you haven't thought about using it
00:16:58.550 --> 00:17:00.660
as kind of a white boarding tool,
00:17:00.660 --> 00:17:03.053
that's going to be my
recommendation to you.
00:17:05.270 --> 00:17:07.800
And that's really, again,
if you're a Google school
00:17:07.800 --> 00:17:09.430
'cause that's tied with Google.
00:17:09.430 --> 00:17:11.790
So let's move on from Google schools.
00:17:11.790 --> 00:17:14.220
And if you're using Zoom,
00:17:14.220 --> 00:17:18.510
Zoom has a whiteboard built right in.
00:17:18.510 --> 00:17:21.920
So I have a demo here again,
00:17:21.920 --> 00:17:23.790
if you want to watch this after the fact,
00:17:23.790 --> 00:17:25.070
you can just press play
00:17:25.070 --> 00:17:28.210
and watch how to get
started with the tool,
00:17:28.210 --> 00:17:32.600
but it is one of the
simplest options available.
00:17:32.600 --> 00:17:33.980
And what's more in Zoom,
00:17:33.980 --> 00:17:37.280
you can actually write
anywhere on your screen.
00:17:37.280 --> 00:17:40.910
So it doesn't have to just be a whiteboard
00:17:40.910 --> 00:17:42.010
that you're writing on.
00:17:42.010 --> 00:17:46.070
You can ink up anything
using the annotation tools
00:17:46.070 --> 00:17:48.220
that are in Zoom.
00:17:48.220 --> 00:17:51.120
So if you haven't used that before,
00:17:51.120 --> 00:17:54.140
and if you're using Zoom, then again,
00:17:54.140 --> 00:17:55.610
you use your Wacom tablet.
00:17:55.610 --> 00:17:57.390
Now you have an actual pen,
00:17:57.390 --> 00:18:02.060
and you can be hand writing
instead of, you know,
00:18:02.060 --> 00:18:05.050
just using your mouse,
which is very difficult.
00:18:05.050 --> 00:18:09.464
So that Zoom again, if you're using that,
00:18:09.464 --> 00:18:11.530
I would definitely check out this video
00:18:11.530 --> 00:18:12.703
if you're not already.
00:18:13.570 --> 00:18:17.070
Final white boarding tool
that I'm going to showcase is
00:18:17.926 --> 00:18:19.840
if you want something
that's not tied to Google
00:18:19.840 --> 00:18:24.320
and not tied to Zoom but is
very simple to get started with.
00:18:24.320 --> 00:18:29.320
I like AWW app, which is for a
right here, a web whiteboard,
00:18:31.730 --> 00:18:33.410
and I'm just using it for free.
00:18:33.410 --> 00:18:35.540
So you do get advertisements.
00:18:35.540 --> 00:18:38.281
That is the only downside to this,
00:18:38.281 --> 00:18:41.450
but otherwise it can be
a collaborative board
00:18:41.450 --> 00:18:43.530
so I can invite other people to it.
00:18:43.530 --> 00:18:44.790
So it can be collaborative,
00:18:44.790 --> 00:18:48.130
or I can just be doing my
screenshare and writing.
00:18:48.130 --> 00:18:50.200
There are some more options in this one.
00:18:50.200 --> 00:18:52.950
So this is actually a tool
that I use quite often
00:18:52.950 --> 00:18:55.180
'cause it's simple
00:18:55.180 --> 00:18:57.880
but also there's a little
bit more functionality,
00:18:57.880 --> 00:19:01.400
so I can upload a picture or even a PDF.
00:19:01.400 --> 00:19:05.270
I usually just would upload
like a picture of a question
00:19:05.270 --> 00:19:08.060
that I want to solve as a class.
00:19:08.060 --> 00:19:11.960
And then I can choose
from more of a variety
00:19:11.960 --> 00:19:13.480
of color palettes right here.
00:19:13.480 --> 00:19:15.350
Or you can choose from the color wheel
00:19:15.350 --> 00:19:18.240
so you can get more colors
right there available to you.
00:19:18.240 --> 00:19:20.560
There's an undo button very easily.
00:19:20.560 --> 00:19:24.960
And then again, you can be
writing as you're talking,
00:19:24.960 --> 00:19:26.950
you have the eraser tool,
00:19:26.950 --> 00:19:29.880
and this one gives you a
variety of options here
00:19:29.880 --> 00:19:32.168
where it's like you can
change the size of the eraser.
00:19:32.168 --> 00:19:36.300
You can also like erase the
whole thing in one click
00:19:36.300 --> 00:19:37.983
which makes it a little bit easier to use
00:19:37.983 --> 00:19:41.010
than just erasing little
bit by little bit,
00:19:41.010 --> 00:19:43.490
especially when you're
doing like a whole lesson.
00:19:43.490 --> 00:19:45.920
I know it sounds minor,
but it can be very helpful.
00:19:45.920 --> 00:19:47.910
Again, you have some shape tools
00:19:47.910 --> 00:19:50.291
and then you have some text.
00:19:50.291 --> 00:19:52.710
What I like about this app too,
00:19:52.710 --> 00:19:54.500
is that as you're writing,
00:19:54.500 --> 00:19:58.200
so, you know, you can be doing a problem.
00:19:58.200 --> 00:20:00.873
Let me change color like over here.
00:20:01.770 --> 00:20:06.770
And then you can do is you
can actually zoom in and out
00:20:08.890 --> 00:20:11.190
and you can write on
different parts of the board.
00:20:11.190 --> 00:20:16.190
So I can be zooming out. I can
move my, write over here too.
00:20:17.640 --> 00:20:20.230
Then I can move my whole board over.
00:20:20.230 --> 00:20:23.530
So I just have, this is
kind of like a huge canvas
00:20:23.530 --> 00:20:27.080
that I can have and I can keep writing.
00:20:27.080 --> 00:20:30.240
And if I want to see everything,
a snapshot of everything
00:20:30.240 --> 00:20:32.620
at the end of class, I can zoom way out.
00:20:32.620 --> 00:20:34.283
I can do full screen,
00:20:35.380 --> 00:20:38.360
and I can move around a
little bit more easily
00:20:38.360 --> 00:20:40.740
with this little mini map tool here.
00:20:40.740 --> 00:20:43.416
So it's, again, one of
those that you can explore
00:20:43.416 --> 00:20:46.510
a little bit more, but
I've really liked this one.
00:20:46.510 --> 00:20:49.870
It's very, but also a
little bit more robust
00:20:49.870 --> 00:20:54.870
in terms of being, you know,
kind of like that canvas feel,
00:20:55.140 --> 00:20:58.430
which I like, if you know, I
want to solve a big problem,
00:20:58.430 --> 00:21:01.040
I don't have enough
retail space on my screen.
00:21:01.040 --> 00:21:04.330
I can play a little bit more
with some of these options.
00:21:04.330 --> 00:21:08.230
So that is AWW app.
00:21:08.230 --> 00:21:10.550
And again, there's a paid
version or a free version.
00:21:10.550 --> 00:21:11.950
I'm just using the free one.
00:21:14.650 --> 00:21:15.483
All right.
00:21:15.483 --> 00:21:16.610
- [Jeremy] Stacey, as you're
going to the next section.
00:21:16.610 --> 00:21:18.130
I just want to give a shout out.
00:21:18.130 --> 00:21:20.010
You're getting so much love on the chat.
00:21:20.010 --> 00:21:22.960
People are saying, Oh, I
love Kami. I love Jamboard.
00:21:22.960 --> 00:21:23.793
I love AWW.
00:21:23.793 --> 00:21:25.780
So everyone is sharing
their favorite tools
00:21:25.780 --> 00:21:27.580
and there are even some additional
ones that are popping up.
00:21:27.580 --> 00:21:29.900
So thank you for sparking
the conversation.
00:21:29.900 --> 00:21:31.840
- Oh, fantastic. I know.
00:21:31.840 --> 00:21:33.150
And that's the hardest thing,
00:21:33.150 --> 00:21:35.450
I want to come on here and like make this
00:21:35.450 --> 00:21:38.830
as simple as possible for
everybody and say, you know,
00:21:38.830 --> 00:21:42.550
like this is the best
one, but the problem is
00:21:42.550 --> 00:21:44.130
there isn't a best one.
00:21:44.130 --> 00:21:46.950
And as you can probably see
that coming into the chat,
00:21:46.950 --> 00:21:48.430
there's probably a lot of conversation
00:21:48.430 --> 00:21:49.970
about what people love.
00:21:49.970 --> 00:21:54.152
And so again, I encourage
you to kind of think about
00:21:54.152 --> 00:21:57.320
what tools your school's already using
00:21:57.320 --> 00:22:00.410
and maybe there's one that
already resonates with you,
00:22:00.410 --> 00:22:03.410
but also like getting
students on it more easily.
00:22:03.410 --> 00:22:04.640
If you're already a Google school,
00:22:04.640 --> 00:22:06.640
Jamboard is going to
be super simple for you
00:22:06.640 --> 00:22:08.030
and for your students.
00:22:08.030 --> 00:22:10.430
If your students are already using Kami,
00:22:10.430 --> 00:22:12.830
that's going to be super simple to them.
00:22:12.830 --> 00:22:13.780
You know, at this point
00:22:13.780 --> 00:22:17.870
I don't want to present too
many more tools in my classroom
00:22:17.870 --> 00:22:20.520
because we already went through, you know,
00:22:20.520 --> 00:22:22.878
kind of some of the
pain, the growing pains
00:22:22.878 --> 00:22:24.560
of getting onboard.
00:22:24.560 --> 00:22:27.450
And that's always the hardest
part. Now we're in a routine.
00:22:27.450 --> 00:22:30.190
So, all right.
00:22:30.190 --> 00:22:35.190
So let's go ahead and dig
into using the scratch pad
00:22:35.960 --> 00:22:39.233
in Khan Academy in case
you're not using that already.
00:22:40.710 --> 00:22:44.020
So I'm going to go ahead right
now, actually, let me go back
00:22:44.020 --> 00:22:45.600
and just tell you what
I'm going to talk about.
00:22:45.600 --> 00:22:47.460
So the first thing I'm going to talk about
00:22:47.460 --> 00:22:50.010
is using it in the student view.
00:22:50.010 --> 00:22:52.838
So this would be from the assign tab,
00:22:52.838 --> 00:22:56.960
and this is something that
students also have access to.
00:22:56.960 --> 00:23:00.450
So even if they don't
have a device, you know,
00:23:00.450 --> 00:23:02.580
even if they just need to use their mouse,
00:23:02.580 --> 00:23:05.700
they can at least ink up a little bit
00:23:05.700 --> 00:23:07.420
as they're thinking through things,
00:23:07.420 --> 00:23:08.703
which I know is very difficult,
00:23:08.703 --> 00:23:11.640
but you as a teacher can also use it.
00:23:11.640 --> 00:23:13.310
So let me show you what I mean.
00:23:13.310 --> 00:23:17.003
So if I am in that
assigned tab right here,
00:23:19.500 --> 00:23:22.680
and then I click on to
any of the assignments
00:23:22.680 --> 00:23:24.520
that I have given.
00:23:24.520 --> 00:23:28.143
So let me go ahead and
click into this exercise.
00:23:30.630 --> 00:23:34.680
And then if I click on student
view, so say for example,
00:23:34.680 --> 00:23:37.160
I just want to do like
an introductory lesson.
00:23:37.160 --> 00:23:39.010
I found some really nice questions
00:23:39.010 --> 00:23:40.920
that were in Khan Academy.
00:23:40.920 --> 00:23:43.350
I don't want to assign
them for students yet
00:23:43.350 --> 00:23:44.250
to do on their own.
00:23:44.250 --> 00:23:46.830
I want to just have a class
conversation about it.
00:23:46.830 --> 00:23:49.450
I can go ahead and pull
this up on the board.
00:23:49.450 --> 00:23:52.270
And then if you click on here,
00:23:52.270 --> 00:23:55.790
the little white boarding tool,
then you'll see that again.
00:23:55.790 --> 00:23:57.670
I get kind of like my grid paper
00:23:57.670 --> 00:24:00.260
which I know we love as math teachers.
00:24:00.260 --> 00:24:02.850
And I can just mark it up.
00:24:02.850 --> 00:24:05.950
So, you know, I can be
writing and talking.
00:24:05.950 --> 00:24:09.320
I think there's real power
in being able to highlight
00:24:09.320 --> 00:24:10.640
while I'm talking,
00:24:10.640 --> 00:24:13.930
being able to write so students
can follow what I'm doing.
00:24:13.930 --> 00:24:15.010
So I'm saying, you know,
00:24:15.010 --> 00:24:17.310
the limit as X approaches negative two.
00:24:17.310 --> 00:24:19.210
So now I'm telling everybody, you know,
00:24:19.210 --> 00:24:23.130
pull your eye to negative two here.
00:24:23.130 --> 00:24:25.981
And again, it's just
this quick little visual
00:24:25.981 --> 00:24:30.840
of like what's going on so
I can pull that out for them
00:24:30.840 --> 00:24:33.470
and then say, you know, well,
what do you see going on
00:24:33.470 --> 00:24:35.130
from the left-hand side?
00:24:35.130 --> 00:24:38.650
And I can just be drawing
and talking at the same time.
00:24:38.650 --> 00:24:41.270
And then my students can
maybe unmute their mic,
00:24:41.270 --> 00:24:44.023
chat it out, we can talk about it.
00:24:44.023 --> 00:24:44.960
And then, you know, just what's happening
00:24:44.960 --> 00:24:46.350
from the right hand side.
00:24:46.350 --> 00:24:48.810
And so we can discuss it.
00:24:48.810 --> 00:24:50.582
And I think that just makes
00:24:50.582 --> 00:24:51.900
for a really nice little discussion
00:24:51.900 --> 00:24:53.930
and then we can choose
the answer together.
00:24:53.930 --> 00:24:57.140
So this is, again, this could
be used for class instruction
00:24:57.140 --> 00:25:00.323
or maybe you assigned something
00:25:00.323 --> 00:25:01.610
and students got something wrong.
00:25:01.610 --> 00:25:05.220
You could pull this up or you
could have them pull it up
00:25:05.220 --> 00:25:06.920
on their screen share
00:25:06.920 --> 00:25:10.530
and ask them to kind of use these tools
00:25:10.530 --> 00:25:14.040
to try and explain what they were thinking
00:25:14.040 --> 00:25:17.290
so that you can work through
it and coach them together.
00:25:17.290 --> 00:25:20.060
So that's a really nice little tool
00:25:20.060 --> 00:25:22.500
in case you haven't used it before.
00:25:22.500 --> 00:25:26.137
And then the other way
that I wanted to show it is
00:25:26.137 --> 00:25:28.540
after students have responded.
00:25:28.540 --> 00:25:31.760
So say that you already
gave an assignment.
00:25:31.760 --> 00:25:33.060
Everybody did it for homework.
00:25:33.060 --> 00:25:35.010
Now you want to discuss it in class.
00:25:35.010 --> 00:25:36.760
You can use a teacher report.
00:25:36.760 --> 00:25:40.050
And again, there is a
drawing tool that's available
00:25:40.050 --> 00:25:42.550
more on a sidebar in this case.
00:25:42.550 --> 00:25:44.303
So let me go ahead and go back.
00:25:45.410 --> 00:25:50.350
And this time I'm going to go
ahead and go into my scores
00:25:52.320 --> 00:25:53.993
And let me click on this.
00:25:56.470 --> 00:25:59.380
So now if we're reviewing
all students here,
00:25:59.380 --> 00:26:03.238
say that I want to discuss this one.
00:26:03.238 --> 00:26:04.071
This one person got it wrong.
00:26:04.071 --> 00:26:07.170
So I can go ahead and pull
up the draw tool right here.
00:26:07.170 --> 00:26:10.180
And then I can just write on the side.
00:26:10.180 --> 00:26:11.940
So again, super simple.
00:26:11.940 --> 00:26:14.290
I can't draw on the drawing
itself in this case,
00:26:14.290 --> 00:26:19.110
but here was an example that
I just laid out right here.
00:26:19.110 --> 00:26:21.280
For example, you know, you might say,
00:26:21.280 --> 00:26:24.450
what are the three things
that you are looking for here?
00:26:24.450 --> 00:26:25.930
And I could just write that out
00:26:25.930 --> 00:26:28.030
and then I'm able to write that out
00:26:28.030 --> 00:26:31.620
because I have the pen
tool on my Wacom tablet.
00:26:31.620 --> 00:26:32.820
If I was using my mouse,
00:26:32.820 --> 00:26:34.760
I would not be able to write that out.
00:26:34.760 --> 00:26:38.090
So again, that can be a really nice way
00:26:38.090 --> 00:26:40.820
to just talk about things in class.
00:26:40.820 --> 00:26:44.671
So those are my two favorite
ways of the whiteboard
00:26:44.671 --> 00:26:49.300
right within Khan Academy to
bring things out during class
00:26:49.300 --> 00:26:52.540
or to do kind of one-on-one
individualized coaching,
00:26:52.540 --> 00:26:54.490
the students also.
00:26:54.490 --> 00:26:57.770
So let me pause again and
see if there's any questions
00:26:57.770 --> 00:26:59.130
coming in before we get into
00:26:59.130 --> 00:27:01.990
some simple screencasting options.
00:27:01.990 --> 00:27:04.340
- [Jeremy] Yeah. So there are
so many questions, Stacey.
00:27:04.340 --> 00:27:07.320
What I would recommend is why
don't we finish up the content
00:27:07.320 --> 00:27:09.160
and then save maybe like 10, 15 minutes
00:27:09.160 --> 00:27:11.340
and really dig deep into these questions.
00:27:11.340 --> 00:27:14.470
- Sounds good to me. All right.
00:27:14.470 --> 00:27:18.170
So again, I'm presenting four options here
00:27:18.170 --> 00:27:21.940
depending on what you
need for screencasting.
00:27:21.940 --> 00:27:23.410
When it comes to screencasting,
00:27:23.410 --> 00:27:25.660
there are a lot of options out there.
00:27:25.660 --> 00:27:27.620
I'm going to set it, again.
00:27:27.620 --> 00:27:30.759
If you're a Google school
already using Google Meet
00:27:30.759 --> 00:27:33.830
and if you already have
the ability to record,
00:27:33.830 --> 00:27:35.890
not everybody has the ability
to record in Google Meet,
00:27:35.890 --> 00:27:38.470
but if you have the ability
to record in Google Meet,
00:27:38.470 --> 00:27:40.639
you would see it under your three dots
00:27:40.639 --> 00:27:41.472
and you'd be able to record.
00:27:41.472 --> 00:27:43.730
Everybody who's using Google
for education right now
00:27:43.730 --> 00:27:45.950
should be able to record in Google.
00:27:45.950 --> 00:27:48.050
They've made that available for this year.
00:27:49.180 --> 00:27:52.830
So if you're doing that for
class already, you know what?
00:27:52.830 --> 00:27:55.870
You can join a Google
Meet, just you and yourself
00:27:55.870 --> 00:27:57.580
and make a nice little screencast
00:27:57.580 --> 00:27:59.950
because you will have
created a video, right?
00:27:59.950 --> 00:28:03.580
So you could just join the
Google Meet all by yourself.
00:28:03.580 --> 00:28:07.650
You can open up, pop open
a Jamboard, for example
00:28:07.650 --> 00:28:09.420
and use the white boarding.
00:28:09.420 --> 00:28:10.253
There you go.
00:28:10.253 --> 00:28:13.770
Simple whiteboard screencasts
that you can then,
00:28:13.770 --> 00:28:15.610
it will upload it to your Google Drive.
00:28:15.610 --> 00:28:19.400
And then you can give it to
students to go ahead and review.
00:28:19.400 --> 00:28:22.020
If you are using Zoom,
there's a record option,
00:28:22.020 --> 00:28:22.923
right in Zoom.
00:28:24.017 --> 00:28:25.320
So you could use the
white boarding tool again
00:28:25.320 --> 00:28:26.273
right in Zoom.
00:28:27.300 --> 00:28:29.970
And you can just record.
Let's keep it simple.
00:28:29.970 --> 00:28:34.010
If you are wanting a Chrome extension,
00:28:34.010 --> 00:28:34.940
there are a couple.
00:28:34.940 --> 00:28:38.370
You may have used Screencastify or Loom.
00:28:38.370 --> 00:28:40.936
They're both very similar.
00:28:40.936 --> 00:28:43.900
I usually recommend Loom because
it is free for educators.
00:28:43.900 --> 00:28:46.890
Screencastify has a
limit for what you can do
00:28:46.890 --> 00:28:48.040
with the free version.
00:28:48.040 --> 00:28:49.330
So that's why I say Loom.
00:28:49.330 --> 00:28:51.210
If you sign up as an educator,
00:28:51.210 --> 00:28:52.440
not everybody knows about that.
00:28:52.440 --> 00:28:54.670
There's an educator form
that you can fill out
00:28:54.670 --> 00:28:57.886
in which case you get free access to Loom.
00:28:57.886 --> 00:29:01.410
So that does allow you to
do both like, you know,
00:29:01.410 --> 00:29:04.670
the little video and your
screencast at the same time
00:29:04.670 --> 00:29:06.240
or you can just do the screencast.
00:29:06.240 --> 00:29:08.550
You get to choose what
you want to do there,
00:29:08.550 --> 00:29:12.910
screen only, screen and cam,
and you can record again.
00:29:12.910 --> 00:29:14.940
You can upload that to your Google Drive.
00:29:14.940 --> 00:29:17.660
You have some different options there.
00:29:17.660 --> 00:29:20.670
And then lastly I'm going
to present one paid option,
00:29:20.670 --> 00:29:22.100
which is Camtasia.
00:29:22.100 --> 00:29:26.040
And I present that because
that's actually what I use
00:29:26.040 --> 00:29:27.700
to record my videos.
00:29:27.700 --> 00:29:31.820
That's what I've been
using since 2010 actually.
00:29:31.820 --> 00:29:33.690
I use that to record my videos
00:29:33.690 --> 00:29:36.780
and I use that to edit my videos.
00:29:36.780 --> 00:29:38.840
So that's what I like about that is that
00:29:38.840 --> 00:29:41.570
it does have a pretty robust editor also.
00:29:41.570 --> 00:29:45.010
I can add in like little
annotations at the end.
00:29:45.010 --> 00:29:47.800
I can cut things if I made a mistake,
00:29:47.800 --> 00:29:51.890
I can do some transitions,
all of that good stuff.
00:29:51.890 --> 00:29:54.560
So if you want to invest
a little bit more time
00:29:54.560 --> 00:29:58.410
and energy into creating
videos and editing them,
00:29:58.410 --> 00:30:00.050
that's something that you enjoy.
00:30:00.050 --> 00:30:02.240
I really enjoy editing my videos.
00:30:02.240 --> 00:30:06.480
Then I would recommend looking
into a Camtasia license
00:30:06.480 --> 00:30:09.410
and make sure that you look
for an educator discount
00:30:09.410 --> 00:30:12.400
on that because you have some
educator discounts available
00:30:13.480 --> 00:30:14.740
but that is a paid option
00:30:14.740 --> 00:30:18.683
and it is available
for both a PC or a Mac.
00:30:19.560 --> 00:30:24.560
So I'm going to keep this
as simple as possible.
00:30:25.480 --> 00:30:30.290
Again, one of the easiest ways
to start inking up anything
00:30:30.290 --> 00:30:33.010
is to use PowerPoint actually.
00:30:33.010 --> 00:30:37.470
And there is a pen tool available
even in PowerPoint Online.
00:30:37.470 --> 00:30:39.620
So I'm going to show you PowerPoint Online
00:30:39.620 --> 00:30:41.990
because this is how I actually
got started with things.
00:30:41.990 --> 00:30:43.360
I just opened up a PowerPoint.
00:30:43.360 --> 00:30:46.960
Like I had my PowerPoint as
my base, my presentation.
00:30:46.960 --> 00:30:51.360
I had a question and a
lot of blank, white space
00:30:51.360 --> 00:30:54.290
as you can see here, that's
kind of what it looked like.
00:30:54.290 --> 00:30:55.890
Whatever's in red is what I wrote
00:30:55.890 --> 00:30:58.610
while I was making the screencast itself.
00:30:58.610 --> 00:31:01.130
And so when you do this in PowerPoint,
00:31:01.130 --> 00:31:03.700
it's going to save all
the annotations too.
00:31:03.700 --> 00:31:06.940
So then you have a kind
of a final version.
00:31:06.940 --> 00:31:08.930
And I usually save my original version.
00:31:08.930 --> 00:31:13.100
And I usually, I print out the
blank version for my students
00:31:13.100 --> 00:31:15.020
so that they can take notes
right on the PowerPoint
00:31:15.020 --> 00:31:16.500
as they're watching the video.
00:31:16.500 --> 00:31:19.440
And then you can just go ahead
and go to this drawing tab.
00:31:19.440 --> 00:31:21.180
I'm in PowerPoint Online here.
00:31:21.180 --> 00:31:22.890
And then you go to the drawing tab
00:31:22.890 --> 00:31:25.790
and you can choose from a
bunch of different colors.
00:31:25.790 --> 00:31:27.760
And it's nice that it
has your recent colors
00:31:27.760 --> 00:31:29.020
that are saved right here.
00:31:29.020 --> 00:31:31.660
You can change the
thickness of the pen tool
00:31:33.240 --> 00:31:35.930
and then you can also use
this different pen tool.
00:31:35.930 --> 00:31:40.610
They're a little bit
different and have the colors.
00:31:40.610 --> 00:31:43.350
You have the eraser,
you have a highlighter,
00:31:43.350 --> 00:31:46.700
and you can just get started
with making a screencast.
00:31:46.700 --> 00:31:48.870
So again, you could open this up,
00:31:48.870 --> 00:31:51.480
then use one of screencasting
tools we talked about.
00:31:51.480 --> 00:31:53.808
So you could open up a
Google Meet with you yourself
00:31:53.808 --> 00:31:56.350
and press record.
00:31:56.350 --> 00:31:58.840
You can open up Zoom and record yourself.
00:31:58.840 --> 00:32:00.463
You could also use Screencastify.
00:32:00.463 --> 00:32:02.160
I use Camtasia.
00:32:02.160 --> 00:32:04.080
When I use Camtasia, something
else I like about that
00:32:04.080 --> 00:32:06.917
is I can just like choose
what portion of the screen
00:32:06.917 --> 00:32:07.900
I want to record.
00:32:07.900 --> 00:32:11.040
So I would just like select
this portion of the screen
00:32:11.040 --> 00:32:13.610
with my mouse, you know?
00:32:13.610 --> 00:32:17.144
So it would like record just this portion.
00:32:17.144 --> 00:32:21.150
And then obviously I was
not using my tablet there.
00:32:21.150 --> 00:32:24.400
So it was very messy, but I
would just record that portion
00:32:24.400 --> 00:32:26.530
and you wouldn't be able to see
any of the background stuff.
00:32:26.530 --> 00:32:29.100
And so a lot of the different tools
00:32:29.100 --> 00:32:31.160
allow you to choose just
a piece of your screen
00:32:31.160 --> 00:32:33.470
instead of recording the entire screen.
00:32:33.470 --> 00:32:35.350
So that's something to keep in mind also.
00:32:35.350 --> 00:32:37.900
Loom has that ability, I know.
00:32:37.900 --> 00:32:41.390
So yeah, that's the
easiest way to honestly,
00:32:41.390 --> 00:32:44.580
to get started here,
PowerPoint, you use it
00:32:44.580 --> 00:32:45.543
and it's all free.
00:32:47.220 --> 00:32:50.713
If you have PowerPoint,
like the desktop version,
00:32:51.660 --> 00:32:53.500
this is coming to Mac.
00:32:53.500 --> 00:32:55.170
I don't think it's
rolled out to everybody.
00:32:55.170 --> 00:32:56.630
I know I'm in a program
00:32:56.630 --> 00:32:58.240
where I get some early releases of things.
00:32:58.240 --> 00:33:02.410
So it is available on, I am
using it on my Mac right now.
00:33:02.410 --> 00:33:03.640
There is a record slideshow.
00:33:03.640 --> 00:33:06.220
It's been available on a PC for years.
00:33:06.220 --> 00:33:08.730
If you have PowerPoint
downloaded to your computer.
00:33:08.730 --> 00:33:10.750
You can actually, it's a one-stop shop
00:33:10.750 --> 00:33:14.880
where you can create a
video and record your screen
00:33:14.880 --> 00:33:17.620
right using PowerPoint all in one.
00:33:17.620 --> 00:33:19.700
Like you don't even need a second tool.
00:33:19.700 --> 00:33:21.390
If that's something that interests you,
00:33:21.390 --> 00:33:24.661
I have a reference article
and also a video tutorial.
00:33:24.661 --> 00:33:27.690
That is a Windows specific one
00:33:27.690 --> 00:33:31.650
but it's should be similar
for the Mac starting soon.
00:33:31.650 --> 00:33:34.230
Anyway, I just wanted to
present that as an option
00:33:34.230 --> 00:33:35.560
if you're using PowerPoint,
00:33:35.560 --> 00:33:38.660
this is something that a lot
of people aren't aware of,
00:33:38.660 --> 00:33:40.980
again, it's record slideshow,
00:33:40.980 --> 00:33:43.070
it's right baked into PowerPoint
00:33:43.070 --> 00:33:45.930
and you can export it as a MP4.
00:33:45.930 --> 00:33:48.780
If you want students
to watch it as a video
00:33:48.780 --> 00:33:51.760
or you can also give a share link.
00:33:51.760 --> 00:33:54.744
And that share link is kind of like
00:33:54.744 --> 00:33:57.900
if I shared these Google
slides with you right now
00:33:57.900 --> 00:34:00.350
where students can press
like the next button
00:34:00.350 --> 00:34:03.000
and the next button, but
it will play like a video.
00:34:03.000 --> 00:34:05.760
It's really cool. I encourage
you to check it out.
00:34:05.760 --> 00:34:08.480
If you are a PowerPoint fan,
00:34:08.480 --> 00:34:09.530
if you're not, though
00:34:10.406 --> 00:34:13.163
I've provided some other options
for you to explore today.
00:34:16.440 --> 00:34:21.000
So I did want to show
you my actual process.
00:34:21.000 --> 00:34:23.600
And this is a video of my actual process.
00:34:23.600 --> 00:34:26.550
These days I use Notability on my Mac.
00:34:26.550 --> 00:34:28.204
I pay for that.
00:34:28.204 --> 00:34:31.861
It wasn't very expensive,
but I did purchase Notability
00:34:31.861 --> 00:34:34.550
which is a, you might be familiar.
00:34:34.550 --> 00:34:39.550
There is an iOS
application for Notability,
00:34:40.320 --> 00:34:42.270
but there's also a Mac application.
00:34:42.270 --> 00:34:45.860
And I just like it as like I
have it as my digital notebook.
00:34:45.860 --> 00:34:47.540
So that's what I'm using these days.
00:34:47.540 --> 00:34:50.240
But honestly, I start
off with a PowerPoint,
00:34:50.240 --> 00:34:52.782
and you can replicate the
same thing in PowerPoint.
00:34:52.782 --> 00:34:56.350
And I use Camtasia to
make my screen recordings.
00:34:56.350 --> 00:34:59.943
Then I upload those for students to watch.
00:35:01.500 --> 00:35:03.710
So again, if you want
to see my exact process,
00:35:03.710 --> 00:35:05.173
that video is available.
00:35:06.360 --> 00:35:07.193
All right.
00:35:08.540 --> 00:35:10.360
Last, I think this is like
almost my last question for you.
00:35:10.360 --> 00:35:12.763
How many Flipgrid fans
do I have here today?
00:35:15.100 --> 00:35:17.550
- [Jeremy] Okay, so let's
queue this one up here.
00:35:18.420 --> 00:35:20.110
So we launched the Flipgrid poll
00:35:22.200 --> 00:35:25.630
and it's looking like
a lot of folks love it.
00:35:25.630 --> 00:35:27.280
Maybe more have never used it before.
00:35:27.280 --> 00:35:30.230
So this is great, great chance
to share something powerful.
00:35:31.260 --> 00:35:32.203
- All right.
00:35:33.300 --> 00:35:34.620
- [Jeremy] So go ahead
and share those results.
00:35:34.620 --> 00:35:37.540
It looks like about
70% have not tried yet.
00:35:37.540 --> 00:35:39.240
So feel free to share more Stacey.
00:35:40.430 --> 00:35:45.240
- Okay. So I am obviously
in the love it camp.
00:35:45.240 --> 00:35:47.303
So Flipgrid, there's two main things
00:35:47.303 --> 00:35:48.760
that you can do in Flipgrid.
00:35:48.760 --> 00:35:51.750
One is that you can record, sorry.
00:35:51.750 --> 00:35:53.790
You can have students record responses.
00:35:53.790 --> 00:35:57.520
So it comes in all like a
grid of student replies.
00:35:57.520 --> 00:35:59.390
I'm not going to focus on that today,
00:35:59.390 --> 00:36:01.190
even though that is amazing.
00:36:01.190 --> 00:36:03.410
I use it in my math class
all the time for students
00:36:03.410 --> 00:36:08.410
to explain their math
thinking and I don't use,
00:36:08.430 --> 00:36:10.020
they don't use any special white boarding
00:36:10.020 --> 00:36:11.060
or anything like that.
00:36:11.060 --> 00:36:13.260
They just use a phone and they hover it
00:36:13.260 --> 00:36:14.220
over their piece of paper
00:36:14.220 --> 00:36:15.750
and they talk about their math solutions
00:36:15.750 --> 00:36:17.770
and it's all posted on one big grid.
00:36:17.770 --> 00:36:19.210
But what I'm going to talk about today
00:36:19.210 --> 00:36:24.210
is more of like the teacher
created portion here,
00:36:24.269 --> 00:36:25.640
since that is the focus
of our session today.
00:36:25.640 --> 00:36:28.050
So when you're in
Flipgrid and this is free,
00:36:28.050 --> 00:36:29.750
free available for everybody,
00:36:29.750 --> 00:36:31.590
there is something
called the shorts camera.
00:36:31.590 --> 00:36:34.080
And that is to record a short video.
00:36:34.080 --> 00:36:36.350
You can record up to 10 minutes in here.
00:36:36.350 --> 00:36:39.960
So when I record a short, that's gonna be,
00:36:39.960 --> 00:36:42.350
that's going to do my
whole screen recording
00:36:42.350 --> 00:36:44.040
and provide me with a whiteboard.
00:36:44.040 --> 00:36:46.550
This is super simple. All right.
00:36:46.550 --> 00:36:48.460
So what I'm going to do here is I'm going
00:36:48.460 --> 00:36:50.720
to go to my effects.
00:36:50.720 --> 00:36:52.340
I know I'm covering a lot rather quickly.
00:36:52.340 --> 00:36:53.720
So here we go,
00:36:53.720 --> 00:36:57.806
and you can choose a board
and I can choose a whiteboard.
00:36:57.806 --> 00:37:01.084
What you can do here is you
can also split the screen.
00:37:01.084 --> 00:37:03.680
So I could be like in
the side of the video,
00:37:03.680 --> 00:37:06.510
or I can just be like, I
want only a whiteboard.
00:37:06.510 --> 00:37:09.460
And again, I have some
different types of paper
00:37:09.460 --> 00:37:10.630
that I can choose from.
00:37:10.630 --> 00:37:13.623
And then all I have to do
is press the record button.
00:37:17.560 --> 00:37:20.120
Now it's actually recording
everything that I do,
00:37:20.120 --> 00:37:23.030
so I can go ahead and I
can open up a pen tool.
00:37:23.030 --> 00:37:27.990
I can change the color of my
pen and I can get to drawing.
00:37:27.990 --> 00:37:30.440
So it's very simple, very quick.
00:37:30.440 --> 00:37:32.550
I would just have this one screen.
00:37:32.550 --> 00:37:37.550
I can always pause if I needed
to, I could reset my screen
00:37:37.560 --> 00:37:39.313
so I could delete everything.
00:37:40.270 --> 00:37:43.610
You can even in here,
just to let you know,
00:37:43.610 --> 00:37:45.930
there is a record screen feature in here.
00:37:45.930 --> 00:37:50.450
If you ever want to use
that to record your screen.
00:37:50.450 --> 00:37:53.060
If I didn't already give
you enough options, right.
00:37:53.060 --> 00:37:56.607
But what happens is once
you make this recording,
00:37:58.236 --> 00:37:59.690
everything that I do so I can go ahead
00:37:59.690 --> 00:38:01.940
and I can open up a pen tool.
00:38:01.940 --> 00:38:05.010
All right, so if you
made a little mistake,
00:38:05.010 --> 00:38:07.640
there is a very simple
editor here where you can,
00:38:07.640 --> 00:38:09.720
like double, sorry,
00:38:09.720 --> 00:38:11.060
you can double click and you can,
00:38:11.060 --> 00:38:11.980
you know how you can trim
00:38:11.980 --> 00:38:13.470
like the beginning or end of the video.
00:38:13.470 --> 00:38:16.480
You're able to do that
here. So I can do that.
00:38:16.480 --> 00:38:21.010
I can confirm. And now, say,
you forgot to add a clip.
00:38:21.010 --> 00:38:23.650
You can add more or you
want multiple boards.
00:38:23.650 --> 00:38:24.860
You can do that.
00:38:24.860 --> 00:38:29.150
Another way that I really
like to use this is to, again,
00:38:29.150 --> 00:38:30.900
just upload a little image.
00:38:30.900 --> 00:38:33.130
So maybe I have an image of a graph
00:38:33.130 --> 00:38:35.840
and then I can just draw on that graph.
00:38:35.840 --> 00:38:38.553
Let me show you how you do that. Add more.
00:38:40.420 --> 00:38:44.280
I can go ahead into my effects
and I can use the photo
00:38:44.280 --> 00:38:46.590
and you can go ahead
and upload a screenshot,
00:38:46.590 --> 00:38:49.550
maybe from your textbook
or whatever it may be.
00:38:49.550 --> 00:38:52.500
And then you would be able
to just ink on top of it,
00:38:52.500 --> 00:38:54.310
how you can ink on top of it, again,
00:38:54.310 --> 00:38:57.750
is you just go into these
drawing tools right here.
00:38:57.750 --> 00:38:59.730
And that's really, that's really it.
00:38:59.730 --> 00:39:02.270
I won't show you all the
fancy frames that you can do
00:39:02.270 --> 00:39:04.770
which the kids love, you
know, all that good stuff.
00:39:04.770 --> 00:39:09.280
And then when you're all
done, you go to the next,
00:39:09.280 --> 00:39:12.300
next, you can title it if you want,
00:39:12.300 --> 00:39:13.883
you choose a cover photo.
00:39:16.330 --> 00:39:19.023
So let's just choose something
from the middle there.
00:39:22.986 --> 00:39:25.317
There we go. Confirm, great image.
00:39:27.960 --> 00:39:30.410
And the beauty of this is
it's going to generate a link
00:39:30.410 --> 00:39:31.760
for me right now.
00:39:31.760 --> 00:39:34.060
And that's the link that
I share with my students.
00:39:34.060 --> 00:39:36.600
That's it. And now this is a video.
00:39:36.600 --> 00:39:38.750
There's nothing else to
do. There's no uploading.
00:39:38.750 --> 00:39:39.970
There's no downloading.
00:39:39.970 --> 00:39:42.300
This is a quick whiteboard style video.
00:39:42.300 --> 00:39:45.453
I guess it's preparing
it still. That's it.
00:39:47.100 --> 00:39:50.940
See, it's available already. That's it.
00:39:50.940 --> 00:39:52.880
And now it's actually.
00:39:52.880 --> 00:39:55.650
So I'll just stick with that.
00:39:55.650 --> 00:39:58.340
There's so much more in
Flipgrid that you can do,
00:39:58.340 --> 00:40:00.800
but I'll stick with the simple again,
00:40:00.800 --> 00:40:02.360
if I talked about that too quickly,
00:40:02.360 --> 00:40:04.200
and this is an option that you're like,
00:40:04.200 --> 00:40:07.532
Oh this is great, simple, let's
get started with that one.
00:40:07.532 --> 00:40:09.420
I have a little video tutorial
00:40:09.420 --> 00:40:11.150
on how to set up your Flipgrid,
00:40:11.150 --> 00:40:13.883
how to get started with that also.
00:40:15.353 --> 00:40:19.010
All right, so I want to leave
plenty of time for that Q&A,
00:40:19.010 --> 00:40:21.500
like you said, the last piece,
00:40:21.500 --> 00:40:23.370
which I'm not going to get in today,
00:40:23.370 --> 00:40:25.954
but I just wanted to present is,
00:40:25.954 --> 00:40:28.210
the last piece of like,
00:40:28.210 --> 00:40:31.070
how do we engage our
students during class?
00:40:31.070 --> 00:40:35.711
Because this is more like
instructional stuff that we do,
00:40:35.711 --> 00:40:39.320
but what do you do during
class time to make sure
00:40:39.320 --> 00:40:41.580
that all students are
really participating?
00:40:41.580 --> 00:40:45.500
I am really lucky in that
I actually have a class set
00:40:45.500 --> 00:40:46.670
of these Wacom tablets.
00:40:46.670 --> 00:40:49.470
So you can see my students
writing with the Wacom tablet.
00:40:49.470 --> 00:40:51.950
I pair this up with Pear Deck
00:40:51.950 --> 00:40:55.300
and Pear Deck is a
add-on for Google Slides.
00:40:55.300 --> 00:41:00.230
It's also available for,
for PowerPoint Online.
00:41:00.230 --> 00:41:03.350
And it allows me to see the
work of all different students
00:41:03.350 --> 00:41:06.060
in this dashboard view in real time.
00:41:06.060 --> 00:41:10.460
And this is how I how I was using it now,
00:41:10.460 --> 00:41:12.310
where students don't
actually have a tablet.
00:41:12.310 --> 00:41:14.560
I'm just doing the writing with my tablet.
00:41:14.560 --> 00:41:16.710
Students can still like circle an answer
00:41:16.710 --> 00:41:20.220
so I can see if students are all trying.
00:41:20.220 --> 00:41:24.467
If they're all responding, if
they're giving it some effort,
00:41:24.467 --> 00:41:29.467
and then I can kind of, you
know, write out my reply.
00:41:29.500 --> 00:41:31.620
And so the only reason
that I bring this up
00:41:31.620 --> 00:41:33.450
is that we might have an opportunity
00:41:33.450 --> 00:41:35.370
to bring you all another webinar.
00:41:35.370 --> 00:41:37.881
So we just wanted to gauge some interest
00:41:37.881 --> 00:41:41.430
to see if you would be
interested in learning more
00:41:41.430 --> 00:41:43.170
about like that class discussion piece,
00:41:43.170 --> 00:41:46.320
learning more specifically
about how I use Pear Deck.
00:41:46.320 --> 00:41:47.872
We could probably,
00:41:47.872 --> 00:41:49.448
we could definitely do
a whole webinar on that.
00:41:49.448 --> 00:41:53.070
So we're going to do a
quick little survey right
00:41:53.070 --> 00:41:57.790
after the session ends to
see if that is something
00:41:57.790 --> 00:41:59.373
that you are interested in.
00:42:02.610 --> 00:42:07.240
I'm going to just close with this quote.
00:42:07.240 --> 00:42:09.950
I really believe if we empower
students with the resources
00:42:09.950 --> 00:42:12.230
they need and coach
them through the process
00:42:12.230 --> 00:42:15.490
of using these tools, then
students can take ownership
00:42:15.490 --> 00:42:18.252
for their learning and that's
where the real magic happens.
00:42:18.252 --> 00:42:21.180
And so for me, flipping my classroom,
00:42:21.180 --> 00:42:24.300
giving my students all the
resources through the video
00:42:24.300 --> 00:42:27.820
that I prepared them with before
they even walk into class,
00:42:27.820 --> 00:42:29.690
oh my gosh, it's been so transformational.
00:42:29.690 --> 00:42:31.716
I really didn't even get to
talk about my flip classroom,
00:42:31.716 --> 00:42:35.930
kind of how that's
transformed my teaching.
00:42:35.930 --> 00:42:39.300
I assign my videos through a tool
00:42:39.300 --> 00:42:41.500
where I can see how students
are watching the videos.
00:42:41.500 --> 00:42:43.810
I can embed questions in the videos.
00:42:43.810 --> 00:42:48.310
I come to class prepared because
I know what students need
00:42:48.310 --> 00:42:52.200
and that has been really
transformational for me.
00:42:52.200 --> 00:42:53.390
But of course the first step
00:42:53.390 --> 00:42:55.150
is knowing how to make the videos.
00:42:55.150 --> 00:42:59.072
So hopefully you got some ideas today
00:42:59.072 --> 00:43:02.222
and we'll have plenty of time for Q&A.
00:43:02.222 --> 00:43:06.930
Of course, I want to share
that code for you all
00:43:06.930 --> 00:43:11.593
to get a discount on a Wacom product.
00:43:11.593 --> 00:43:15.680
Thank you again, to Wacom
for offering this discount
00:43:15.680 --> 00:43:17.330
for everybody joining today.
00:43:17.330 --> 00:43:20.740
So there are a lot of
different products to explore.
00:43:20.740 --> 00:43:23.860
So this link will be
dropped into the chat.
00:43:23.860 --> 00:43:26.750
I see Jeremy's already
done that. Thank you.
00:43:26.750 --> 00:43:30.740
And you can explore the different
devices that are available
00:43:30.740 --> 00:43:35.253
and you would save 10% with the
code that's available there.
00:43:37.341 --> 00:43:39.740
All right, should we dig into the Q&A?
00:43:39.740 --> 00:43:40.573
- Let's do it.
00:43:40.573 --> 00:43:42.280
And I'm going to give you
a huge shout out, Stacey
00:43:42.280 --> 00:43:43.770
because I know you can't see it
00:43:43.770 --> 00:43:46.310
but there is so much love
pouring into the question section
00:43:46.310 --> 00:43:48.301
saying, best professional
development ever.
00:43:48.301 --> 00:43:50.020
I've learned more in 40 minutes
00:43:50.878 --> 00:43:52.770
than I learned in life 40
hours of traditional training.
00:43:52.770 --> 00:43:55.460
So thank you for being
really, really actionable
00:43:55.460 --> 00:43:58.150
with the kinds of tools that
teachers can use tomorrow
00:43:58.150 --> 00:43:59.090
wherever their students are.
00:43:59.090 --> 00:44:01.400
But let's back up one little bit here
00:44:02.656 --> 00:44:03.710
because at the very
beginning of this session,
00:44:03.710 --> 00:44:04.980
Michael wants to know,
00:44:04.980 --> 00:44:06.560
what do these tablets even look like?
00:44:06.560 --> 00:44:09.137
Like, what does it look
like when a teacher uses it?
00:44:09.137 --> 00:44:10.310
If you don't mind holding up yours,
00:44:10.310 --> 00:44:13.290
just give a sense of how
it looks and how it feels.
00:44:13.290 --> 00:44:16.270
- Okay. So this is the one
that's really portable.
00:44:16.270 --> 00:44:17.103
This is the Intuos One.
00:44:17.103 --> 00:44:19.619
This is a small Intuos.
00:44:19.619 --> 00:44:20.860
So it's the one that you're
seeing like on my screen share
00:44:20.860 --> 00:44:22.844
actually right now, it's a small one,
00:44:22.844 --> 00:44:23.750
the one all the way on the right.
00:44:23.750 --> 00:44:25.520
And so this is the
Bluetooth version of it.
00:44:25.520 --> 00:44:26.850
And so literally, you know,
00:44:26.850 --> 00:44:29.240
you just press the button
to turn it on and off.
00:44:29.240 --> 00:44:30.700
And it's Bluetooth enabled.
00:44:30.700 --> 00:44:35.140
And when I am using the pen here,
00:44:35.140 --> 00:44:38.840
it works exactly like a huge mouse pad.
00:44:38.840 --> 00:44:41.340
Okay. So you think of this as a mouse pad.
00:44:41.340 --> 00:44:43.850
So like this top left corner corresponds
00:44:43.850 --> 00:44:45.980
to the top left of my screen.
00:44:45.980 --> 00:44:47.890
And this top, the bottom right
00:44:47.890 --> 00:44:49.540
is like the bottom right of my screen.
00:44:49.540 --> 00:44:52.056
So wherever I'm positioning my pen
00:44:52.056 --> 00:44:55.420
is where I'm going to be
writing on the screen.
00:44:55.420 --> 00:44:59.810
And so then I have a pen,
so it mimics exactly.
00:44:59.810 --> 00:45:01.605
It's like a giant mouse pad,
00:45:01.605 --> 00:45:04.120
and I'm able to write with the pen.
00:45:04.120 --> 00:45:07.860
So that's this style of
tablet. I don't see my screen.
00:45:07.860 --> 00:45:09.870
I have to like look up at my screen
00:45:09.870 --> 00:45:11.200
to see where I'm writing.
00:45:11.200 --> 00:45:13.360
So you might be thinking
this is so difficult.
00:45:13.360 --> 00:45:16.060
Here's what I found. My
students all have one of these.
00:45:16.060 --> 00:45:19.540
I have a classroom set of
these. It takes about a month.
00:45:19.540 --> 00:45:21.220
So the first time they use it,
00:45:21.220 --> 00:45:22.680
they're like, what is this thing?
00:45:22.680 --> 00:45:23.900
How am I supposed to write with this?
00:45:23.900 --> 00:45:26.400
It does take about a
month to get used to it,
00:45:26.400 --> 00:45:28.580
to get used to like where
you're writing on the screen.
00:45:28.580 --> 00:45:30.193
You're not dragging it like a mouse,
00:45:30.193 --> 00:45:33.600
but you're actually just writing
on the part of the screen.
00:45:33.600 --> 00:45:37.930
But once you get used
to it and you can't see,
00:45:37.930 --> 00:45:40.010
but like there's these
little grids on it too.
00:45:40.010 --> 00:45:43.630
So it's easy to like
align and write straight.
00:45:43.630 --> 00:45:45.690
It's really helpful to have
those little grid lines.
00:45:45.690 --> 00:45:48.870
I use it a lot. There's
also little buttons here.
00:45:48.870 --> 00:45:50.270
If like you need to click
00:45:51.423 --> 00:45:53.570
and so use it as like a
right click or something.
00:45:53.570 --> 00:45:56.746
So you really can use
this to navigate anything
00:45:56.746 --> 00:45:58.560
that you need.
00:45:58.560 --> 00:46:02.010
And then yeah, I found you get
used to it in about a month.
00:46:02.010 --> 00:46:04.610
And the writing on this is so wonderful.
00:46:04.610 --> 00:46:06.441
Like this is used by artists.
00:46:06.441 --> 00:46:09.540
So it's way more than I
need as a math teacher,
00:46:09.540 --> 00:46:10.690
but it feels wonderful.
00:46:10.690 --> 00:46:12.930
It feels like you're
writing on a piece of paper,
00:46:12.930 --> 00:46:14.100
which is what I love.
00:46:14.100 --> 00:46:16.013
And then the other one.
00:46:17.980 --> 00:46:20.330
So what I use more often,
especially now, since I'm at home,
00:46:20.330 --> 00:46:22.090
this is the Wacom One.
00:46:22.090 --> 00:46:26.930
So it is like, okay,
let's see, much bigger.
00:46:26.930 --> 00:46:29.870
It's 13 inches, okay?
00:46:29.870 --> 00:46:34.060
This one, and this is a
pen display style One.
00:46:34.060 --> 00:46:35.680
I don't have it plugged in right now
00:46:35.680 --> 00:46:37.390
because I just didn't want to, like,
00:46:37.390 --> 00:46:41.040
I was afraid with all these
people on that I was going,
00:46:41.040 --> 00:46:42.650
my internet would lag or something
00:46:42.650 --> 00:46:44.829
when I had too many screens plugged in,
00:46:44.829 --> 00:46:45.662
and I have so many things plugged into
00:46:45.662 --> 00:46:47.423
my computer right now.
00:46:47.423 --> 00:46:48.256
So that's why I don't have it on,
00:46:48.256 --> 00:46:49.440
but pretty much I keep this thing on,
00:46:49.440 --> 00:46:52.130
plugged in all the time into my computer.
00:46:52.130 --> 00:46:56.620
So again, you plug it in with
a USB into your computer.
00:46:56.620 --> 00:46:57.870
So you plug it in with the USB.
00:46:57.870 --> 00:47:00.640
You also do have to power
this one into a wall.
00:47:00.640 --> 00:47:02.110
So that's just something to know.
00:47:02.110 --> 00:47:03.590
But if you're making videos,
00:47:03.590 --> 00:47:06.930
so you can see like kind
of on my screen here,
00:47:06.930 --> 00:47:09.930
this would be the image,
it's mirroring your screen.
00:47:09.930 --> 00:47:12.310
It's just like, if you're in a classroom
00:47:12.310 --> 00:47:14.160
and you have a projector.
00:47:14.160 --> 00:47:17.000
You know how it mirrors
exactly what's on your screen?
00:47:17.000 --> 00:47:18.330
That's exactly how this works.
00:47:18.330 --> 00:47:20.960
So it is like a second display,
00:47:20.960 --> 00:47:23.540
and you're able to see
what you're writing on.
00:47:23.540 --> 00:47:25.970
So it feels a lot more comfortable.
00:47:25.970 --> 00:47:28.363
I mean, I definitely like my Wacom One,
00:47:28.363 --> 00:47:31.425
what I use more often.
00:47:31.425 --> 00:47:34.110
It's totally what I use for, all right.
00:47:34.110 --> 00:47:36.270
So I use it for making my videos.
00:47:36.270 --> 00:47:38.320
I also use it for grading student work.
00:47:38.320 --> 00:47:40.630
So grading student work,
I actually use Kami.
00:47:40.630 --> 00:47:43.110
Students just turn in a PDF.
00:47:43.110 --> 00:47:45.660
I open it. I open up the PDF in Kami.
00:47:45.660 --> 00:47:47.800
And I'm able to hand write all over it.
00:47:47.800 --> 00:47:50.020
I'm also able to leave video comments
00:47:50.020 --> 00:47:51.730
and able to leave voice comments
00:47:51.730 --> 00:47:54.193
because we have a paid
subscription to Kami.
00:47:55.150 --> 00:47:56.450
It's a huge tool.
00:47:56.450 --> 00:47:57.880
If your school already has it
00:47:57.880 --> 00:47:59.730
and you haven't explored it yet,
00:47:59.730 --> 00:48:01.840
I really recommend checking it out.
00:48:01.840 --> 00:48:02.850
If you have any questions,
00:48:02.850 --> 00:48:06.380
I have like a video
library on Kami itself,
00:48:06.380 --> 00:48:08.500
but I use it for that.
00:48:08.500 --> 00:48:10.320
I use it for lesson planning
00:48:10.320 --> 00:48:14.920
and I use it as like my daily like notes
00:48:14.920 --> 00:48:18.610
because I can just mind
map whatever I want to do.
00:48:18.610 --> 00:48:20.750
And I'm using my Wacom One for that
00:48:20.750 --> 00:48:23.800
because I'm plugged in pretty
much all the time right now.
00:48:23.800 --> 00:48:26.330
So I hope that helps.
00:48:26.330 --> 00:48:27.163
- Oh, that's great.
00:48:27.163 --> 00:48:29.180
And so, you know, the next
obvious follow up question
00:48:29.180 --> 00:48:31.170
is like, Hey, this looks amazing,
00:48:31.170 --> 00:48:34.100
but Max Sellers want to know,
does it work with my platform,
00:48:34.100 --> 00:48:36.820
with my tools, in general,
are these compatible
00:48:36.820 --> 00:48:38.360
with like Macs, PCs, Chromebooks?
00:48:38.360 --> 00:48:40.090
Do you know about that?
00:48:40.090 --> 00:48:41.070
- Yeah. Great question.
00:48:41.070 --> 00:48:43.957
It is compatible with Macs and PCs.
00:48:43.957 --> 00:48:47.183
It is not compatible with Chromebooks.
00:48:48.120 --> 00:48:49.280
- Okay. Got it.
00:48:49.280 --> 00:48:51.630
And then you were showing us
so many of these applications,
00:48:51.630 --> 00:48:53.700
whether it was Jamboard or Kami.
00:48:53.700 --> 00:48:56.320
I assume pretty much anything
where you're on a Mac and a PC
00:48:56.320 --> 00:48:58.305
and you have a document that
you're interacting with.
00:48:58.305 --> 00:48:59.910
You can use the tablet on it.
00:48:59.910 --> 00:49:01.032
Is that right?
00:49:01.032 --> 00:49:05.600
- Yeah. So again, any
of these Wacom devices.
00:49:05.600 --> 00:49:07.620
Think of it as like how you're,
00:49:07.620 --> 00:49:10.660
if your mouse currently
works with the program
00:49:10.660 --> 00:49:13.569
and you're able to currently
like press the pen tool
00:49:13.569 --> 00:49:15.033
and draw with a mouse
00:49:15.033 --> 00:49:17.430
and you know the unpleasant experience
00:49:17.430 --> 00:49:20.790
of trying to do that, then with the Wacom,
00:49:20.790 --> 00:49:23.200
you just literally now have a pen
00:49:23.200 --> 00:49:26.887
that you're writing, like you
are writing on the screen.
00:49:26.887 --> 00:49:29.380
So think of it as your
mouse pad with a pen.
00:49:29.380 --> 00:49:30.850
- Cool, cool. That's really helpful.
00:49:30.850 --> 00:49:33.186
And then I think the
elephant in the room question
00:49:33.186 --> 00:49:34.900
comes from Janette, who says,
00:49:34.900 --> 00:49:38.970
Hey, I want one of these so
bad, but how do I afford it?
00:49:38.970 --> 00:49:41.110
Have you heard about
teachers using Donors Choose
00:49:41.110 --> 00:49:43.580
or other platforms to
make this more available
00:49:43.580 --> 00:49:44.530
to their classroom?
00:49:45.370 --> 00:49:48.920
- Yeah. I mean, definitely people have,
00:49:48.920 --> 00:49:51.506
people have asked their schools too.
00:49:51.506 --> 00:49:55.033
I know a lot of schools are
providing them this year.
00:49:56.040 --> 00:49:59.850
So, again, if you wanted to ask
00:49:59.850 --> 00:50:04.270
for the most affordable
option, the Wacom Intuos line
00:50:04.270 --> 00:50:08.280
would be the one that
I would go for there.
00:50:08.280 --> 00:50:10.360
And honestly, I would
ask for the Bluetooth one
00:50:10.360 --> 00:50:13.140
because it's only like
$10 more for the Bluetooth
00:50:13.140 --> 00:50:14.560
versus the wired one.
00:50:14.560 --> 00:50:16.530
And it's something, this is my thing.
00:50:16.530 --> 00:50:18.060
And I've talked to some
teachers about this
00:50:18.060 --> 00:50:20.060
who want to ask their school about it.
00:50:20.060 --> 00:50:24.150
This is not a device that
we are using just now
00:50:24.150 --> 00:50:25.513
because of remote learning.
00:50:27.370 --> 00:50:30.850
I've been using these devices
for years and years and years.
00:50:30.850 --> 00:50:33.310
This is a device that's going to amp up
00:50:33.310 --> 00:50:35.560
our classroom in all different ways.
00:50:35.560 --> 00:50:37.020
There's so many ways we can use it.
00:50:37.020 --> 00:50:38.410
We can use it in class.
00:50:38.410 --> 00:50:41.730
We can use it before class to, you know,
00:50:41.730 --> 00:50:43.830
make our flip classroom lead videos.
00:50:43.830 --> 00:50:47.670
We can also use it post-class
to grade student work,
00:50:47.670 --> 00:50:50.166
to make everything be in
one space for students.
00:50:50.166 --> 00:50:54.440
There's also a lot of benefit
to having all of this saved
00:50:54.440 --> 00:50:58.290
for students in their Google
Drive or whatever it may be
00:50:58.290 --> 00:51:01.910
because don't forget if you
are making this digital work,
00:51:01.910 --> 00:51:04.290
and you're saving it for
them in a digital way,
00:51:04.290 --> 00:51:05.950
giving them that digital feedback.
00:51:05.950 --> 00:51:08.040
Now it becomes searchable.
00:51:08.040 --> 00:51:10.490
So that's something else
that's really powerful.
00:51:10.490 --> 00:51:13.080
So again, I've talked a
little bit about Kami today,
00:51:13.080 --> 00:51:15.360
but Kami is what I use.
00:51:15.360 --> 00:51:17.470
And I grade the student work in that too.
00:51:17.470 --> 00:51:20.870
And this has OCR, optical
character recognition.
00:51:20.870 --> 00:51:23.910
And that means that
anything that's on here,
00:51:23.910 --> 00:51:28.000
even like hand written
stuff becomes searchable,
00:51:28.000 --> 00:51:29.420
super powerful there.
00:51:29.420 --> 00:51:32.240
So that's what I would say is like,
00:51:32.240 --> 00:51:34.626
this is not something that we're going to
00:51:34.626 --> 00:51:36.130
just be using this year, not to mention.
00:51:36.130 --> 00:51:39.000
So I showed you some of the
newer Wacom products right now,
00:51:39.000 --> 00:51:41.350
but I'm being completely honest here.
00:51:41.350 --> 00:51:42.210
I'm not just saying this because
00:51:42.210 --> 00:51:44.080
you know Wacom's here with me,
00:51:44.080 --> 00:51:46.410
but the class set of
tablets that I showed you,
00:51:46.410 --> 00:51:48.420
like this class set here,
00:51:48.420 --> 00:51:50.040
you can see that this
tablet looks different
00:51:50.040 --> 00:51:50.873
than the one I showed you.
00:51:50.873 --> 00:51:53.140
That's because this is an older version.
00:51:53.140 --> 00:51:57.170
I got this class that in 2013.
It is still going strong.
00:51:57.170 --> 00:52:01.260
I'm still using the same class
set of tablets since 2013.
00:52:01.260 --> 00:52:04.860
Like what other technology are
you using seven years later?
00:52:04.860 --> 00:52:09.079
And it works just as well
as it worked on day one.
00:52:09.079 --> 00:52:11.200
And that's the, I think
the power of these things
00:52:11.200 --> 00:52:14.300
is because like it's not
tied to an operating system
00:52:14.300 --> 00:52:15.483
or anything like that.
00:52:16.573 --> 00:52:18.338
You just plug it in to your computer
00:52:18.338 --> 00:52:21.270
and you know, like worst case scenario.
00:52:21.270 --> 00:52:24.720
Now the USB doesn't plug in
and I need a USBC adapter.
00:52:24.720 --> 00:52:26.710
Like that's really the only difference,
00:52:26.710 --> 00:52:28.440
but they have true staying power.
00:52:28.440 --> 00:52:30.503
These things are built to last.
00:52:31.777 --> 00:52:35.900
And so it's going to be
to me an investment for,
00:52:35.900 --> 00:52:37.660
if you're making an
argument to your school
00:52:37.660 --> 00:52:39.930
it's an investment for your school.
00:52:39.930 --> 00:52:40.930
- Very cool.
00:52:40.930 --> 00:52:42.250
Well, speaking of staying power,
00:52:42.250 --> 00:52:44.073
I'm thinking so many
questions about battery life
00:52:44.073 --> 00:52:46.110
because I think here in 2020,
00:52:46.110 --> 00:52:48.320
our phones are dying, our iPods are dying.
00:52:48.320 --> 00:52:52.110
We can't even get enough
chargers to plug everything in.
00:52:52.110 --> 00:52:54.110
What's the battery life on these things?
00:52:55.590 --> 00:52:57.640
- I don't know what the battery life is
00:52:57.640 --> 00:53:00.490
on the Bluetooth one.
00:53:00.490 --> 00:53:04.250
It lasts a really long time.
I mean, I really don't know.
00:53:04.250 --> 00:53:06.210
I just plug it in occasionally.
00:53:06.210 --> 00:53:10.250
It's not like it's not going
to run out during my class day.
00:53:10.250 --> 00:53:12.590
It also doesn't stay on the whole time.
00:53:12.590 --> 00:53:14.570
So I don't worry about that.
00:53:14.570 --> 00:53:17.654
The Wacom One has to be plugged
into the wall all the time.
00:53:17.654 --> 00:53:19.730
So there's that.
00:53:19.730 --> 00:53:21.550
And then the class set that I have
00:53:21.550 --> 00:53:24.630
is the one where they plug it in.
00:53:24.630 --> 00:53:27.000
So I've never run into that before
00:53:27.000 --> 00:53:29.340
because it doesn't, there's no battery.
00:53:29.340 --> 00:53:32.200
So I don't know the exact specs
00:53:32.200 --> 00:53:34.350
on how long the battery lasts.
00:53:34.350 --> 00:53:35.183
- Very cool.
00:53:36.897 --> 00:53:37.970
I see a lot of questions coming in
00:53:37.970 --> 00:53:40.170
about like using this
for specific use cases.
00:53:40.170 --> 00:53:43.030
I know you're a math
teacher, but you know,
00:53:43.030 --> 00:53:44.700
if you were imagining a teacher,
00:53:44.700 --> 00:53:47.520
especially in a special ed
special education environment,
00:53:47.520 --> 00:53:49.730
who wants to use it to really
energize their students
00:53:49.730 --> 00:53:51.420
during this very difficult time,
00:53:51.420 --> 00:53:52.975
are there any tips you might recommend
00:53:52.975 --> 00:53:55.870
to really use this to engage and harness
00:53:55.870 --> 00:53:57.520
the creativity of their students?
00:53:58.630 --> 00:54:01.210
- Yeah. Okay.
00:54:01.210 --> 00:54:04.150
So, I guess the first thing
that I really believe in,
00:54:04.150 --> 00:54:06.490
I really do believe in
the power of handwriting,
00:54:06.490 --> 00:54:08.920
both for students and for us as teachers.
00:54:08.920 --> 00:54:11.650
So for example, when I make
my flip classroom videos,
00:54:11.650 --> 00:54:14.490
I'm always writing, as I'm talking.
00:54:14.490 --> 00:54:16.250
I've seen some people,
00:54:16.250 --> 00:54:17.980
they feel like their
videos look a little bit
00:54:17.980 --> 00:54:19.650
more professional when
they write it all out
00:54:19.650 --> 00:54:22.050
ahead of time because their
handwriting looks neater.
00:54:22.050 --> 00:54:23.760
Like they're kind of scripting it.
00:54:23.760 --> 00:54:26.700
They're able to write and then talk.
00:54:26.700 --> 00:54:30.610
For me, students follow as I'm writing.
00:54:30.610 --> 00:54:34.540
So I like to write and talk
because they're doing the same
00:54:34.540 --> 00:54:36.590
and I want them to be taking notes
00:54:36.590 --> 00:54:39.180
and they're able to kind of
see how I'm working through
00:54:39.180 --> 00:54:40.500
the flow of that problem.
00:54:40.500 --> 00:54:42.410
So I think there's huge power
00:54:42.410 --> 00:54:45.060
in being able to write and talk.
00:54:45.060 --> 00:54:47.970
So like, to me, a lot of times
00:54:47.970 --> 00:54:51.976
I think that making a lesson
where I kind of have maybe,
00:54:51.976 --> 00:54:55.259
even I'm just using the
Jamboard very simply
00:54:55.259 --> 00:54:58.850
and I have a little bit of bullet points,
00:54:58.850 --> 00:55:01.200
but then I'm writing as I'm talking.
00:55:01.200 --> 00:55:03.250
I'm writing out some bullet points there.
00:55:03.250 --> 00:55:04.960
I think it's more engaging
00:55:04.960 --> 00:55:08.300
because students are seeing
something on the screen
00:55:08.300 --> 00:55:11.954
versus just the flat text.
00:55:11.954 --> 00:55:13.410
Do you know what I mean?
00:55:13.410 --> 00:55:17.791
And even if you just draw
little images as you're going,
00:55:17.791 --> 00:55:20.580
that can be really powerful too.
00:55:20.580 --> 00:55:25.400
So I think it's auto
sketch that it's like,
00:55:25.400 --> 00:55:26.270
is that what it's called?
00:55:26.270 --> 00:55:29.730
I really liked that, auto
draw, that's what it's called.
00:55:29.730 --> 00:55:31.740
Obviously it's saved to my thing
00:55:31.740 --> 00:55:35.400
because like you can be
sketching as you're doing class.
00:55:35.400 --> 00:55:37.090
I don't use it in my math class
00:55:37.090 --> 00:55:39.500
but it recognizes what you're doing.
00:55:39.500 --> 00:55:42.703
So like if I start drawing something,
00:55:45.220 --> 00:55:46.510
it will recognize it,
00:55:46.510 --> 00:55:49.860
so I can have terrible
drawing and be like, Oh yeah,
00:55:49.860 --> 00:55:53.850
I was trying to draw a van
and so, you know, again,
00:55:53.850 --> 00:55:57.280
so it can just be like the
power of having some visuals.
00:55:57.280 --> 00:55:59.170
The students can see that
00:55:59.170 --> 00:56:03.743
and maybe you could
allow them to, you know,
00:56:04.738 --> 00:56:06.010
you could pass a tablet around
00:56:06.973 --> 00:56:07.806
and allow them to sketch notes.
00:56:07.806 --> 00:56:10.230
I think that's something else
that can be really powerful.
00:56:10.230 --> 00:56:14.290
Having students summarize
what they're learning
00:56:14.290 --> 00:56:17.970
through sketches and little annotations.
00:56:17.970 --> 00:56:22.500
So again, you could
have them here drawing,
00:56:22.500 --> 00:56:25.600
and then also they can use
just the regular draw tool here
00:56:25.600 --> 00:56:27.230
and they can actually hand write there.
00:56:27.230 --> 00:56:28.660
That wouldn't be auto recognized.
00:56:28.660 --> 00:56:31.384
This magical one is the one
that's going to auto recognize
00:56:31.384 --> 00:56:32.780
whatever you're writing.
00:56:32.780 --> 00:56:37.780
So yeah, that could be just a
simple, really powerful tool.
00:56:37.970 --> 00:56:39.810
- Yeah. I think that's
powerful for every student.
00:56:39.810 --> 00:56:41.972
Like, especially in this
moment, we're all apart,
00:56:41.972 --> 00:56:45.310
to bring more visuals, more
sort of eye catching moments
00:56:45.310 --> 00:56:47.475
into our teaching is so powerful.
00:56:47.475 --> 00:56:49.410
What about for younger students?
00:56:49.410 --> 00:56:52.400
Again, I know that you teach
older students in your day job
00:56:52.400 --> 00:56:54.810
but have you heard about
teachers using this successfully
00:56:54.810 --> 00:56:55.990
with younger students,
00:56:55.990 --> 00:56:57.920
especially if you're
giving them the tablets
00:56:57.920 --> 00:57:01.270
and asking them to input
their own handwriting?
00:57:01.270 --> 00:57:05.340
- Yeah, so I'm lucky I
work at a K-12 school,
00:57:05.340 --> 00:57:09.534
so I get to see the younger
kids in our lower school grades.
00:57:09.534 --> 00:57:12.420
All of our students are
actually using Seesaw.
00:57:12.420 --> 00:57:14.497
So if your school is using Seesaw,
00:57:14.497 --> 00:57:16.400
it's already built in there,
00:57:16.400 --> 00:57:17.830
that they're able to draw on anything,
00:57:17.830 --> 00:57:20.720
they're able to actually draw
and record at the same time.
00:57:20.720 --> 00:57:22.970
So they can talk out their math thinking
00:57:22.970 --> 00:57:25.360
or whatever thinking that they are doing.
00:57:25.360 --> 00:57:27.360
And if you're able to pass out the tablet,
00:57:27.360 --> 00:57:29.892
then they can really
practice the writing also,
00:57:29.892 --> 00:57:33.220
which can be, you know, super powerful.
00:57:33.220 --> 00:57:35.134
For our youngest students, they do,
00:57:35.134 --> 00:57:38.833
I will say that they do very
well with just using a mouse.
00:57:38.833 --> 00:57:42.700
And usually what they're
drawing is rather simple.
00:57:42.700 --> 00:57:44.350
So maybe they're drawing some shapes
00:57:44.350 --> 00:57:47.493
or you're trying to help them
like learn about counting.
00:57:47.493 --> 00:57:51.423
And that's one of the most
difficult things right now.
00:57:52.430 --> 00:57:54.800
I also have a niece that's six years old
00:57:54.800 --> 00:57:56.360
and she's also using Seesaw.
00:57:56.360 --> 00:57:58.640
And sometimes we get on the
video and we'd do it together.
00:57:58.640 --> 00:58:01.310
And it's like, she's
trying to add the numbers
00:58:01.310 --> 00:58:02.990
and she's doing really well with it,
00:58:02.990 --> 00:58:04.980
but sometimes she just
needs those visuals.
00:58:04.980 --> 00:58:07.730
So we're able to either draw them out.
00:58:07.730 --> 00:58:10.840
Sometimes I tell my sister
to go get her some crackers
00:58:10.840 --> 00:58:14.250
so that she can pull those up too.
00:58:14.250 --> 00:58:16.370
And, but, you know, you
could even take a picture
00:58:16.370 --> 00:58:20.470
of some of those, pull them
into Seesaw or whatever it is,
00:58:20.470 --> 00:58:23.617
and then use the pen to
cross things out too.
00:58:23.617 --> 00:58:25.560
I think that's the power,
00:58:25.560 --> 00:58:28.830
like starting to verbalize
your thinking process.
00:58:28.830 --> 00:58:31.500
So whether that's a student
or you as the teacher
00:58:31.500 --> 00:58:35.430
who has a device and you're
able to really make it visual
00:58:35.430 --> 00:58:37.960
to students what's going on.
00:58:37.960 --> 00:58:40.710
And again, not just like
a PowerPoint presentation,
00:58:40.710 --> 00:58:42.690
with some fancy animations,
00:58:42.690 --> 00:58:44.810
I personally just find
those harder to follow.
00:58:44.810 --> 00:58:47.113
I need to see the writing, the flow.
00:58:48.470 --> 00:58:50.423
I also need to be doing the writing,
00:58:51.270 --> 00:58:53.360
that to me, like I cannot,
00:58:53.360 --> 00:58:55.750
I don't know about other math teachers.
00:58:55.750 --> 00:58:58.590
I cannot like type a math solution.
00:58:58.590 --> 00:59:01.670
Like when I'm doing my solutions,
I have to hand write it.
00:59:01.670 --> 00:59:03.210
Maybe I'll type it up afterwards,
00:59:03.210 --> 00:59:04.983
but I can't think like that.
00:59:06.190 --> 00:59:07.960
- There's something about,
like, the sketching,
00:59:07.960 --> 00:59:09.760
the doodling that actually
unlocks your brain
00:59:09.760 --> 00:59:10.723
in a powerful way.
00:59:11.570 --> 00:59:14.720
- Yeah. I also don't
think completely linearly.
00:59:14.720 --> 00:59:15.910
I think that's it too.
00:59:15.910 --> 00:59:18.716
Like with all these white boarding apps,
00:59:18.716 --> 00:59:21.500
we can be writing in
different spaces on the screen
00:59:21.500 --> 00:59:23.980
and it doesn't have to be so linear.
00:59:23.980 --> 00:59:27.440
So we really can map information together
00:59:27.440 --> 00:59:29.420
and help our students understand
00:59:29.420 --> 00:59:31.440
how all this stuff webs together.
00:59:31.440 --> 00:59:33.590
I think that's why I liked the AWW app
00:59:33.590 --> 00:59:35.740
that I showed you too,
because you can have, like,
00:59:35.740 --> 00:59:38.500
you can be writing here
and here and here and here
00:59:38.500 --> 00:59:42.330
and then you can zoom out and
see that web all come together
00:59:42.330 --> 00:59:44.220
and make those connections.
00:59:44.220 --> 00:59:46.370
- Very cool, well, speaking
of making connections
00:59:46.370 --> 00:59:48.840
you've connected so many
educators across the country
00:59:48.840 --> 00:59:51.380
tonight, Stacey, to each other,
00:59:51.380 --> 00:59:53.517
to awesome opportunities
in their classrooms.
00:59:53.517 --> 00:59:56.779
So I have to thank you so much
on behalf of this audience.
00:59:56.779 --> 00:59:59.620
That being said, any final words of wisdom
00:59:59.620 --> 01:00:01.450
as folks get ready for the end of the year
01:00:01.450 --> 01:00:03.630
and the start of a new one?
01:00:03.630 --> 01:00:05.083
- Oh my gosh. Right.
01:00:06.580 --> 01:00:08.490
First, I just want to say
thank you to everybody
01:00:08.490 --> 01:00:12.020
who is on this call today
because I know how much
01:00:12.020 --> 01:00:13.800
everybody's already doing right now.
01:00:13.800 --> 01:00:15.860
And then taking the time out this evening
01:00:15.860 --> 01:00:19.090
to just further grow as an educator.
01:00:19.090 --> 01:00:21.560
I mean, this is why I love teachers.
01:00:21.560 --> 01:00:23.490
When I first started teaching, I was like,
01:00:23.490 --> 01:00:24.850
I know I'm in the right profession
01:00:24.850 --> 01:00:27.440
as soon as I saw how
generous educators are
01:00:27.440 --> 01:00:30.764
and just like that love of learning.
01:00:30.764 --> 01:00:32.930
So I really appreciate you being here,
01:00:32.930 --> 01:00:36.730
and everything that, you know,
you all are doing right now
01:00:36.730 --> 01:00:39.986
in the classroom and
trying to make it all work.
01:00:39.986 --> 01:00:44.986
If I can help in any way,
please do reach out again.
01:00:45.270 --> 01:00:49.750
My information is here. Contact
information is on my blog.
01:00:49.750 --> 01:00:52.660
Also, if you are on Twitter,
I'm very active on Twitter
01:00:52.660 --> 01:00:54.960
and you can go ahead
and leave me a message.
01:00:54.960 --> 01:00:57.540
And I will definitely respond back to you.
01:00:57.540 --> 01:01:02.520
If you click on any of the
videos that I shared today, again
01:01:02.520 --> 01:01:05.170
they're also in the PDF that
you can take home later.
01:01:05.170 --> 01:01:07.960
If you watch some of those
videos that I have on YouTube,
01:01:07.960 --> 01:01:10.070
and you have a question,
01:01:10.070 --> 01:01:12.170
please just put it in
the comments on YouTube.
01:01:12.170 --> 01:01:15.760
I definitely get to all
of my YouTube comments.
01:01:15.760 --> 01:01:18.530
So that's sometimes the
easiest way, you know,
01:01:18.530 --> 01:01:20.300
you were watching it
and you're like, well,
01:01:20.300 --> 01:01:21.623
what do I do here?
01:01:22.620 --> 01:01:23.510
Just let me know.
01:01:23.510 --> 01:01:26.580
Because as I said, I just
wish that I could have come
01:01:26.580 --> 01:01:27.890
to this today and said like,
01:01:27.890 --> 01:01:30.077
these are the three apps that you need,
01:01:30.077 --> 01:01:32.776
but that wouldn't be me being real.
01:01:32.776 --> 01:01:36.510
Me being real is trying
to find what you're doing
01:01:36.510 --> 01:01:39.210
at your school already
and offering a solution
01:01:39.210 --> 01:01:41.770
that's going to work well
for you and your students,
01:01:41.770 --> 01:01:43.620
even though I might have a favorite one,
01:01:43.620 --> 01:01:46.960
that might not be what's best
for you and your setting.
01:01:46.960 --> 01:01:50.975
So I hope that the variety of
tools kind of got you thinking
01:01:50.975 --> 01:01:54.760
and then you will be able
to click on one of them,
01:01:54.760 --> 01:01:56.150
zone in on that.
01:01:56.150 --> 01:01:58.693
And as you do and as questions come up,
01:01:58.693 --> 01:02:03.003
please do reach out and
I'll do my best to answer.
01:02:03.860 --> 01:02:05.420
- Cool. Thank you so much, Stacey.
01:02:05.420 --> 01:02:07.640
And thank you again to
everyone for joining tonight.
01:02:07.640 --> 01:02:10.840
Just as a quick recap,
you will get an email
01:02:10.840 --> 01:02:13.719
with a recording of the session,
as well as Stacey's PDF.
01:02:13.719 --> 01:02:17.121
You'll get a link to that
generous discount offered by Wacom
01:02:17.121 --> 01:02:19.990
and everyone who joined will automatically
01:02:19.990 --> 01:02:23.430
be entered into a drawing for
one of five Wacom tablets.
01:02:23.430 --> 01:02:25.860
And we'll notify those winners shortly.
01:02:25.860 --> 01:02:27.900
In the meantime, thank you as Stacey said,
01:02:27.900 --> 01:02:29.390
for all that you do.
01:02:29.390 --> 01:02:31.177
We wish you a tremendous
conclusion to the year
01:02:31.177 --> 01:02:33.420
and a great start to 2021.
01:02:33.420 --> 01:02:35.160
And we can't wait to see
all the incredible things
01:02:35.160 --> 01:02:37.560
you do next based on some
of these awesome tips.
01:02:37.560 --> 01:02:39.710
Thank you so much, Stacey,
and good night, everyone.
01:02:39.710 --> 01:02:41.133
- Thank you. Bye.
|
3 Mindfulness Exercises to Inspire You + Your Students | https://www.youtube.com/watch?v=4PXlyPY6Uzg | vtt | https://www.youtube.com/api/timedtext?v=4PXlyPY6Uzg&ei=7lWUZbSPJd-ip-oPgauT8A8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=79D94686B2C5A8CE5A429A1CF6509C3C670C4BE4.96C280D88DD69D7A6757A8A82D8461DEBB29921D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:03.010 --> 00:00:03.843
- Hey everyone.
00:00:03.843 --> 00:00:06.020
This is Jeremy Schifeling
with Khan Academy.
00:00:06.020 --> 00:00:08.230
Thank you so much for joining us today.
00:00:08.230 --> 00:00:12.490
I'm super excited for a really
action packed session today,
00:00:12.490 --> 00:00:14.194
and I think this is a very
timely session as well
00:00:14.194 --> 00:00:17.370
as we head into the last month
of an incredibly tough year.
00:00:17.370 --> 00:00:21.210
I think one of the things
that 2020 has taught us is,
00:00:21.210 --> 00:00:23.770
even in this moment of social isolation,
00:00:23.770 --> 00:00:24.840
how much we need each other,
00:00:24.840 --> 00:00:28.050
how much we need partners and
collaborators in our lives.
00:00:28.050 --> 00:00:30.090
And that's why I'm so
grateful in this moment
00:00:30.090 --> 00:00:32.820
of gratitude for our
partners at Headspace,
00:00:32.820 --> 00:00:35.210
because as much as we at Khan Academy love
00:00:35.210 --> 00:00:39.440
to focus on academics and
Scholastic development.
00:00:39.440 --> 00:00:41.220
We also know this year is about that more
00:00:41.220 --> 00:00:43.700
holistic idea of serving your students.
00:00:43.700 --> 00:00:45.720
How do you make sure that their social
00:00:45.720 --> 00:00:46.900
and emotional needs are met,
00:00:46.900 --> 00:00:48.920
as well as your own as educators?
00:00:48.920 --> 00:00:51.160
And so that's why I'm
thrilled to introduce you
00:00:51.160 --> 00:00:54.010
to two rockstar presenters from Headspace.
00:00:54.010 --> 00:00:55.490
First, we have Sam Snowden,
00:00:55.490 --> 00:00:58.160
who is a mindfulness
facilitator who specializes
00:00:58.160 --> 00:01:00.250
in supporting students and teachers,
00:01:00.250 --> 00:01:01.640
so has worked with tons of folks
00:01:01.640 --> 00:01:04.740
exactly like yourselves
for years at this point,
00:01:04.740 --> 00:01:06.930
and has actually worked directly
with elementary schools,
00:01:06.930 --> 00:01:09.770
with principals, with
educators across the world.
00:01:09.770 --> 00:01:11.910
And she's joined by Alice Nathoo,
00:01:11.910 --> 00:01:14.190
who's the head of social
impact at Headspace.
00:01:14.190 --> 00:01:16.810
And what she does there
is a larger portfolio
00:01:16.810 --> 00:01:19.450
that also includes
Headspace for Educators,
00:01:19.450 --> 00:01:20.870
which is an amazing program if you
00:01:20.870 --> 00:01:22.270
haven't checked it out already,
00:01:22.270 --> 00:01:23.340
which basically gets you all
00:01:23.340 --> 00:01:25.330
the power of Headspace for free,
00:01:25.330 --> 00:01:27.720
just for doing the great work
that you do as an educator.
00:01:27.720 --> 00:01:30.340
And Alice will share more
about that in a little bit.
00:01:30.340 --> 00:01:32.010
In the meantime, before we dive in,
00:01:32.010 --> 00:01:33.890
I want to answer sort
of three housekeeping
00:01:33.890 --> 00:01:35.710
questions that typically come up.
00:01:35.710 --> 00:01:38.130
Number one, in true webinar fashion,
00:01:38.130 --> 00:01:39.750
yes, the session will be recorded,
00:01:39.750 --> 00:01:41.580
and you will get a copy
of it automatically
00:01:41.580 --> 00:01:44.330
in your inbox right after the session.
00:01:44.330 --> 00:01:47.080
Number two, as educators ourselves,
00:01:47.080 --> 00:01:48.720
we want to make this super interactive.
00:01:48.720 --> 00:01:51.800
So ask questions at any
point using the questions tab
00:01:51.800 --> 00:01:53.650
on your go to webinar control panel,
00:01:53.650 --> 00:01:55.800
and also join lots of our pop quizzes
00:01:55.800 --> 00:01:57.930
that Sam will be sending
your way throughout.
00:01:57.930 --> 00:01:59.140
And then third and finally,
00:01:59.140 --> 00:02:00.500
I know a lot of you were interested
00:02:00.500 --> 00:02:02.290
in the Headspace swag bag,
00:02:02.290 --> 00:02:04.500
so free access to the Headspace platform
00:02:04.500 --> 00:02:05.890
for friends and family,
00:02:05.890 --> 00:02:08.970
as well as a copy of their
best-selling book on mindfulness.
00:02:08.970 --> 00:02:11.110
Just for being here live with us today,
00:02:11.110 --> 00:02:13.110
you're automatically
entered into a drawing
00:02:13.110 --> 00:02:15.060
for one of those five swag bags,
00:02:15.060 --> 00:02:16.702
and we will notify you after the session
00:02:16.702 --> 00:02:18.990
if you're one of those lucky winners.
00:02:18.990 --> 00:02:20.220
So that being said,
00:02:20.220 --> 00:02:21.745
thank you all again for making time
00:02:21.745 --> 00:02:24.220
and investing in today's session with us.
00:02:24.220 --> 00:02:25.053
And with that being said,
00:02:25.053 --> 00:02:27.612
I want to turn it over to Sam and Alice
00:02:27.612 --> 00:02:29.770
- Well, what an introduction.
00:02:29.770 --> 00:02:31.399
Thank you so much, Jeremy.
00:02:31.399 --> 00:02:34.470
And thank you Khan Academy, you know,
00:02:34.470 --> 00:02:36.960
for this opportunity to talk to you all.
00:02:36.960 --> 00:02:38.376
Hello, welcome,
00:02:38.376 --> 00:02:42.589
congratulations for making
this time for yourself.
00:02:42.589 --> 00:02:45.216
As Jeremy said, I'm Alice Nathoo,
00:02:45.216 --> 00:02:48.230
and I run Headspace for Educators.
00:02:48.230 --> 00:02:49.460
As a parent, you know,
00:02:49.460 --> 00:02:51.470
this has been such a hard year,
00:02:51.470 --> 00:02:54.430
and I can only imagine
for you all as educators,
00:02:54.430 --> 00:02:56.890
renewed respect for the jobs that you do.
00:02:56.890 --> 00:02:57.960
The incredible job you do,
00:02:57.960 --> 00:03:01.733
and how challenging it's been
this year for you, I'm sure.
00:03:01.733 --> 00:03:05.743
So I'm really excited to introduce Sam.
00:03:06.850 --> 00:03:08.537
I have to say my meetings with Sam
00:03:08.537 --> 00:03:09.900
are my favorite part of the day.
00:03:09.900 --> 00:03:10.733
There's just something about her
00:03:10.733 --> 00:03:13.223
that just is instantly relaxing.
00:03:14.510 --> 00:03:16.340
So I'm so excited we get to spend
00:03:16.340 --> 00:03:18.390
this half an hour together.
00:03:18.390 --> 00:03:19.970
But first, we thought we'd just,
00:03:19.970 --> 00:03:21.350
before I sort of introduce Sam,
00:03:21.350 --> 00:03:22.410
just to give you a little idea
00:03:22.410 --> 00:03:24.260
of what we're going to cover today.
00:03:24.260 --> 00:03:26.810
As Jeremy said, we want
this to be really practical.
00:03:26.810 --> 00:03:29.700
I mean, what we say at Headspace
is meditation made simple,
00:03:29.700 --> 00:03:32.210
and that's what we
thought about for today.
00:03:32.210 --> 00:03:34.230
What are some simple exercises for you
00:03:34.230 --> 00:03:37.510
to use for yourself and for your students?
00:03:37.510 --> 00:03:40.870
So Sam's going to talk a bit
about what mindfulness is.
00:03:40.870 --> 00:03:41.960
Don't worry if you've got,
00:03:41.960 --> 00:03:42.797
if you have a lot of experience,
00:03:42.797 --> 00:03:45.470
or you have no experience at all,
00:03:45.470 --> 00:03:47.700
hopefully there'll be
something for everyone here.
00:03:47.700 --> 00:03:49.600
And really then how it can help you
00:03:49.600 --> 00:03:51.793
optimize your learning environment,
00:03:51.793 --> 00:03:56.230
both remotely and hopefully
back in the classroom too.
00:03:56.230 --> 00:03:59.290
And then we'll finish
off with some Q and A.
00:03:59.290 --> 00:04:02.188
So I'm so excited to introduce Samantha.
00:04:02.188 --> 00:04:04.500
Jeremy did a wonderful introduction.
00:04:04.500 --> 00:04:06.020
You know, we're really excited to work
00:04:06.020 --> 00:04:09.168
with her on Headspace for educators.
00:04:09.168 --> 00:04:11.500
She's an amazing human being.
00:04:11.500 --> 00:04:14.460
So welcome my friend
and colleague Samantha.
00:04:14.460 --> 00:04:16.350
- Thank you so much, Alice.
00:04:16.350 --> 00:04:18.990
I feel completely overwhelmed with love,
00:04:18.990 --> 00:04:21.250
and it's a great way to start.
00:04:21.250 --> 00:04:24.210
And I just want to thank all of you,
00:04:24.210 --> 00:04:27.930
all the teachers for
showing up and caring about,
00:04:27.930 --> 00:04:31.230
you know, bettering of
your teaching practice.
00:04:31.230 --> 00:04:34.790
And I've also been a
teacher in the classroom,
00:04:34.790 --> 00:04:35.940
so I know the struggle.
00:04:35.940 --> 00:04:37.370
I've been a substitute teacher,
00:04:37.370 --> 00:04:41.070
which is kind of the hardest gig, I think.
00:04:41.070 --> 00:04:44.050
So all of the things
that I'll be offering you
00:04:44.050 --> 00:04:47.100
definitely come from a place
of embodied experience.
00:04:47.100 --> 00:04:48.400
I've tried them out,
00:04:48.400 --> 00:04:52.610
they're tried and true methods
for bringing mindfulness
00:04:52.610 --> 00:04:55.720
into your own life and also
into your students' lives.
00:04:55.720 --> 00:04:58.530
So I'm just so grateful to be here.
00:04:58.530 --> 00:05:00.586
And I'm so grateful to all of you
00:05:00.586 --> 00:05:02.463
for all the hard work you're doing.
00:05:05.310 --> 00:05:09.079
So I wanted us to start out
actually with a practice.
00:05:09.079 --> 00:05:11.633
We'll be doing a couple
practices together,
00:05:11.633 --> 00:05:14.130
and the reason for that is that,
00:05:14.130 --> 00:05:15.950
when you embody the practice,
00:05:15.950 --> 00:05:17.838
when you do it yourself,
00:05:17.838 --> 00:05:22.710
you have a better idea of how
to lead it with your students.
00:05:22.710 --> 00:05:26.188
And so I want to just preface that with
00:05:26.188 --> 00:05:29.910
if you want to keep your
eyes open the whole time,
00:05:29.910 --> 00:05:31.570
I'm going to invite you
to keep your eyes closed,
00:05:31.570 --> 00:05:32.820
but if you want to keep them open
00:05:32.820 --> 00:05:36.150
you can just rest your attention
on a spot in front of you,
00:05:36.150 --> 00:05:38.690
a few inches or a few
feet in front of you,
00:05:38.690 --> 00:05:42.350
and just let your eyelids
kind of rest halfway closed.
00:05:42.350 --> 00:05:43.490
And the first practice we're going
00:05:43.490 --> 00:05:45.840
to be doing is working with anchors.
00:05:45.840 --> 00:05:47.930
And when I talk about
anchors with my students
00:05:47.930 --> 00:05:49.850
I often show them this little bell.
00:05:49.850 --> 00:05:53.046
And I talk about how anchors keep a boat,
00:05:53.046 --> 00:05:55.600
right, from drifting too far away.
00:05:55.600 --> 00:05:57.210
So if this is our anchor and our
00:05:57.210 --> 00:05:59.560
boat wants to follow the waves,
00:05:59.560 --> 00:06:01.760
or if this is like our
mind and our mind wants
00:06:01.760 --> 00:06:03.890
to follow different streams of thought,
00:06:03.890 --> 00:06:05.640
the anchor brings it back.
00:06:05.640 --> 00:06:06.870
And it brings it back again,
00:06:06.870 --> 00:06:08.330
and again, and again.
00:06:08.330 --> 00:06:11.170
And over time we get much
better at paying attention.
00:06:11.170 --> 00:06:13.470
We get more control over our attention
00:06:13.470 --> 00:06:17.470
so that it doesn't feel like
it is being taken away from us,
00:06:17.470 --> 00:06:20.260
but we have some mastery over it.
00:06:20.260 --> 00:06:22.340
So this is really a foundational practice
00:06:22.340 --> 00:06:24.460
that you can do with your students.
00:06:24.460 --> 00:06:25.730
We're going to do a three minute,
00:06:25.730 --> 00:06:27.190
around a three-minute practice,
00:06:27.190 --> 00:06:29.480
but you can even shorten it to a one
00:06:29.480 --> 00:06:31.680
minute practice with your students.
00:06:31.680 --> 00:06:34.620
So if you're ready, I don't know you,
00:06:34.620 --> 00:06:36.120
maybe you're driving in a car,
00:06:36.120 --> 00:06:37.960
or if it's not safe to do a practice,
00:06:37.960 --> 00:06:38.919
please, you know,
00:06:38.919 --> 00:06:41.990
just listen and participate that way.
00:06:41.990 --> 00:06:44.220
But if you are in a semi-private space
00:06:44.220 --> 00:06:46.150
and you feel comfortable,
00:06:46.150 --> 00:06:48.060
you can join along with me.
00:06:48.060 --> 00:06:51.210
So the first thing we start
with is our body posture.
00:06:51.210 --> 00:06:54.230
So you want to have your
feet flat on the floor,
00:06:54.230 --> 00:06:56.760
and you just want to bring
some length to your spine.
00:06:56.760 --> 00:06:58.960
I like to tell the kids
to imagine that someone
00:06:58.960 --> 00:07:01.350
has a string right at
the top of their head,
00:07:01.350 --> 00:07:03.250
and they're just gently
pulling that string
00:07:03.250 --> 00:07:05.113
and it's lengthening the spine.
00:07:06.820 --> 00:07:09.703
And then when you're ready,
you can close your eyes.
00:07:11.250 --> 00:07:12.570
And I like to start with just
00:07:12.570 --> 00:07:15.740
a little bit of squeezing and releasing.
00:07:15.740 --> 00:07:17.880
We call this progressive
muscle relaxation,
00:07:17.880 --> 00:07:20.030
just to help you get into your body.
00:07:20.030 --> 00:07:22.030
So let's just start with our shoulders.
00:07:22.030 --> 00:07:24.400
Just bringing your shoulders
up toward your ears,
00:07:24.400 --> 00:07:25.943
and giving a little squeeze.
00:07:27.930 --> 00:07:30.663
And hold this for just a few seconds.
00:07:33.600 --> 00:07:36.303
And then take a nice deep
breath in through your nose.
00:07:38.770 --> 00:07:43.580
And as you exhale, just let
the shoulders relax down,
00:07:43.580 --> 00:07:45.143
away from your ears.
00:07:47.310 --> 00:07:49.430
And so we've all arrived, hopefully,
00:07:49.430 --> 00:07:51.083
in this still posture.
00:07:53.110 --> 00:07:56.490
And as we're sitting still for
maybe the first time today,
00:07:56.490 --> 00:07:59.253
we might notice our mind is so busy.
00:08:02.720 --> 00:08:06.030
So we're going to bring
just a natural curiosity
00:08:06.030 --> 00:08:09.860
to notice what our body
feels like in this moment.
00:08:09.860 --> 00:08:11.780
Are our eyelids fluttering,
00:08:11.780 --> 00:08:16.050
is our heartbeat racing
or is it really slow?
00:08:16.050 --> 00:08:17.283
Do we feel sleepy?
00:08:19.800 --> 00:08:21.013
So just notice.
00:08:26.670 --> 00:08:27.950
And then you're just going to start
00:08:27.950 --> 00:08:29.890
to take a couple of deep breaths,
00:08:29.890 --> 00:08:33.210
feeling your belly go out
and in as you breathe.
00:08:33.210 --> 00:08:35.113
So let's breathe in through our nose,
00:08:36.942 --> 00:08:38.733
and out through our nose.
00:08:41.300 --> 00:08:43.783
You can think of the words breathing in,
00:08:45.840 --> 00:08:46.927
breathing out.
00:08:48.696 --> 00:08:50.270
And then imagine it as a whisper,
00:08:50.270 --> 00:08:54.433
breathing in, breathing out.
00:08:56.610 --> 00:08:58.960
And now just hear it as
a whisper in your mind.
00:09:08.050 --> 00:09:11.400
See if you can let go of any
control over your breathing,
00:09:11.400 --> 00:09:13.750
so that your breath is just natural.
00:09:13.750 --> 00:09:16.823
You don't have to remember
to breathe or try to breathe.
00:09:18.290 --> 00:09:20.433
Breathing will just happen on it's own.
00:09:26.202 --> 00:09:28.920
And we're just breathing our breath,
00:09:28.920 --> 00:09:32.144
staying with the feeling or the sensation
00:09:32.144 --> 00:09:35.357
of the belly going out and in.
00:09:44.437 --> 00:09:46.730
And if your mind starts to drift away,
00:09:46.730 --> 00:09:50.410
just like the boat
drifting away on the waves,
00:09:50.410 --> 00:09:54.673
just label your thinking
as thinking, or planning,
00:09:55.610 --> 00:09:57.583
or maybe noticing sounds.
00:09:59.190 --> 00:10:00.580
And then very gently,
00:10:00.580 --> 00:10:04.380
very kindly come back to
the words breathing in,
00:10:04.380 --> 00:10:06.110
breathing out,
00:10:06.110 --> 00:10:08.583
and the sensations in
your belly as you breathe.
00:10:25.442 --> 00:10:26.890
And before we end our practice,
00:10:26.890 --> 00:10:29.590
see if there's one thing
that you noticed today
00:10:29.590 --> 00:10:32.283
about your breath that
you never noticed before.
00:10:44.570 --> 00:10:49.030
When you're ready, you
can slowly open your eyes,
00:10:49.030 --> 00:10:51.123
coming back to our space together.
00:10:54.330 --> 00:10:56.180
And I'm just curious,
00:10:56.180 --> 00:10:58.630
maybe in the chat you can mention
00:10:58.630 --> 00:11:00.343
one thing that you noticed.
00:11:01.260 --> 00:11:02.490
You might've noticed.
00:11:02.490 --> 00:11:06.170
I notice usually if I'm amped
up and I have a lot of energy,
00:11:06.170 --> 00:11:11.170
that my eyelids are fluttering
or that my heart is beating.
00:11:11.340 --> 00:11:12.730
So it's very sematic.
00:11:12.730 --> 00:11:15.480
It's very body driven if I'm amped up.
00:11:15.480 --> 00:11:19.080
But if I'm sleepy I might
notice heaviness in my eyes.
00:11:19.080 --> 00:11:21.100
I might notice, you know,
00:11:21.100 --> 00:11:24.010
dreams of falling asleep or, you know,
00:11:24.010 --> 00:11:26.820
cravings to get in my bed and sleep.
00:11:26.820 --> 00:11:28.440
So it's different.
00:11:28.440 --> 00:11:30.720
What we're noticing is different each,
00:11:30.720 --> 00:11:32.060
depending on how we're feeling.
00:11:32.060 --> 00:11:34.640
So if you'd like to share something
00:11:34.640 --> 00:11:37.560
that you've noticed from this practice,
00:11:37.560 --> 00:11:39.543
you can go ahead and share in the chat.
00:11:41.985 --> 00:11:43.370
And I believe I can see--
00:11:43.370 --> 00:11:45.160
- [Jeremy] A lot of folks are really
00:11:45.160 --> 00:11:46.680
sort of getting into this.
00:11:46.680 --> 00:11:48.940
Deanna mentioned the tension in her neck.
00:11:48.940 --> 00:11:51.660
Kim says, I noticed my
head hurt a little bit.
00:11:51.660 --> 00:11:53.440
Emily noticed, here we are in December,
00:11:53.440 --> 00:11:54.813
and I have a stuffy nose.
00:11:55.694 --> 00:11:58.387
So definitely a lot of sense of heaviness
00:11:58.387 --> 00:12:00.763
and weariness at this point of the year.
00:12:01.850 --> 00:12:03.730
- Thank you guys for sharing that too.
00:12:03.730 --> 00:12:05.620
And so anything you're noticing,
00:12:05.620 --> 00:12:07.200
whether it's pleasant,
00:12:07.200 --> 00:12:08.710
unpleasant, or neutral,
00:12:08.710 --> 00:12:10.900
is practicing mindfulness.
00:12:10.900 --> 00:12:13.480
That's the muscle that
we're trying to flex
00:12:13.480 --> 00:12:15.730
with ourselves and with our students.
00:12:15.730 --> 00:12:18.720
So that's really good noticing,
00:12:18.720 --> 00:12:20.220
and they're things that,
00:12:20.220 --> 00:12:22.140
if you think about the
categories of things,
00:12:22.140 --> 00:12:23.910
we can pay attention to.
00:12:23.910 --> 00:12:25.570
The one that we all mentioned
00:12:25.570 --> 00:12:27.770
in this practice was sensation, right?
00:12:27.770 --> 00:12:29.070
That's a huge category.
00:12:29.070 --> 00:12:31.285
Our internal body sensations.
00:12:31.285 --> 00:12:34.080
Another category is mental activity.
00:12:34.080 --> 00:12:36.027
So things that we're feeling,
00:12:36.027 --> 00:12:38.000
things that we're thinking about,
00:12:38.000 --> 00:12:39.580
or urges that we're having,
00:12:39.580 --> 00:12:42.250
or even images that
arise in our mind, right?
00:12:42.250 --> 00:12:45.524
Like flashes of memories from the day.
00:12:45.524 --> 00:12:48.300
Another category is our five senses.
00:12:48.300 --> 00:12:51.030
So we might be, when we close
our eyes like we just did,
00:12:51.030 --> 00:12:52.710
we might notice wind.
00:12:52.710 --> 00:12:54.820
I noticed the heater in my house.
00:12:54.820 --> 00:12:57.820
So it's nice and toasty
and warm for my skin.
00:12:57.820 --> 00:12:59.780
Or you might notice smells,
00:12:59.780 --> 00:13:02.650
if you have a candle or
any scents in the house.
00:13:02.650 --> 00:13:05.090
So that's another category,
00:13:05.090 --> 00:13:07.850
and the final category of
things we pay attention to
00:13:07.850 --> 00:13:09.660
has to do with our relationships.
00:13:09.660 --> 00:13:12.593
So you might've had a memory of someone
00:13:12.593 --> 00:13:15.310
that you love that's in your house.
00:13:15.310 --> 00:13:16.143
That's, you know,
00:13:16.143 --> 00:13:16.976
that you just thought, oh,
00:13:16.976 --> 00:13:18.158
I really like that person.
00:13:18.158 --> 00:13:21.900
Or I wonder how they're
doing, or I hope they're well.
00:13:21.900 --> 00:13:23.583
So any, any of these,
00:13:25.560 --> 00:13:27.690
any of the stimuli from
these different categories
00:13:27.690 --> 00:13:29.700
can pop up during our practice,
00:13:29.700 --> 00:13:31.490
and when we're being mindful,
00:13:31.490 --> 00:13:34.540
we're just noticing them
with this kind of curiosity
00:13:34.540 --> 00:13:37.253
and this openness to experience.
00:13:38.250 --> 00:13:39.580
So this is great.
00:13:39.580 --> 00:13:43.130
And when you're thinking about how
00:13:43.130 --> 00:13:45.470
to bring this into your classroom,
00:13:45.470 --> 00:13:47.569
or how to practice it with your students,
00:13:47.569 --> 00:13:51.230
you can teach them about
anchoring just like I taught you.
00:13:51.230 --> 00:13:53.330
And then you can set a
timer for one minute.
00:13:53.330 --> 00:13:55.930
So once they know how
to feel their breath,
00:13:55.930 --> 00:13:57.810
notice sensations in their body,
00:13:57.810 --> 00:14:00.740
and think of the words
breathing in and breathing out,
00:14:00.740 --> 00:14:02.800
they can practice in silence.
00:14:02.800 --> 00:14:05.610
And you might start with 30 seconds
00:14:05.610 --> 00:14:07.260
if they're really young children
00:14:07.260 --> 00:14:11.430
and then work up and progress
to longer periods of time.
00:14:11.430 --> 00:14:13.300
Or you can just keep it at a minute.
00:14:13.300 --> 00:14:15.371
That's sufficient for a lot of students
00:14:15.371 --> 00:14:17.663
in a lot of different age groups.
00:14:19.030 --> 00:14:20.810
So that's one practice.
00:14:20.810 --> 00:14:22.177
The second practice I want to talk to you
00:14:22.177 --> 00:14:24.720
a little bit about is the stop practice.
00:14:24.720 --> 00:14:27.770
And this one I've taught
to many, many children.
00:14:27.770 --> 00:14:29.630
And I think this is their favorite,
00:14:29.630 --> 00:14:31.890
because it's an acronym, first of all,
00:14:31.890 --> 00:14:35.160
so they can remember the
steps and what to do.
00:14:35.160 --> 00:14:37.590
And it's helpful because
the way we're going
00:14:37.590 --> 00:14:39.730
to practice it now and
how you can practice it
00:14:39.730 --> 00:14:43.157
in your classroom is to
ring a bell randomly,
00:14:43.157 --> 00:14:45.040
or any kind of sound,
00:14:45.040 --> 00:14:45.990
you can, you know,
00:14:45.990 --> 00:14:47.520
program your phone to go off
00:14:47.520 --> 00:14:49.620
at different times during the class.
00:14:49.620 --> 00:14:51.100
And then when you hear the sound,
00:14:51.100 --> 00:14:53.640
you're going to practice these four steps.
00:14:53.640 --> 00:14:54.700
So the four steps,
00:14:54.700 --> 00:14:58.100
we'll just do them kind
of briefly together.
00:14:58.100 --> 00:14:59.990
We stop what we're doing.
00:14:59.990 --> 00:15:02.310
And that's actually one of the
hardest things to do, right?
00:15:02.310 --> 00:15:05.250
Is to stop ourselves from
continuing to ruminate,
00:15:05.250 --> 00:15:07.680
or continuing to believe the thought
00:15:07.680 --> 00:15:09.120
pattern that we're having.
00:15:09.120 --> 00:15:12.430
So we stop, we take a deep breath,
00:15:12.430 --> 00:15:14.520
and we can do this again
with our eyes closed.
00:15:14.520 --> 00:15:16.463
So let's take a deep breath together.
00:15:22.028 --> 00:15:23.830
And then we just observe.
00:15:23.830 --> 00:15:27.060
And for this activity I'm
going to have us observe
00:15:27.060 --> 00:15:29.540
one thing in each of our senses.
00:15:29.540 --> 00:15:31.860
So let's start by observing a sound,
00:15:31.860 --> 00:15:34.133
just listening to a sound we can hear.
00:15:38.830 --> 00:15:41.113
Let's notice a smell, a scent.
00:15:46.490 --> 00:15:49.070
Let's notice a taste in our mouths,
00:15:49.070 --> 00:15:51.790
or just anything we notice if we run
00:15:51.790 --> 00:15:53.243
our tongue across our teeth.
00:15:58.120 --> 00:16:02.610
Let's notice the feeling of
our clothes against our skin.
00:16:02.610 --> 00:16:06.203
So the insolation of our
shirts or our sweaters,
00:16:07.060 --> 00:16:08.840
and just the feeling of being supported
00:16:08.840 --> 00:16:10.360
by whatever surface you're on,
00:16:10.360 --> 00:16:11.560
the weight of your body.
00:16:14.844 --> 00:16:16.930
And finally, as we open our eyes,
00:16:16.930 --> 00:16:20.430
just look around you and
notice something beautiful,
00:16:20.430 --> 00:16:22.960
or something that you're grateful for.
00:16:22.960 --> 00:16:24.490
Something that you're really glad
00:16:24.490 --> 00:16:26.653
you have in your personal space.
00:16:31.900 --> 00:16:32.733
Great.
00:16:32.733 --> 00:16:34.660
So that's the stop practice.
00:16:34.660 --> 00:16:36.883
And as far as observing,
00:16:38.120 --> 00:16:39.900
you can prompt your students to observe
00:16:39.900 --> 00:16:41.930
their five senses like we just did,
00:16:41.930 --> 00:16:43.650
or you can just have them observe
00:16:43.650 --> 00:16:45.440
whatever they're noticing in their mind.
00:16:45.440 --> 00:16:46.730
A thought, a feeling,
00:16:46.730 --> 00:16:47.990
a sensation.
00:16:47.990 --> 00:16:50.750
So it's up to you depending
on what's going on
00:16:50.750 --> 00:16:52.740
in the room or in the class.
00:16:52.740 --> 00:16:54.870
So whenever, I'm going to read,
00:16:54.870 --> 00:16:56.910
ring the bell twice
during our presentation.
00:16:56.910 --> 00:16:58.193
It'll sound like this.
00:17:00.028 --> 00:17:03.320
And I'm going to do it randomly
when you don't expect it,
00:17:03.320 --> 00:17:05.100
and we're going to do the stop practice.
00:17:05.100 --> 00:17:07.963
So I'll just say each word
and we'll practice together.
00:17:09.370 --> 00:17:11.090
I just wanted to share a quick story
00:17:11.090 --> 00:17:12.510
about the stop practice.
00:17:12.510 --> 00:17:14.862
I had a student who was
about eight years old,
00:17:14.862 --> 00:17:17.280
and I taught him the stop practice.
00:17:17.280 --> 00:17:20.180
And then the next
session the parents came,
00:17:20.180 --> 00:17:23.330
and his mom raised her hand and said,
00:17:23.330 --> 00:17:24.530
I really want to thank you
00:17:24.530 --> 00:17:27.520
for teaching my child this practice.
00:17:27.520 --> 00:17:30.980
And she said that when
they had lost their dog,
00:17:30.980 --> 00:17:32.580
their dog had run away,
00:17:32.580 --> 00:17:35.410
the mom was getting frantic and panicky.
00:17:35.410 --> 00:17:36.650
And she said her son said,
00:17:36.650 --> 00:17:38.020
mom, let's stop.
00:17:38.020 --> 00:17:39.290
Let's take a breath.
00:17:39.290 --> 00:17:41.430
Let's observe the sensation.
00:17:41.430 --> 00:17:43.592
And then let's proceed with more calm.
00:17:43.592 --> 00:17:45.420
And he had led her through it,
00:17:45.420 --> 00:17:47.620
and she said it made such a difference.
00:17:47.620 --> 00:17:50.340
So we never know when
we're teaching our students
00:17:50.340 --> 00:17:52.560
how this is impacting their families,
00:17:52.560 --> 00:17:54.580
and how they're internalizing.
00:17:54.580 --> 00:17:58.150
They often don't, aren't very emphatic,
00:17:58.150 --> 00:18:01.870
or they're not gushing
about the experiences
00:18:01.870 --> 00:18:03.759
they're having or learning.
00:18:03.759 --> 00:18:05.990
But then when you hear stories like this,
00:18:05.990 --> 00:18:09.483
it's very inspiring and
motivates you to keep going.
00:18:11.120 --> 00:18:14.910
So I wanted to talk a little
bit about what meditation is,
00:18:14.910 --> 00:18:17.970
and our expectations versus the reality.
00:18:17.970 --> 00:18:19.890
So I'm not sure,
00:18:19.890 --> 00:18:21.100
we're going to do a little poll to see
00:18:21.100 --> 00:18:24.070
what your meditation background is.
00:18:24.070 --> 00:18:27.340
So I don't know if many of you
have practiced before or not.
00:18:27.340 --> 00:18:29.250
But when you first start to practice,
00:18:29.250 --> 00:18:31.620
many people get really turned off,
00:18:31.620 --> 00:18:35.170
get turned away by the fact
that when you close your eyes
00:18:35.170 --> 00:18:36.810
you're bombarded with thoughts.
00:18:36.810 --> 00:18:37.940
You're bombarded with the busyness
00:18:37.940 --> 00:18:42.940
and the rush of your mind.
00:18:43.210 --> 00:18:45.950
And so a lot of people will
just give up at that point,
00:18:45.950 --> 00:18:47.830
and say, this isn't what I expected,
00:18:47.830 --> 00:18:50.860
because there's an expectation
that we'll get calm,
00:18:50.860 --> 00:18:52.290
that our thoughts will start
00:18:52.290 --> 00:18:55.053
to slow down when we want them to.
00:18:55.053 --> 00:18:58.660
But the reality is that
we're facing the busyness,
00:18:58.660 --> 00:19:01.210
that rush, that speed of thought
00:19:01.210 --> 00:19:03.660
that reflects the speed of our lives.
00:19:03.660 --> 00:19:05.530
So what we're really doing,
00:19:05.530 --> 00:19:09.830
what we're trying to cultivate
is a sense of kindness,
00:19:09.830 --> 00:19:13.050
openness, and a willingness
to be with things as they are.
00:19:13.050 --> 00:19:16.430
So we're sitting with whatever
shows up in our practice,
00:19:16.430 --> 00:19:17.900
and that's why we set a timer,
00:19:17.900 --> 00:19:19.493
because if we did this indefinitely
00:19:19.493 --> 00:19:21.720
it would be unsustainable.
00:19:21.720 --> 00:19:23.680
But we set a timer for, you know,
00:19:23.680 --> 00:19:25.040
five, if we're adults,
00:19:25.040 --> 00:19:29.193
five to 20 minutes, and
we see what shows up.
00:19:29.193 --> 00:19:31.770
That willingness to be
with things as they are
00:19:31.770 --> 00:19:35.680
changes the relationship we
have to our internal world.
00:19:35.680 --> 00:19:37.890
And it becomes a lot more peaceful,
00:19:37.890 --> 00:19:41.090
a lot more manageable
to confront our worries,
00:19:41.090 --> 00:19:43.650
our thoughts, our projections,
00:19:43.650 --> 00:19:45.470
and it prevents us from ruminating.
00:19:45.470 --> 00:19:47.760
We catch ourselves in
the middle of the day,
00:19:47.760 --> 00:19:48.780
in the middle of our lives,
00:19:48.780 --> 00:19:53.270
when our mind starts to
ruminate or starts to overthink.
00:19:53.270 --> 00:19:55.100
We don't want to discourage
thinking of course,
00:19:55.100 --> 00:19:57.680
but overthinking can be problematic.
00:19:57.680 --> 00:20:01.640
So that's a little bit
about how our expectations
00:20:01.640 --> 00:20:03.830
really match up with with the reality
00:20:03.830 --> 00:20:07.100
of meditation and mindfulness.
00:20:07.100 --> 00:20:08.550
So here's a great poll.
00:20:08.550 --> 00:20:11.460
What is your familiarity with mindfulness?
00:20:11.460 --> 00:20:14.420
Are you new to it, have you
tried it a couple of times,
00:20:14.420 --> 00:20:16.550
or do you have a regular practice?
00:20:16.550 --> 00:20:19.100
And, oh,
00:20:19.100 --> 00:20:21.080
I can't vote, sorry.
00:20:21.080 --> 00:20:22.534
- [Jeremy] Sorry about that--
00:20:22.534 --> 00:20:24.063
- That's okay!
00:20:24.063 --> 00:20:24.896
- [Jeremy] The answers are coming in
00:20:24.896 --> 00:20:25.960
fast and furious though.
00:20:26.950 --> 00:20:30.360
More than 400 teachers across
the country have now voted,
00:20:30.360 --> 00:20:32.430
and we'll close it in about five seconds.
00:20:32.430 --> 00:20:33.690
- Cool.
00:20:33.690 --> 00:20:35.720
- [Jeremy] And it looks like,
00:20:35.720 --> 00:20:37.630
as you can see here on the screen,
00:20:37.630 --> 00:20:39.840
a lot of folks have dabbled with it,
00:20:39.840 --> 00:20:41.740
but also a lot of newbies as well.
00:20:41.740 --> 00:20:42.573
- Nice.
00:20:42.573 --> 00:20:43.406
Okay, great.
00:20:43.406 --> 00:20:46.200
So about half have tried it a few times,
00:20:46.200 --> 00:20:48.790
and a quarter of you
have a regular practice.
00:20:48.790 --> 00:20:51.500
So that's, you know exactly
what I'm talking about.
00:20:51.500 --> 00:20:54.499
And if we were together and
we could have a dialogue,
00:20:54.499 --> 00:20:56.830
I would ask you what helps you
00:20:56.830 --> 00:20:58.053
sustain that regular practice?
00:20:58.053 --> 00:21:00.394
What keeps you coming back?
00:21:00.394 --> 00:21:03.000
I know for a lot of
people, if we struggle,
00:21:03.000 --> 00:21:04.990
I myself have struggled with anxiety,
00:21:04.990 --> 00:21:07.260
so mindfulness was the,
00:21:07.260 --> 00:21:09.971
it was just an amazing tool for my life.
00:21:09.971 --> 00:21:11.700
I never thought I would teach it,
00:21:11.700 --> 00:21:15.120
but I started practicing
at 15 and never stopped.
00:21:15.120 --> 00:21:17.410
So it's an incredible tool.
00:21:17.410 --> 00:21:20.180
And you all have your own
reasons for being drawn to it
00:21:20.180 --> 00:21:22.263
or for continuing to practice it.
00:21:25.330 --> 00:21:26.163
Awesome.
00:21:28.800 --> 00:21:31.683
So we can go to the next slide.
00:21:34.810 --> 00:21:36.310
- [Jeremy] Lena, if you wouldn't mind
00:21:36.310 --> 00:21:37.360
sharing your screen once more.
00:21:37.360 --> 00:21:38.320
Sorry about that.
00:21:38.320 --> 00:21:39.920
We'll switch back from the poll.
00:21:43.010 --> 00:21:43.843
There we go.
00:21:44.801 --> 00:21:45.634
- Perfect.
00:21:46.770 --> 00:21:48.070
- [Jeremy] Thanks everyone
for those great answers,
00:21:48.070 --> 00:21:49.752
keep them coming.
00:21:49.752 --> 00:21:50.835
- Let's just.
00:21:51.965 --> 00:21:55.046
(bell ringing)
00:21:55.046 --> 00:21:58.213
Stop, take a breath.
00:22:02.925 --> 00:22:06.457
And this time observe the
sensation in your body.
00:22:11.076 --> 00:22:13.743
With your hands, with your face,
00:22:16.370 --> 00:22:17.763
and then we'll proceed.
00:22:19.050 --> 00:22:19.883
Nice.
00:22:20.970 --> 00:22:23.440
So, what is mindfulness?
00:22:23.440 --> 00:22:26.660
To those of you that
have not tried it before,
00:22:26.660 --> 00:22:27.980
or maybe only once or twice,
00:22:27.980 --> 00:22:30.480
mindfulness is this way of being
00:22:30.480 --> 00:22:32.420
that we actually naturally have.
00:22:32.420 --> 00:22:33.670
It's a propensity we have,
00:22:33.670 --> 00:22:36.814
we don't have to learn it like
we would need to learn math.
00:22:36.814 --> 00:22:41.814
But it's often not accessible
because we're so busy,
00:22:43.530 --> 00:22:46.810
or it's very hard to cultivate deeply,
00:22:46.810 --> 00:22:51.220
because for the reasons I
mentioned that there's this
00:22:51.220 --> 00:22:53.160
little learning curve we have to get over
00:22:53.160 --> 00:22:56.530
to really rest in the practice.
00:22:56.530 --> 00:22:59.180
So a quick definition of it is that
00:22:59.180 --> 00:23:01.106
it's our our ability to be present
00:23:01.106 --> 00:23:03.790
and attentive with openness,
00:23:03.790 --> 00:23:06.470
curiosity, and a kind mind.
00:23:06.470 --> 00:23:09.070
So building that relationship of kindness
00:23:09.070 --> 00:23:11.040
and openness to our experiences.
00:23:11.040 --> 00:23:13.640
And being willing, like I said before,
00:23:13.640 --> 00:23:17.070
being willing to show up
however you are, right?
00:23:17.070 --> 00:23:20.310
Like showing up to yourself and
witnessing what's coming up,
00:23:20.310 --> 00:23:21.550
however it shows up.
00:23:21.550 --> 00:23:23.650
So there's a lot of acceptance.
00:23:23.650 --> 00:23:27.200
And when we accept what's
happening, we're not rejecting it,
00:23:27.200 --> 00:23:30.500
because the rejection is what
causes us a lot of stress.
00:23:30.500 --> 00:23:31.440
Trying to change,
00:23:31.440 --> 00:23:33.350
trying to get to a certain
mindset that we want
00:23:33.350 --> 00:23:36.060
to get to can produce kind of this inner
00:23:36.060 --> 00:23:39.160
conflict that becomes unsustainable,
00:23:39.160 --> 00:23:41.533
and kind of zaps us of our energy.
00:23:45.840 --> 00:23:48.540
So why do we practice mindfulness?
00:23:48.540 --> 00:23:51.450
I think, when I think of
teaching in the classroom,
00:23:51.450 --> 00:23:53.930
I think of these moments I've had where
00:23:53.930 --> 00:23:56.350
I've become a different person,
00:23:56.350 --> 00:23:59.500
especially with students in
classrooms where there was
00:23:59.500 --> 00:24:02.120
just no interest when I
was a substitute teacher,
00:24:02.120 --> 00:24:05.800
and people expected to have a day off,
00:24:05.800 --> 00:24:08.960
and I would get so agitated and so upset.
00:24:08.960 --> 00:24:11.240
And if I didn't have
my mindfulness skills,
00:24:11.240 --> 00:24:12.900
I think I would have turned into someone
00:24:12.900 --> 00:24:14.840
that I didn't even recognize.
00:24:14.840 --> 00:24:16.350
I would have probably, you know,
00:24:16.350 --> 00:24:18.141
screamed or hit a table,
00:24:18.141 --> 00:24:21.010
or something really, really drastic,
00:24:21.010 --> 00:24:24.850
because there's so many moments
where there's frustration.
00:24:24.850 --> 00:24:26.530
But if we think about using it as
00:24:26.530 --> 00:24:28.500
a stress management tool in the classroom,
00:24:28.500 --> 00:24:30.390
we're stopping to notice.
00:24:30.390 --> 00:24:34.100
We're taking a moment to notice
what's going on within us.
00:24:34.100 --> 00:24:37.240
And just the acknowledgement
of that sensation,
00:24:37.240 --> 00:24:39.070
that thought, that emotion,
00:24:39.070 --> 00:24:40.470
helps it to settle.
00:24:40.470 --> 00:24:42.150
Just the pure acknowledgement of it.
00:24:42.150 --> 00:24:43.400
We don't have to do anything more
00:24:43.400 --> 00:24:45.260
than that most of the time.
00:24:45.260 --> 00:24:47.270
And that allows us to stay resilient,
00:24:47.270 --> 00:24:50.580
and to meet our students with more calm,
00:24:50.580 --> 00:24:52.860
and to meet them with more bandwidth,
00:24:52.860 --> 00:24:55.400
which makes the teaching
profession a sustainable one,
00:24:55.400 --> 00:24:56.450
instead of a, you know,
00:24:56.450 --> 00:25:00.330
one where you get burnt out in
the course of a year or two.
00:25:00.330 --> 00:25:02.460
It also helps our physical health.
00:25:02.460 --> 00:25:04.460
So it increases our immune system.
00:25:04.460 --> 00:25:06.640
It strengthens our immune system.
00:25:06.640 --> 00:25:08.780
It's correlated with longevity,
00:25:08.780 --> 00:25:10.260
and that has to do with telomeres,
00:25:10.260 --> 00:25:12.447
which are the little
strands at the end of,
00:25:12.447 --> 00:25:15.060
these little frills at the end of our
00:25:15.060 --> 00:25:17.530
DNA strands that deteriorate over time.
00:25:17.530 --> 00:25:20.070
So studies have shown that it preserves,
00:25:20.070 --> 00:25:24.690
it keeps those telomeres intact
for longer periods of time.
00:25:24.690 --> 00:25:28.730
And it also helps prevent
cardiovascular disease
00:25:28.730 --> 00:25:31.070
and inflammation in our body.
00:25:31.070 --> 00:25:33.430
So it has tremendous health benefits,
00:25:33.430 --> 00:25:36.383
not to mention sleep duration
and quality of sleep.
00:25:37.460 --> 00:25:38.690
And then for our students,
00:25:38.690 --> 00:25:41.000
it's giving them this tool to focus
00:25:41.000 --> 00:25:43.530
and to be able to
regulate their attention,
00:25:43.530 --> 00:25:46.260
so that when they feel their
attention drifting away,
00:25:46.260 --> 00:25:47.790
they have a strategy.
00:25:47.790 --> 00:25:49.880
I often ask children I work with,
00:25:49.880 --> 00:25:52.810
who's ever told you to pay
attention, raise your hand.
00:25:52.810 --> 00:25:54.240
And then my follow-up question is,
00:25:54.240 --> 00:25:56.437
who's ever taught you
how to pay attention.
00:25:56.437 --> 00:25:58.410
And there are no hands, right?
00:25:58.410 --> 00:25:59.910
Because it's something that we,
00:25:59.910 --> 00:26:02.600
if we're not taught we
don't really know how to do.
00:26:02.600 --> 00:26:03.620
Some of us are naturally better at it,
00:26:03.620 --> 00:26:07.490
and most of us I would
say are not great at it.
00:26:07.490 --> 00:26:10.180
And it's also a tool for
emotional regulation.
00:26:10.180 --> 00:26:12.820
So when we notice an
emotion that we're having,
00:26:12.820 --> 00:26:14.650
and we're able to discern it, right?
00:26:14.650 --> 00:26:18.470
We're able to finally discern
between frustration and anger,
00:26:18.470 --> 00:26:21.600
for example, or worry and regret.
00:26:21.600 --> 00:26:24.850
When we give kids this
vocabulary to explain,
00:26:24.850 --> 00:26:26.940
or name, or label how they're feeling,
00:26:26.940 --> 00:26:29.330
again, the intensity comes down,
00:26:29.330 --> 00:26:31.820
and they stay in that zone of resilience
00:26:31.820 --> 00:26:33.509
which allows them to bounce back
00:26:33.509 --> 00:26:35.770
and actually resume learning,
00:26:35.770 --> 00:26:38.220
because learning will temporarily pause
00:26:38.220 --> 00:26:40.423
or stop if the emotion is too intense.
00:26:46.970 --> 00:26:49.493
Thanks, we can go to the next slide.
00:26:50.700 --> 00:26:52.540
So here's another poll for us.
00:26:52.540 --> 00:26:53.670
In a few words,
00:26:53.670 --> 00:26:55.410
what is one of the biggest challenges
00:26:55.410 --> 00:26:57.203
you experienced as an educator?
00:26:59.440 --> 00:27:03.260
And I just think of so many,
so let's see what we have here.
00:27:03.260 --> 00:27:06.210
Burnt-out, students not showing up.
00:27:06.210 --> 00:27:07.560
That's a big one right now.
00:27:08.420 --> 00:27:11.650
Keeping students motivated,
grappling with technology,
00:27:11.650 --> 00:27:14.603
and students struggling
academically or emotionally.
00:27:16.630 --> 00:27:17.480
- [Jeremy] And this one,
00:27:17.480 --> 00:27:20.600
educators can actually
choose as many as apply.
00:27:20.600 --> 00:27:24.320
And we're seeing actually quite
a few choosing the burnout,
00:27:24.320 --> 00:27:27.420
which is certainly topical tonight,
00:27:27.420 --> 00:27:29.330
the motivation piece which also fits in
00:27:29.330 --> 00:27:30.780
with what we're talking about.
00:27:30.780 --> 00:27:33.190
And the struggle is probably
academically and emotionally.
00:27:33.190 --> 00:27:36.979
So definitely all things
that we can address
00:27:36.979 --> 00:27:39.430
with some of these mindfulness practices.
00:27:39.430 --> 00:27:40.680
- Yes, okay.
00:27:40.680 --> 00:27:44.100
So the biggest ones here are
the motivation component,
00:27:44.100 --> 00:27:47.800
and then the struggle, the
academic or emotional struggle.
00:27:47.800 --> 00:27:48.877
Absolutely.
00:27:48.877 --> 00:27:51.480
And a lot of students right now,
00:27:51.480 --> 00:27:53.810
I know a lot of high school
students are finding,
00:27:53.810 --> 00:27:56.380
because friendships are so important
00:27:56.380 --> 00:27:58.730
in their lives at that
developmental period,
00:27:58.730 --> 00:28:01.422
that having restricted
access to their friend groups
00:28:01.422 --> 00:28:04.950
is causing depression in a lot of them.
00:28:04.950 --> 00:28:06.860
And also just this, like what is,
00:28:06.860 --> 00:28:08.970
what is life even for anymore?
00:28:08.970 --> 00:28:09.803
What is, you know,
00:28:09.803 --> 00:28:12.870
like these existential
issues that are coming up.
00:28:12.870 --> 00:28:14.280
So, yeah.
00:28:14.280 --> 00:28:18.200
And I think when we're
thinking about how to address
00:28:18.200 --> 00:28:20.090
that from a mindfulness perspective,
00:28:20.090 --> 00:28:21.898
I think of the word compassion.
00:28:21.898 --> 00:28:24.760
You know, just witnessing when a student's
00:28:24.760 --> 00:28:27.833
sharing something like that with us,
00:28:27.833 --> 00:28:30.480
just being the source of witness
00:28:30.480 --> 00:28:32.680
and being the source of containment
00:28:32.680 --> 00:28:35.787
for their emotional experience.
00:28:35.787 --> 00:28:37.310
And relating to it!
00:28:37.310 --> 00:28:38.990
Letting them know that they're not alone,
00:28:38.990 --> 00:28:40.950
that this is part of the human experience,
00:28:40.950 --> 00:28:44.870
and that a lot of students
are feeling this way too.
00:28:44.870 --> 00:28:47.090
And then if we had more time,
00:28:47.090 --> 00:28:48.560
maybe we'll have this practice
00:28:48.560 --> 00:28:51.590
in our Headspace for
Educators group on Facebook,
00:28:51.590 --> 00:28:55.170
but there are practices that
help you build resiliency
00:28:55.170 --> 00:28:58.360
and help build a feeling of connection,
00:28:58.360 --> 00:29:03.253
and joy, and ease in the midst
of these difficult emotions.
00:29:05.370 --> 00:29:07.940
- [Jeremy] And Sam, I know
that some of the folks
00:29:07.940 --> 00:29:10.210
from the very first exercise we did
00:29:10.210 --> 00:29:11.960
said they had their dinner in the oven,
00:29:11.960 --> 00:29:14.395
the ratatouille was cooking in some cases.
00:29:14.395 --> 00:29:17.470
Do you want to finish up
with a final exercise,
00:29:17.470 --> 00:29:19.150
or should we go into some
Q and A at this point?
00:29:19.150 --> 00:29:19.983
What do you think is the best--
00:29:19.983 --> 00:29:21.957
- I think we should go into some Q and A.
00:29:21.957 --> 00:29:25.580
I want to give everyone a
chance to ask questions.
00:29:25.580 --> 00:29:29.000
I know we're at our end time, so yeah.
00:29:29.000 --> 00:29:31.160
Please feel free to ask any questions,
00:29:31.160 --> 00:29:34.115
and I'm happy to address them.
00:29:34.115 --> 00:29:36.640
And the stuff we didn't get to, again,
00:29:36.640 --> 00:29:39.030
we have this Headspace for
Educators group on Facebook,
00:29:39.030 --> 00:29:41.290
and we're going to be featuring
00:29:41.290 --> 00:29:43.300
these techniques on that page.
00:29:43.300 --> 00:29:46.003
So you can join and take part,
00:29:47.070 --> 00:29:49.650
so that you won't miss any of this last
00:29:49.650 --> 00:29:52.550
exercise that we didn't get
to on compassionate breathing.
00:29:53.440 --> 00:29:54.273
- [Jeremy] Very cool.
00:29:54.273 --> 00:29:55.890
And Alice, before we
dive into the Q and A,
00:29:55.890 --> 00:29:58.100
and of course people should
feel free to ask questions
00:29:58.100 --> 00:30:00.010
via the questions tab at any point,
00:30:00.010 --> 00:30:01.140
did you want to call out anything
00:30:01.140 --> 00:30:04.570
around Headspace for Educators
and how they access that?
00:30:04.570 --> 00:30:05.403
- Yeah, I mean,
00:30:05.403 --> 00:30:06.630
we've got the information here,
00:30:06.630 --> 00:30:08.013
and as Sam said,
00:30:08.013 --> 00:30:11.808
we'll be sharing exercises every
week in the Facebook group,
00:30:11.808 --> 00:30:14.341
which is called Headspace for Educators.
00:30:14.341 --> 00:30:18.190
Yeah, and I just encourage
if anyone wants to sign up,
00:30:18.190 --> 00:30:21.800
they can just go to our
headspace.com landing page,
00:30:21.800 --> 00:30:24.915
forward slash educators, and
all the information is there.
00:30:24.915 --> 00:30:26.140
So yeah.
00:30:26.140 --> 00:30:28.680
We're just excited to be able
00:30:28.680 --> 00:30:29.990
to share these practices today,
00:30:29.990 --> 00:30:32.250
but also welcome you to come back
00:30:32.250 --> 00:30:34.653
and check out more through
the Facebook group.
00:30:35.560 --> 00:30:36.393
- [Jeremy] That's awesome.
00:30:36.393 --> 00:30:37.880
And again, like super
generous in any year,
00:30:37.880 --> 00:30:39.480
but especially pertinent in this one.
00:30:39.480 --> 00:30:41.330
So thank you all for sharing that
00:30:41.330 --> 00:30:43.540
so broadly across the world.
00:30:43.540 --> 00:30:45.480
Lots of questions are coming in.
00:30:45.480 --> 00:30:47.880
And so I want to start with
one that Kelly had asked
00:30:47.880 --> 00:30:49.830
at the very beginning of the session, Sam,
00:30:49.830 --> 00:30:53.840
which is all of this is
awesome in a teacher led way,
00:30:53.840 --> 00:30:56.043
she can really imagine
using it with her students,
00:30:56.043 --> 00:30:58.210
but are there practices that you can help
00:30:58.210 --> 00:31:00.350
your students with that do on their own?
00:31:00.350 --> 00:31:02.470
So they sort of take that learning,
00:31:02.470 --> 00:31:04.100
and make it part of their own practice
00:31:04.100 --> 00:31:05.800
even when the teacher's not there.
00:31:07.760 --> 00:31:09.860
- Absolutely, that's such a good question.
00:31:09.860 --> 00:31:13.090
And I think I would say
to start with anchoring.
00:31:13.090 --> 00:31:15.650
So to encourage them to
set a timer for one minute
00:31:15.650 --> 00:31:19.410
after you teach them the
exercise we did in the beginning.
00:31:19.410 --> 00:31:21.530
Using an anchor word like where it's,
00:31:21.530 --> 00:31:23.050
like breathing in, breathing out.
00:31:23.050 --> 00:31:26.090
Noting what they're feeling,
coming back to their anchor.
00:31:26.090 --> 00:31:28.750
Just that simple practice is going
00:31:28.750 --> 00:31:31.700
to help them develop
mindfulness as a trait,
00:31:31.700 --> 00:31:34.410
as a kind of default way of relating
00:31:34.410 --> 00:31:36.390
to their internal experiences.
00:31:36.390 --> 00:31:38.540
So if there was one, I would point out,
00:31:38.540 --> 00:31:40.130
I would say that one.
00:31:40.130 --> 00:31:43.250
Another one that we'll
feature on the Facebook
00:31:43.250 --> 00:31:46.420
group is loving kindness practice.
00:31:46.420 --> 00:31:48.000
Or if your children are younger,
00:31:48.000 --> 00:31:49.810
you can call them friendly wishes.
00:31:49.810 --> 00:31:51.840
And that involves thinking about
00:31:51.840 --> 00:31:53.700
someone that you find easy to like,
00:31:53.700 --> 00:31:55.760
or love, a friend or loved one,
00:31:55.760 --> 00:31:57.090
and wishing them happiness,
00:31:57.090 --> 00:32:00.010
wishing them peace and
wishing them health.
00:32:00.010 --> 00:32:05.010
And there's a practice
for that and recordings
00:32:05.058 --> 00:32:07.840
so that they can practice it on their own.
00:32:07.840 --> 00:32:10.330
We also have a lot of
material like that on the app.
00:32:10.330 --> 00:32:14.960
So kids can access it
themselves and just press play,
00:32:14.960 --> 00:32:17.910
and be guided through those exercises.
00:32:17.910 --> 00:32:21.470
But I would say the anchoring
practice and friendly wishes
00:32:21.470 --> 00:32:24.030
are two really good practices that kids,
00:32:24.030 --> 00:32:25.020
once they learn them,
00:32:25.020 --> 00:32:27.470
they do say that they
practice them on their own.
00:32:28.800 --> 00:32:29.633
- [Jeremy] That's awesome, yeah.
00:32:29.633 --> 00:32:31.620
I'm so jealous in retrospect that I didn't
00:32:31.620 --> 00:32:32.900
learn this when I was at that age,
00:32:32.900 --> 00:32:33.870
'cause I feel like it's such
00:32:33.870 --> 00:32:35.373
a foundation for a great life.
00:32:37.180 --> 00:32:38.750
You know, sort of a companion question,
00:32:38.750 --> 00:32:41.320
very much speaking to the reality of 2020.
00:32:41.320 --> 00:32:44.582
Carol says, if a student
wants to practice at home,
00:32:44.582 --> 00:32:46.670
but right now home is so chaotic,
00:32:46.670 --> 00:32:49.150
so noisy with all of the distractions
00:32:49.150 --> 00:32:50.900
that are facing us digitally,
00:32:50.900 --> 00:32:52.540
do you have any practical recommendations
00:32:52.540 --> 00:32:55.242
for how students can find
that space in their home lives
00:32:55.242 --> 00:32:57.880
to really invest in this practice?
00:32:57.880 --> 00:32:59.040
- Absolutely, yeah.
00:32:59.040 --> 00:33:01.500
So I mean, one way,
00:33:01.500 --> 00:33:04.460
it might be really cold wherever you are,
00:33:04.460 --> 00:33:06.870
so outside might not be accessible,
00:33:06.870 --> 00:33:07.960
but if it is, you know,
00:33:07.960 --> 00:33:11.713
going outside and just starting
the day with five senses.
00:33:12.590 --> 00:33:13.760
I do this myself,
00:33:13.760 --> 00:33:16.870
like I'll sit on my stairs
outside and I close my eyes.
00:33:16.870 --> 00:33:18.660
I feel the sun on my face.
00:33:18.660 --> 00:33:20.140
I take in a deep breath,
00:33:20.140 --> 00:33:22.780
and I just tap into each
one of my five senses
00:33:22.780 --> 00:33:24.240
and end with gratitude.
00:33:24.240 --> 00:33:25.500
I just say, I ask myself,
00:33:25.500 --> 00:33:27.377
what's one thing I'm grateful for?
00:33:27.377 --> 00:33:31.410
So that's a very easy accessible
practice for them to do.
00:33:31.410 --> 00:33:33.350
And I think what I'm speaking to
00:33:33.350 --> 00:33:37.230
is the fact that it's
important to emphasize
00:33:37.230 --> 00:33:40.200
to students that one minute is enough.
00:33:40.200 --> 00:33:41.300
You know, even if they're,
00:33:41.300 --> 00:33:43.190
it's a reset button,
00:33:43.190 --> 00:33:46.090
and it's a way of setting
the tone for your day.
00:33:46.090 --> 00:33:48.090
So they don't need to carve out
00:33:48.090 --> 00:33:49.810
large periods of time or find,
00:33:49.810 --> 00:33:52.170
you know, an hour of quiet
somewhere in their house.
00:33:52.170 --> 00:33:55.140
They can just find a
little spot, you know,
00:33:55.140 --> 00:33:56.530
maybe even in their bed.
00:33:56.530 --> 00:33:58.530
Just sitting upright in their bed
00:33:58.530 --> 00:34:01.300
before they get up and
start the rest of their day,
00:34:01.300 --> 00:34:04.805
to do one minute of breathing
with a timer on their phone.
00:34:04.805 --> 00:34:08.580
Or even lying down
before they fall asleep.
00:34:08.580 --> 00:34:12.620
A lot of kids use the app and guided
00:34:12.620 --> 00:34:14.380
meditation just to fall asleep,
00:34:14.380 --> 00:34:17.090
because their minds are so
busy at the end of the day
00:34:17.090 --> 00:34:18.980
that it's incredibly difficult.
00:34:18.980 --> 00:34:20.640
So those are some recommendations.
00:34:20.640 --> 00:34:23.830
I think most kids have a bed of their own,
00:34:23.830 --> 00:34:27.330
and that's like a sacred space for them.
00:34:27.330 --> 00:34:29.810
So encouraging them to do
practices in the morning
00:34:29.810 --> 00:34:33.193
or before they fall asleep can
be really helpful for them.
00:34:34.150 --> 00:34:34.983
- [Jeremy] I love that.
00:34:34.983 --> 00:34:35.920
And I think that'll resonate.
00:34:35.920 --> 00:34:36.753
Oh, go ahead.
00:34:36.753 --> 00:34:37.586
Go ahead, Alice.
00:34:37.586 --> 00:34:38.419
My apologies.
00:34:38.419 --> 00:34:39.550
- I was just going to add,
it's a such great suggestion.
00:34:39.550 --> 00:34:42.910
We see the sleep cast being
used a lot by young people.
00:34:42.910 --> 00:34:44.450
And I think if,
00:34:44.450 --> 00:34:46.600
obviously the app is free for teachers.
00:34:46.600 --> 00:34:49.290
If any of your students
want to access the content,
00:34:49.290 --> 00:34:51.120
there's a lot of free content on YouTube,
00:34:51.120 --> 00:34:52.490
as well as on the website which we've
00:34:52.490 --> 00:34:54.930
made available to everyone this year,
00:34:54.930 --> 00:34:56.410
especially since COVID hit.
00:34:56.410 --> 00:34:59.732
So there's plenty of free
resources there as well
00:34:59.732 --> 00:35:01.980
even if they don't have
access to the full app.
00:35:01.980 --> 00:35:03.000
So I would encouraged them to go
00:35:03.000 --> 00:35:05.233
to those other channels too.
00:35:06.070 --> 00:35:06.903
- [Jeremy] That's awesome.
00:35:06.903 --> 00:35:09.030
So the next couple of questions are about
00:35:09.030 --> 00:35:10.946
some of the resistance
that educators have gotten
00:35:10.946 --> 00:35:14.290
trying to bring mindfulness
into the classroom in the past.
00:35:14.290 --> 00:35:17.400
Mary and others have referred
to the parental resistance,
00:35:17.400 --> 00:35:18.590
which sometimes is based in a
00:35:18.590 --> 00:35:20.050
religious sort of objection of,
00:35:20.050 --> 00:35:22.140
hey, doesn't this sort of go against
00:35:22.140 --> 00:35:23.500
my own spiritual beliefs?
00:35:23.500 --> 00:35:25.120
Is there a conflict there.
00:35:25.120 --> 00:35:27.420
Have you heard any kind
of complaints about that
00:35:27.420 --> 00:35:29.060
from parents that you've worked with,
00:35:29.060 --> 00:35:32.200
and how can an educator
do that delicate dance?
00:35:32.200 --> 00:35:33.450
- Such a great question.
00:35:33.450 --> 00:35:37.620
Yes actually, when I
first started teaching it,
00:35:37.620 --> 00:35:39.040
I was just in schools.
00:35:39.040 --> 00:35:41.100
I was working for nonprofits
and I was in schools,
00:35:41.100 --> 00:35:42.847
and I would just do it on the fly.
00:35:42.847 --> 00:35:43.840
I would say, okay,
00:35:43.840 --> 00:35:46.380
I see that these kids need
emotional regulation skills,
00:35:46.380 --> 00:35:48.190
so I'm just going to do it.
00:35:48.190 --> 00:35:50.730
And one time I had a
parent withdraw her child
00:35:50.730 --> 00:35:53.700
from my group because
of what you just said,
00:35:53.700 --> 00:35:55.200
these religious reasons.
00:35:55.200 --> 00:35:59.060
She was worried that it was
conflicting with her religion,
00:35:59.060 --> 00:36:01.820
and it brought up a lot of fear for her.
00:36:01.820 --> 00:36:03.490
At the time I didn't
really know what to do.
00:36:03.490 --> 00:36:06.472
I was in my early twenties
and I was very surprised
00:36:06.472 --> 00:36:09.218
that it was being viewed that way.
00:36:09.218 --> 00:36:10.402
But over time,
00:36:10.402 --> 00:36:12.780
I started to realize how it can
00:36:12.780 --> 00:36:15.510
be viewed in a threatening way.
00:36:15.510 --> 00:36:18.300
Like, this is conflicting
with my religious practice.
00:36:18.300 --> 00:36:19.570
And a lot of religious practices
00:36:19.570 --> 00:36:23.440
have their own contemplative format,
00:36:23.440 --> 00:36:26.820
right, through prayer or in other ways.
00:36:26.820 --> 00:36:29.367
So what I would do now, I mean,
00:36:29.367 --> 00:36:31.550
if you can talk to parents,
00:36:31.550 --> 00:36:35.690
invite them to participate
in in the practice,
00:36:35.690 --> 00:36:39.780
and kind of see it as a new
experience with curiosity.
00:36:39.780 --> 00:36:41.630
Let them know that it's not a religion,
00:36:41.630 --> 00:36:43.027
that there's a lot of,
00:36:43.027 --> 00:36:45.085
and you might even provide
them with the scientific
00:36:45.085 --> 00:36:47.780
research that you can find really easily.
00:36:47.780 --> 00:36:49.721
I mean, it's all over the internet.
00:36:49.721 --> 00:36:52.330
But bringing it back
to the brain, you know,
00:36:52.330 --> 00:36:53.910
bringing it back to the neuroscience,
00:36:53.910 --> 00:36:56.730
and how this is helping
their child with attention,
00:36:56.730 --> 00:36:59.063
and focus, and how secular it is.
00:37:00.350 --> 00:37:02.490
And that it, actually,
00:37:02.490 --> 00:37:04.350
I've told some people
I've worked with who are,
00:37:04.350 --> 00:37:07.170
you know, devoutly Christian
or devoutly Jewish,
00:37:07.170 --> 00:37:09.730
that these practices can actually enhance
00:37:09.730 --> 00:37:11.440
your connection to your religion.
00:37:11.440 --> 00:37:14.440
They can actually help
you go deeper into prayer,
00:37:14.440 --> 00:37:17.544
or connect with readings or teachings
00:37:17.544 --> 00:37:21.624
that you find so deeply
meaningful in your life.
00:37:21.624 --> 00:37:25.540
So those are just some
suggestions of bridging that gap.
00:37:25.540 --> 00:37:27.790
You know, bringing in the science,
00:37:27.790 --> 00:37:32.560
inviting them to practice
with you and with their child,
00:37:32.560 --> 00:37:35.875
and encouraging them to use it as a tool.
00:37:35.875 --> 00:37:39.078
And also reminding them
that it's part of our,
00:37:39.078 --> 00:37:41.190
it's a natural capacity we all have.
00:37:41.190 --> 00:37:43.840
We're just strengthening
that capacity with practice.
00:37:45.280 --> 00:37:46.410
- [Jeremy] I love that, well said.
00:37:46.410 --> 00:37:48.154
And I think the sort of flip side
00:37:48.154 --> 00:37:50.920
to that question is from
the student perspective.
00:37:50.920 --> 00:37:52.550
I remember when I was a teacher,
00:37:52.550 --> 00:37:54.380
I would get lots of questions like, Mr. S,
00:37:54.380 --> 00:37:55.390
why do we have to learn this?
00:37:55.390 --> 00:37:56.850
Why does this matter?
00:37:56.850 --> 00:37:58.350
I can certainly imagine students asking
00:37:58.350 --> 00:38:00.490
those questions about mindfulness.
00:38:00.490 --> 00:38:01.860
Maybe if they're younger
and they don't quite
00:38:01.860 --> 00:38:04.180
understand the neuroscience implications,
00:38:04.180 --> 00:38:05.580
what could you tell a student to get them
00:38:05.580 --> 00:38:07.950
really excited about this practice?
00:38:07.950 --> 00:38:10.015
- Yeah, so it depends on their age.
00:38:10.015 --> 00:38:12.970
With kids who are younger,
they just want to play.
00:38:12.970 --> 00:38:15.460
So you can do more movement.
00:38:15.460 --> 00:38:17.470
There's a lot of like, you know,
00:38:17.470 --> 00:38:19.240
drumming or playing a song,
00:38:19.240 --> 00:38:20.290
like freeze dance.
00:38:20.290 --> 00:38:22.850
A lot of classic games
that we were taught as kids
00:38:22.850 --> 00:38:26.320
work really well as a
mindfulness teaching tool,
00:38:26.320 --> 00:38:28.010
like red light green light.
00:38:28.010 --> 00:38:32.730
Or what's the other one, I
have Simon says I use a lot.
00:38:32.730 --> 00:38:34.310
And then we play Simon says,
00:38:34.310 --> 00:38:35.770
and then we talk about attention.
00:38:35.770 --> 00:38:37.317
And then I usually use the bell.
00:38:37.317 --> 00:38:38.920
So I'm not even really talking
00:38:38.920 --> 00:38:40.210
about the benefits with the kids,
00:38:40.210 --> 00:38:41.330
with little, little ones.
00:38:41.330 --> 00:38:44.110
I'm just kind of inviting them to play.
00:38:44.110 --> 00:38:45.720
And while we're playing,
00:38:45.720 --> 00:38:47.710
I'm talking a little bit about attention,
00:38:47.710 --> 00:38:51.020
and about dealing with hard feelings.
00:38:51.020 --> 00:38:51.923
With older kids,
00:38:51.923 --> 00:38:54.820
sometimes I'll read a list
with their eyes closed.
00:38:54.820 --> 00:38:57.320
I'll have, I'll read a list of emotions,
00:38:57.320 --> 00:38:59.100
like anger, fear,
00:38:59.100 --> 00:39:01.570
embarrassment, judgment,
00:39:01.570 --> 00:39:03.880
and I'll ask them to just notice
00:39:03.880 --> 00:39:06.010
what happens as they hear those feelings.
00:39:06.010 --> 00:39:08.510
And some are positive, some
are difficult feelings.
00:39:08.510 --> 00:39:10.190
And then when they open their eyes,
00:39:10.190 --> 00:39:12.040
I'll ask them what they noticed.
00:39:12.040 --> 00:39:13.750
How many of you had all those feelings
00:39:13.750 --> 00:39:15.490
at some point in your life?
00:39:15.490 --> 00:39:17.410
Or how many of you, like,
00:39:17.410 --> 00:39:19.647
what feeling really stuck out to you
00:39:19.647 --> 00:39:21.610
when I was reading that list?
00:39:21.610 --> 00:39:25.210
And this is a jumping off
point to have a conversation
00:39:25.210 --> 00:39:27.913
about how mindfulness
helps us deal with these
00:39:27.913 --> 00:39:32.913
incredibly big emotions that
are arising in adolescents.
00:39:33.042 --> 00:39:35.800
I sometimes even tell teens that, like,
00:39:35.800 --> 00:39:36.900
a little bit about what's going on
00:39:36.900 --> 00:39:38.610
in their brain at that age,
00:39:38.610 --> 00:39:40.570
where their dopamine,
00:39:40.570 --> 00:39:42.440
their brain is is a lot more susceptible
00:39:42.440 --> 00:39:43.660
to the effects of dopamine.
00:39:43.660 --> 00:39:44.890
So their highs are higher,
00:39:44.890 --> 00:39:48.960
their lows are lower than adults over 26.
00:39:48.960 --> 00:39:50.220
And just knowing,
00:39:50.220 --> 00:39:52.930
empowering them with that
knowledge I find so important.
00:39:52.930 --> 00:39:53.930
You know, as teens,
00:39:53.930 --> 00:39:55.060
we had health class.
00:39:55.060 --> 00:39:56.930
Mine was not great. (laughs quickly)
00:39:56.930 --> 00:39:59.880
I don't think I remember or
really retained anything,
00:39:59.880 --> 00:40:03.290
but we feel this responsibility
as teachers and adults
00:40:03.290 --> 00:40:05.560
to educate students about their brain,
00:40:05.560 --> 00:40:06.780
about their body.
00:40:06.780 --> 00:40:08.120
But I think the brain,
00:40:08.120 --> 00:40:11.780
regarding when it pertains
to emotional regulation,
00:40:11.780 --> 00:40:13.717
largely gets neglected.
00:40:13.717 --> 00:40:17.140
So I would say empower
them with that knowledge
00:40:18.340 --> 00:40:20.870
and also come back to the emotion,
00:40:20.870 --> 00:40:23.080
and come back to the, um,
00:40:23.080 --> 00:40:26.490
a lot of students can
relate to the difficulty
00:40:26.490 --> 00:40:28.060
in handling difficult emotions.
00:40:28.060 --> 00:40:32.254
And they'll find a purpose and
a connection to the practice
00:40:32.254 --> 00:40:34.053
as it helps them in that regard.
00:40:35.810 --> 00:40:36.850
- [Jeremy] Awesome.
00:40:36.850 --> 00:40:39.520
I know that ratatouille is
getting very crisp in the oven,
00:40:39.520 --> 00:40:42.662
so let me finish up with one
final, very 2020 question.
00:40:42.662 --> 00:40:45.059
Which of course is Kimberly asking,
00:40:45.059 --> 00:40:48.630
any tips for implementing
all of this effectively,
00:40:48.630 --> 00:40:51.400
especially in a remote or
online learning environment.
00:40:51.400 --> 00:40:52.597
I can imagine how challenging
00:40:52.597 --> 00:40:54.818
this might feel even in person,
00:40:54.818 --> 00:40:58.320
but with this extra barrier
between myself and my students,
00:40:58.320 --> 00:41:01.670
how do I cross that divide
and really make this land?
00:41:01.670 --> 00:41:03.070
- That's a great question.
00:41:03.070 --> 00:41:04.290
So actually, that was on one of our
00:41:04.290 --> 00:41:05.270
slides that we didn't get to,
00:41:05.270 --> 00:41:09.100
but it's important to have a
ritual so that kids expect,
00:41:09.100 --> 00:41:10.030
okay, Fridays,
00:41:10.030 --> 00:41:12.040
we're going to do a minute of mindfulness,
00:41:12.040 --> 00:41:13.710
or mindful Mondays,
00:41:13.710 --> 00:41:16.500
so that you have something realistic.
00:41:16.500 --> 00:41:18.850
And you don't want to kind
of overwhelm yourself with
00:41:18.850 --> 00:41:20.540
every day we're going to do a practice,
00:41:20.540 --> 00:41:22.510
and then you're stressing out to find
00:41:22.510 --> 00:41:25.290
new and interesting material every day.
00:41:25.290 --> 00:41:26.950
So I would say start out small,
00:41:26.950 --> 00:41:29.290
so that it's realistic for you.
00:41:29.290 --> 00:41:30.645
Have a little plan in place,
00:41:30.645 --> 00:41:31.997
so that you know what you're doing
00:41:31.997 --> 00:41:33.995
and what your plan is for the week.
00:41:33.995 --> 00:41:36.200
And then you can use resources.
00:41:36.200 --> 00:41:37.650
Again, on the app we have,
00:41:37.650 --> 00:41:40.150
or even on YouTube, you
can just type in Headspace,
00:41:40.150 --> 00:41:42.370
and then you'll get these great videos.
00:41:42.370 --> 00:41:46.210
You can go through the videos
and choose ones that you like,
00:41:46.210 --> 00:41:47.680
that resonate with you.
00:41:47.680 --> 00:41:49.340
And then use it as, like,
00:41:49.340 --> 00:41:52.770
maybe carve out 10 minutes
in your class time online,
00:41:52.770 --> 00:41:54.160
watch the video together,
00:41:54.160 --> 00:41:57.350
and then have your
students be able to share
00:41:57.350 --> 00:41:59.520
what came up for them while
they watched the video.
00:41:59.520 --> 00:42:00.710
What resonated with them.
00:42:00.710 --> 00:42:03.813
So then it's already pre-prepared for you,
00:42:04.714 --> 00:42:06.210
that lesson and that theme,
00:42:06.210 --> 00:42:07.550
and you don't feel like you have to create
00:42:07.550 --> 00:42:10.440
more material and more
stress on you for that,
00:42:10.440 --> 00:42:13.080
because that's, I think all of us,
00:42:13.080 --> 00:42:15.010
just none of us need that right now.
00:42:15.010 --> 00:42:16.284
We want it to be fun.
00:42:16.284 --> 00:42:19.090
We want it to be a relief for us too.
00:42:19.090 --> 00:42:22.370
That when we show that video
or when we offer a practice,
00:42:22.370 --> 00:42:24.120
that it's something we need as well.
00:42:24.120 --> 00:42:28.030
It bridges this gap between
adults and children,
00:42:28.030 --> 00:42:30.030
adults, or teacher and student.
00:42:30.030 --> 00:42:31.630
And it helps bring us together
00:42:31.630 --> 00:42:33.830
as we realize we all need this pause.
00:42:33.830 --> 00:42:38.830
We all need this ritual in our week.
00:42:40.470 --> 00:42:41.736
- [Jeremy] Wow, I love that.
00:42:41.736 --> 00:42:44.690
I think I'll actually give
Danielle the last word here.
00:42:44.690 --> 00:42:46.950
She says, thank you so much for your time,
00:42:46.950 --> 00:42:48.610
and creating this lovely space.
00:42:48.610 --> 00:42:50.640
I can't wait to use
'stop' with my students.
00:42:50.640 --> 00:42:52.070
And I saw so many other comments
00:42:52.070 --> 00:42:53.760
like that throughout the session.
00:42:53.760 --> 00:42:55.440
So I know there's going to be a lot
00:42:55.440 --> 00:42:57.580
of more mindful classrooms and students,
00:42:57.580 --> 00:42:59.840
and educators, starting tomorrow morning.
00:42:59.840 --> 00:43:02.870
So on behalf of the entire Khan community,
00:43:02.870 --> 00:43:04.520
I want to thank the full Headspace team.
00:43:04.520 --> 00:43:05.353
Sam, Alice,
00:43:05.353 --> 00:43:07.280
Leno has been running the
slides behind the scenes,
00:43:07.280 --> 00:43:09.150
for making this possible.
00:43:09.150 --> 00:43:11.910
Thank you for the swag bags
which we'll announce after this.
00:43:11.910 --> 00:43:13.730
And thank you for Headspace for Educators,
00:43:13.730 --> 00:43:17.108
which as you mentioned is free
at headspace.com/educators.
00:43:17.108 --> 00:43:20.130
One last little request of
all the audience members
00:43:20.130 --> 00:43:21.990
before we go back to our ratatouille,
00:43:21.990 --> 00:43:23.860
is you will get a three question survey
00:43:23.860 --> 00:43:25.730
that pops up right after the session.
00:43:25.730 --> 00:43:27.919
Please let us know what you
thought, what was useful.
00:43:27.919 --> 00:43:29.470
And if you'd like to have Headspace
00:43:29.470 --> 00:43:30.800
come back and do other sessions,
00:43:30.800 --> 00:43:32.060
let us know as well,
00:43:32.060 --> 00:43:34.610
because we can always use
that for future programming.
00:43:34.610 --> 00:43:35.740
That being said,
00:43:35.740 --> 00:43:37.870
a huge thank you to everyone for investing
00:43:37.870 --> 00:43:39.610
your scarce time with us tonight.
00:43:39.610 --> 00:43:41.057
Hope it was well worth your while.
00:43:41.057 --> 00:43:42.130
And thank you, Sam,
00:43:42.130 --> 00:43:43.150
Alice, and Leno,
00:43:43.150 --> 00:43:45.390
for sharing your expertise and your wisdom
00:43:45.390 --> 00:43:46.540
across the country.
00:43:46.540 --> 00:43:48.210
Thank you all so much.
00:43:48.210 --> 00:43:49.870
- Thank you, Jeremy.
00:43:49.870 --> 00:43:51.033
- Thank you, Jeremy.
00:43:52.000 --> 00:43:53.050
- [Jeremy] Night all.
|
Worked example: Balancing a simple redox equation | https://www.youtube.com/watch?v=MxjCto0BYd4 | vtt | https://www.youtube.com/api/timedtext?v=MxjCto0BYd4&ei=7lWUZYPqNdSQvdIP0-O5wAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6B3FA907650AC4AEBBE444C06489B8DC5D94987B.7EDFA14E9ADB4FCCC2B4130E6BD50C7B6CCBDBEA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.440 --> 00:00:04.710
- [Instructor] So what we
have here is a redox reaction.
00:00:04.710 --> 00:00:07.350
Things are getting oxidized and reduced,
00:00:07.350 --> 00:00:08.710
thus the name redox,
00:00:08.710 --> 00:00:11.630
but we wanna balance this redox reaction.
00:00:11.630 --> 00:00:14.820
And when we talk about
balancing a redox reaction,
00:00:14.820 --> 00:00:17.930
we want to make sure we conserve mass
00:00:17.930 --> 00:00:20.810
and charge on both sides of this reaction.
00:00:20.810 --> 00:00:22.320
So how do we do that?
00:00:22.320 --> 00:00:25.890
Well, the first step is to
assign oxidation numbers
00:00:25.890 --> 00:00:29.580
or oxidation states to each
of the constituent elements
00:00:29.580 --> 00:00:31.800
on either side of the reaction.
00:00:31.800 --> 00:00:33.380
Then we'll know who's getting oxidized
00:00:33.380 --> 00:00:34.450
and who's getting reduced.
00:00:34.450 --> 00:00:36.420
And then we can set up the half reactions
00:00:36.420 --> 00:00:38.380
which we can then balance.
00:00:38.380 --> 00:00:41.620
All right, so let's first
look at this aluminum
00:00:41.620 --> 00:00:42.710
right over here.
00:00:42.710 --> 00:00:47.430
It has an oxidation state or
an oxidation number of zero.
00:00:47.430 --> 00:00:49.970
It's just aluminum by itself.
00:00:49.970 --> 00:00:52.140
And then we can go to this hydrogen.
00:00:52.140 --> 00:00:54.500
This is really just a
proton right over here.
00:00:54.500 --> 00:00:56.680
It has a plus one charge.
00:00:56.680 --> 00:00:59.510
And so it's hypothetical
charge, you could say.
00:00:59.510 --> 00:01:01.130
Well, that would be plus one as well,
00:01:01.130 --> 00:01:04.440
which would be its oxidation
number or its oxidation state.
00:01:04.440 --> 00:01:08.070
And then when we get onto the
right side of this reaction,
00:01:08.070 --> 00:01:13.070
we see that the aluminum now
has a positive three charge.
00:01:13.280 --> 00:01:17.070
So its oxidation number
would also be positive three.
00:01:17.070 --> 00:01:19.520
And we can see here that the hydrogen,
00:01:19.520 --> 00:01:20.920
and actually now we have two,
00:01:20.920 --> 00:01:22.660
so we're gonna have to
deal with that later on,
00:01:22.660 --> 00:01:23.840
we only have one here.
00:01:23.840 --> 00:01:26.090
But now each of these hydrogens
00:01:26.090 --> 00:01:28.110
have an oxidation number of zero.
00:01:28.110 --> 00:01:31.560
They're not taking up electrons
or giving away electrons.
00:01:31.560 --> 00:01:35.430
You just have two hydrogens
bonded to each other.
00:01:35.430 --> 00:01:37.860
All right, so now that we've
assigned oxidation numbers,
00:01:37.860 --> 00:01:39.660
we can figure out who's getting oxidized
00:01:39.660 --> 00:01:41.700
and who is getting reduced.
00:01:41.700 --> 00:01:43.540
So if you look at the aluminum,
00:01:43.540 --> 00:01:46.310
aluminum goes from an
oxidation number of zero
00:01:46.310 --> 00:01:48.510
to plus three.
00:01:48.510 --> 00:01:51.810
So if your oxidation number is increasing,
00:01:51.810 --> 00:01:54.610
that means you're getting oxidized.
00:01:54.610 --> 00:01:55.760
Oxidized.
00:01:55.760 --> 00:01:57.630
You might also remember OILRIG,
00:01:57.630 --> 00:02:00.400
oxidation is losing electrons.
00:02:00.400 --> 00:02:01.420
Because you're losing electrons,
00:02:01.420 --> 00:02:03.040
you're having a more positive charge.
00:02:03.040 --> 00:02:04.500
But your oxidation number is going up,
00:02:04.500 --> 00:02:06.060
so you're getting oxidized.
00:02:06.060 --> 00:02:08.890
And if you look at the hydrogen,
00:02:08.890 --> 00:02:12.590
we're going from a plus one to a zero.
00:02:12.590 --> 00:02:15.080
If your oxidation number is reducing,
00:02:15.080 --> 00:02:17.160
you are being reduced.
00:02:17.160 --> 00:02:19.610
So reduced.
00:02:19.610 --> 00:02:22.700
So now let's set up both
of the half reactions,
00:02:22.700 --> 00:02:25.260
the oxidized half reaction for aluminum
00:02:25.260 --> 00:02:27.623
and then the reduction for hydrogen.
00:02:28.600 --> 00:02:30.650
So first, for the aluminum,
00:02:30.650 --> 00:02:33.930
we have an aluminum solid
and its half reaction.
00:02:33.930 --> 00:02:38.930
It is going to now a form of aluminum
00:02:40.290 --> 00:02:45.253
with a plus three charge
in an aqueous state.
00:02:46.190 --> 00:02:48.170
So let's first balance this
00:02:48.170 --> 00:02:50.320
for just the number of aluminums we have.
00:02:50.320 --> 00:02:53.770
We have one aluminum on the
left, one aluminum on the right.
00:02:53.770 --> 00:02:55.470
So that seems balanced.
00:02:55.470 --> 00:02:58.110
Now let's try to balance it for charge.
00:02:58.110 --> 00:03:00.100
So we have no charge here.
00:03:00.100 --> 00:03:02.510
So we should have a total
of no charge on the right
00:03:02.510 --> 00:03:04.280
but we have plus three here.
00:03:04.280 --> 00:03:07.560
And so what we need to
do is add some electrons.
00:03:07.560 --> 00:03:12.330
So let me add three
electrons right over here
00:03:12.330 --> 00:03:13.520
and there we have it.
00:03:13.520 --> 00:03:15.940
We have balanced it for charge.
00:03:15.940 --> 00:03:19.920
And now let's think about the hydrogen.
00:03:19.920 --> 00:03:22.113
So if we take,
00:03:23.430 --> 00:03:25.650
we have a proton on the left.
00:03:25.650 --> 00:03:27.050
Let me just do it like this.
00:03:28.370 --> 00:03:30.900
And it's an aqueous solution.
00:03:30.900 --> 00:03:32.590
And then on the right,
00:03:32.590 --> 00:03:36.170
we just have hydrogen molecules,
neutral hydrogen molecules.
00:03:36.170 --> 00:03:39.720
And so first, let us balance
it for the number of hydrogens.
00:03:39.720 --> 00:03:41.960
We have two on the right, one on the left.
00:03:41.960 --> 00:03:44.490
So we're gonna have to
put a two right over here.
00:03:44.490 --> 00:03:47.040
So we've balanced for
the number of hydrogens
00:03:47.040 --> 00:03:50.520
and now let's balance for charge.
00:03:50.520 --> 00:03:51.610
So let's see.
00:03:51.610 --> 00:03:54.780
On the right-hand side,
we have no net charge
00:03:54.780 --> 00:03:56.340
while on the left-hand
side, right over here,
00:03:56.340 --> 00:03:58.870
we have a positive two net charge.
00:03:58.870 --> 00:04:00.390
So in order to balance this,
00:04:00.390 --> 00:04:04.770
I have to put two electrons
on the left-hand side.
00:04:04.770 --> 00:04:06.420
So let me do that here.
00:04:06.420 --> 00:04:09.390
So two electrons, I'm gonna add over here.
00:04:09.390 --> 00:04:12.510
And now it looks like it
is balanced for charge.
00:04:12.510 --> 00:04:14.830
Now, the next thing we wanna do
00:04:14.830 --> 00:04:19.280
is we want to balance
the number of electrons
00:04:19.280 --> 00:04:21.370
that we have on the right-hand side
00:04:21.370 --> 00:04:24.290
and on the left-hand side
in these half reactions.
00:04:24.290 --> 00:04:26.370
And so how can you do that?
00:04:26.370 --> 00:04:29.330
Let's see, you have three
here and you have two here.
00:04:29.330 --> 00:04:31.760
The least common multiple,
involving a little bit
00:04:31.760 --> 00:04:34.220
of your elementary school mathematics here
00:04:34.220 --> 00:04:36.310
of three and two is six.
00:04:36.310 --> 00:04:38.210
So we can get these both to six.
00:04:38.210 --> 00:04:39.483
And how could we do that?
00:04:40.420 --> 00:04:45.070
Well, we could multiply this
top half reaction by two.
00:04:45.070 --> 00:04:46.560
So let me do that.
00:04:46.560 --> 00:04:49.580
So if I multiply this
top half reaction by two,
00:04:49.580 --> 00:04:52.883
and if I multiply this bottom
half reaction by three.
00:04:53.900 --> 00:04:54.830
Why does that work?
00:04:54.830 --> 00:04:56.780
Well, two times three electrons
00:04:56.780 --> 00:04:58.090
is gonna give us six electrons.
00:04:58.090 --> 00:05:01.290
Three times two electrons is
going to get us six electrons.
00:05:01.290 --> 00:05:03.460
And so let me now rewrite this.
00:05:03.460 --> 00:05:07.070
So if I multiply by two, we're
gonna have two aluminums.
00:05:07.070 --> 00:05:11.780
So we're gonna have two
aluminums, the solid state.
00:05:11.780 --> 00:05:15.020
And then on the right hand
side of this half reaction,
00:05:15.020 --> 00:05:16.750
I'm multiplying everything by two.
00:05:16.750 --> 00:05:21.750
So now I have two aluminums
plus three in aqueous solution.
00:05:23.060 --> 00:05:26.010
And then I'm multiplying these
electrons by two as well.
00:05:26.010 --> 00:05:28.920
So plus six electrons.
00:05:28.920 --> 00:05:30.270
And now let me do this down here.
00:05:30.270 --> 00:05:31.900
Three times two electrons,
00:05:31.900 --> 00:05:35.990
that is going to give us six electrons.
00:05:35.990 --> 00:05:39.060
And then I'm going to multiply
this three times this two.
00:05:39.060 --> 00:05:41.640
So that's gonna give us
six hydrogen protons,
00:05:41.640 --> 00:05:42.960
I guess I could say.
00:05:42.960 --> 00:05:46.910
So plus six hydrogen protons
00:05:46.910 --> 00:05:49.540
that are in an aqueous solution.
00:05:49.540 --> 00:05:52.920
And then on the right hand
side, if I multiplied by three,
00:05:52.920 --> 00:05:56.120
I have three hydrogen molecules,
00:05:56.120 --> 00:05:58.380
each of them with two hydrogen atoms.
00:05:58.380 --> 00:06:00.750
And so now I have balanced
00:06:00.750 --> 00:06:03.340
the number of electrons on both sides.
00:06:03.340 --> 00:06:06.070
And now I'm gonna add
these two half reactions.
00:06:06.070 --> 00:06:08.870
And if I add the two half
reactions, what do I get?
00:06:08.870 --> 00:06:10.820
And let me do it down here.
00:06:10.820 --> 00:06:13.630
So on the left-hand side,
I'm just going to add up
00:06:13.630 --> 00:06:15.790
all of this stuff right over here.
00:06:15.790 --> 00:06:20.790
So I'm gonna get six
electrons plus two aluminums,
00:06:23.350 --> 00:06:28.350
plus six hydrogen protons,
plus six hydrogen protons.
00:06:30.070 --> 00:06:32.330
And then on the right-hand side,
00:06:32.330 --> 00:06:36.560
I am going to add up all of this stuff.
00:06:36.560 --> 00:06:39.250
So I have those two aluminums,
00:06:39.250 --> 00:06:43.870
now with a plus three charge
in an aqueous solution.
00:06:43.870 --> 00:06:47.100
I'm going to have the three hydrogens,
00:06:47.100 --> 00:06:48.960
three hydrogen molecules I should say.
00:06:48.960 --> 00:06:50.630
There's actually six hydrogens here.
00:06:50.630 --> 00:06:52.760
And then I have the six electrons,
00:06:52.760 --> 00:06:54.510
plus six electrons.
00:06:54.510 --> 00:06:56.180
And I have six electrons on the left,
00:06:56.180 --> 00:06:57.300
six electrons on the right.
00:06:57.300 --> 00:06:59.570
I could cancel those out.
00:06:59.570 --> 00:07:04.570
And then what I have here is
our balanced redox reaction.
00:07:04.830 --> 00:07:08.680
Balanced for both mass and charge.
00:07:08.680 --> 00:07:10.173
And we are done.
|
Worked example: Using oxidation numbers to identify oxidation and reduction | https://www.youtube.com/watch?v=CsgVO0ldmQs | vtt | https://www.youtube.com/api/timedtext?v=CsgVO0ldmQs&ei=7lWUZdyQLsPCp-oP8quxoAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1CB47FC76F2E200D8685A0D5065CDC4415E4E497.223294F5A390ADA8CFED235E296BCAF76006939B&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.230 --> 00:00:02.370
- [Instructor] What we
have here is a reaction
00:00:02.370 --> 00:00:06.500
that involves iodine,
manganese, oxygen, and hydrogen.
00:00:06.500 --> 00:00:08.460
And what we wanna do in this video
00:00:08.460 --> 00:00:11.410
is think about which of the
elements are being oxidized
00:00:11.410 --> 00:00:13.750
in this reaction and which of the elements
00:00:13.750 --> 00:00:16.630
are being reduced in this reaction.
00:00:16.630 --> 00:00:19.000
And pause this video and see
if you can figure that out
00:00:19.000 --> 00:00:21.023
before we work through it together.
00:00:22.090 --> 00:00:24.140
All right, now let's
work through it together.
00:00:24.140 --> 00:00:26.470
And the way that I will tackle it,
00:00:26.470 --> 00:00:29.470
and you might have tackled it
or I suggest you tackle it,
00:00:29.470 --> 00:00:32.490
is to figure out the oxidation numbers
00:00:32.490 --> 00:00:35.360
for each of the elements
as we go into the reaction,
00:00:35.360 --> 00:00:37.090
as they are entering the action
00:00:37.090 --> 00:00:39.070
and as they are exiting the reaction,
00:00:39.070 --> 00:00:43.490
or I guess you could say on
either side of the reaction.
00:00:43.490 --> 00:00:47.460
So first, let's look at
this iodine right over here.
00:00:47.460 --> 00:00:51.150
Well, each iodine has
a negative one charge.
00:00:51.150 --> 00:00:54.180
And so it's quote hypothetical charge,
00:00:54.180 --> 00:00:56.270
which isn't so hypothetical in this case,
00:00:56.270 --> 00:01:01.270
which would be its oxidation
number is negative one.
00:01:01.440 --> 00:01:03.890
Now let's move over to
this permanganate ion
00:01:03.890 --> 00:01:05.430
right over here.
00:01:05.430 --> 00:01:07.270
Now this one's a little bit more involved
00:01:07.270 --> 00:01:09.480
to figure out the oxidation numbers.
00:01:09.480 --> 00:01:11.510
But what we generally remember
00:01:11.510 --> 00:01:14.980
is that oxygen is quite electronegative.
00:01:14.980 --> 00:01:18.150
It is likely to hog two
electrons and when we think
00:01:18.150 --> 00:01:21.310
about hypothetical charge
with oxidation numbers,
00:01:21.310 --> 00:01:26.010
oxygen is going to have eight
negative two oxidation number
00:01:26.010 --> 00:01:29.430
because it likes to hog
those two extra electrons.
00:01:29.430 --> 00:01:31.730
And so if each of these four oxygens
00:01:31.730 --> 00:01:34.880
has a hypothetical charge of negative two,
00:01:34.880 --> 00:01:37.720
that would be negative eight total
00:01:37.720 --> 00:01:41.560
and we see that this entire
ion has a negative one charge.
00:01:41.560 --> 00:01:44.440
So that means that the manganese
00:01:44.440 --> 00:01:46.350
has to have a hypothetical charge,
00:01:46.350 --> 00:01:50.880
an oxidation number of plus seven.
00:01:50.880 --> 00:01:52.490
So I just wanna review that one again
00:01:52.490 --> 00:01:54.240
because this is a little bit involved.
00:01:54.240 --> 00:01:56.900
We said oxygen, we're gonna
go with the negative two
00:01:56.900 --> 00:01:59.720
'cause it likes to hog two electrons.
00:01:59.720 --> 00:02:00.930
We have four of them.
00:02:00.930 --> 00:02:02.160
So if you add all that together,
00:02:02.160 --> 00:02:03.600
you're at negative eight
00:02:03.600 --> 00:02:05.920
and the whole ion has a negative one.
00:02:05.920 --> 00:02:08.680
So what plus a negative eight
is going to be negative one?
00:02:08.680 --> 00:02:11.180
Well, positive seven.
00:02:11.180 --> 00:02:14.150
And so that's manganese's oxidation number
00:02:14.150 --> 00:02:17.530
as we enter into the reaction
on this side of the reaction.
00:02:17.530 --> 00:02:21.540
And then let's look at the water.
00:02:21.540 --> 00:02:23.860
Well, water, both the hydrogen and oxygen,
00:02:23.860 --> 00:02:25.650
these are ones you'll see a lot.
00:02:25.650 --> 00:02:27.490
This oxygen is going to have
00:02:27.490 --> 00:02:29.280
a negative two oxidation number
00:02:29.280 --> 00:02:31.580
and each of those hydrogen atoms
00:02:31.580 --> 00:02:34.870
are going to have a plus
one oxidation number
00:02:34.870 --> 00:02:37.110
because in that water molecule.
00:02:37.110 --> 00:02:39.170
We know that the oxygen
hogs the electrons,
00:02:39.170 --> 00:02:40.600
these are covalent bonds.
00:02:40.600 --> 00:02:44.570
But if we had to assign kind
of a hypothetical charge
00:02:44.570 --> 00:02:45.940
where we said, all right, well,
00:02:45.940 --> 00:02:48.820
let's just say the oxygen
takes those two electrons
00:02:48.820 --> 00:02:51.010
and each of those hydrogens
will lose an electron
00:02:51.010 --> 00:02:53.560
and have a plus one oxidation number.
00:02:53.560 --> 00:02:56.960
Now let's look at the right-hand
side of this reaction.
00:02:56.960 --> 00:02:59.690
What's going on with these iodines here?
00:02:59.690 --> 00:03:01.800
Well, in this iodine molecule,
00:03:01.800 --> 00:03:04.090
they aren't gaining or losing electrons,
00:03:04.090 --> 00:03:07.840
so your oxidation number is zero.
00:03:07.840 --> 00:03:11.363
Then let's move on to the next compound.
00:03:12.300 --> 00:03:13.520
Each of these oxygens
00:03:13.520 --> 00:03:16.670
have an oxidation number of negative two.
00:03:16.670 --> 00:03:19.680
And so what would be
manganese's oxidation number?
00:03:19.680 --> 00:03:21.480
Well, the compound is neutral.
00:03:21.480 --> 00:03:24.540
Two oxygens at negative two
is gonna be negative four.
00:03:24.540 --> 00:03:25.390
So in order to be neutral,
00:03:25.390 --> 00:03:27.630
the manganese must be at plus four,
00:03:27.630 --> 00:03:30.400
an oxidation number of plus four.
00:03:30.400 --> 00:03:32.860
And then last but not least,
00:03:32.860 --> 00:03:37.180
if we look at these hydroxide anions,
00:03:37.180 --> 00:03:38.730
each of the oxygen is going to have
00:03:38.730 --> 00:03:41.040
a negative two oxidation number.
00:03:41.040 --> 00:03:43.530
And then the hydrogen is
going to have a plus one
00:03:43.530 --> 00:03:45.040
and we can confirm that that makes sense.
00:03:45.040 --> 00:03:48.650
Negative two plus one is
going to be negative one
00:03:48.650 --> 00:03:51.280
for each of these ions.
00:03:51.280 --> 00:03:53.750
So now, let's just think
about who's been oxidized
00:03:53.750 --> 00:03:55.060
and who's been reduced.
00:03:55.060 --> 00:03:59.700
And remember, oxidation
is losing electrons.
00:03:59.700 --> 00:04:03.200
Oil rig, reduction is gaining electrons,
00:04:03.200 --> 00:04:07.180
or reduction is a reduction
in the oxidation number.
00:04:07.180 --> 00:04:10.300
So first, let's look at the iodine.
00:04:10.300 --> 00:04:14.913
We go from an oxidation number
of negative one to zero.
00:04:15.890 --> 00:04:20.310
So to go from an oxidation
number of negative one to zero,
00:04:20.310 --> 00:04:23.100
you need to lose electrons.
00:04:23.100 --> 00:04:25.690
So it has been oxidized.
00:04:25.690 --> 00:04:27.340
Oxidized.
00:04:27.340 --> 00:04:28.220
Let me write that down.
00:04:28.220 --> 00:04:31.370
The iodine has been oxidized.
00:04:31.370 --> 00:04:33.560
Now let's look at the manganese.
00:04:33.560 --> 00:04:37.060
We go from a plus seven to a plus four.
00:04:37.060 --> 00:04:39.900
Our oxidation number has gone down.
00:04:39.900 --> 00:04:42.063
It has been reduced.
00:04:44.030 --> 00:04:45.840
Now let's look at the oxygen.
00:04:45.840 --> 00:04:49.010
Well, everywhere, the oxygen
has an oxidation number
00:04:49.010 --> 00:04:51.650
of negative two, so nothing there.
00:04:51.650 --> 00:04:53.710
And then same thing for the hydrogens.
00:04:53.710 --> 00:04:56.690
Plus one on both sides, so nothing there.
00:04:56.690 --> 00:04:58.590
So the iodine has been oxidized
00:04:58.590 --> 00:05:01.203
and the manganese has been reduced.
|
Worked example: Relating reaction stoichiometry and the ideal gas law | https://www.youtube.com/watch?v=FRNTJmqMko8 | vtt | https://www.youtube.com/api/timedtext?v=FRNTJmqMko8&ei=7lWUZY6mLqnDmLAPs-ONoAs&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=30CCBE7D3A5CC340AF883B66389400B3BAAAC122.C3511FA615AEAC957232526378802FE5A10BB4BA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:01.460
- [Instructor] So we're
told that silver oxide
00:00:01.460 --> 00:00:04.260
decomposes according to
the following equation.
00:00:04.260 --> 00:00:06.070
So for every two moles of silver oxide
00:00:06.070 --> 00:00:08.940
it decomposes into four moles of silver
00:00:08.940 --> 00:00:11.764
and one mole of molecular oxygen.
00:00:11.764 --> 00:00:15.670
How many grams of silver
oxide are required to produce
00:00:15.670 --> 00:00:19.640
1.50 liters of oxygen gas
00:00:19.640 --> 00:00:23.690
at 1.22 atmospheres
and 30 degrees Celsius?
00:00:23.690 --> 00:00:25.440
So I want you to pause this video
00:00:25.440 --> 00:00:26.740
and see if you can figure this out.
00:00:26.740 --> 00:00:28.530
And I'll give you a little bit of a hint.
00:00:28.530 --> 00:00:31.310
So you're used to saying,
well, if I know how many moles
00:00:31.310 --> 00:00:33.710
of oxygen I need to produce,
00:00:33.710 --> 00:00:36.910
then I need twice as many
moles of silver oxide
00:00:36.910 --> 00:00:38.870
because the ratio of moles of silver oxide
00:00:38.870 --> 00:00:41.440
to molecular oxygen is two to one.
00:00:41.440 --> 00:00:43.670
But they don't tell us how many moles
00:00:43.670 --> 00:00:45.620
of molecular oxygen we're producing.
00:00:45.620 --> 00:00:48.450
They give us volume and
pressure and temperature.
00:00:48.450 --> 00:00:51.270
But a little bit of a
hint is the ideal gas law.
00:00:51.270 --> 00:00:56.060
It tells us that PV is equal to NRT.
00:00:56.060 --> 00:00:57.330
And if we solve for N,
00:00:57.330 --> 00:00:59.060
remember N is just the number of moles.
00:00:59.060 --> 00:01:01.360
So we divide both sides by RT.
00:01:01.360 --> 00:01:06.290
We get PV over RT is equal to N.
00:01:06.290 --> 00:01:08.900
And it looks like they
gave us all of this stuff.
00:01:08.900 --> 00:01:11.130
The pressure is right over here.
00:01:11.130 --> 00:01:13.820
The volume is right over here.
00:01:13.820 --> 00:01:16.380
The ideal gas constant,
we can look that up,
00:01:16.380 --> 00:01:18.120
and then temperature,
we just have to convert
00:01:18.120 --> 00:01:21.110
this right over here into Kelvin.
00:01:21.110 --> 00:01:22.500
And to help you there,
00:01:22.500 --> 00:01:26.320
I will give you some of the
constants and the conversions.
00:01:26.320 --> 00:01:28.863
And so see if you can
have a go at this now.
00:01:29.740 --> 00:01:32.520
All right, now let's work
through this together.
00:01:32.520 --> 00:01:35.960
So the number of moles of oxygen
00:01:35.960 --> 00:01:39.630
is going to be equal to
the pressure of our oxygen.
00:01:39.630 --> 00:01:44.320
So 1.22 atmospheres
00:01:44.320 --> 00:01:46.160
times the volume of oxygen,
00:01:46.160 --> 00:01:49.970
times 1.50 liters
00:01:49.970 --> 00:01:52.520
divided by the ideal gas constant.
00:01:52.520 --> 00:01:54.100
And we have to use the right one
00:01:54.100 --> 00:01:57.260
that is going to deal with
atmospheres, liters and Kelvin.
00:01:57.260 --> 00:02:01.290
So if we're dealing with
atmospheres, liters and Kelvin,
00:02:01.290 --> 00:02:04.960
then we'll use this ideal
gas constant right over here.
00:02:04.960 --> 00:02:06.953
So divided by 0.08206.
00:02:10.180 --> 00:02:11.130
I'll write the units here.
00:02:11.130 --> 00:02:13.763
Liters, atmospheres,
00:02:15.370 --> 00:02:18.340
divided by moles,
00:02:18.340 --> 00:02:21.330
and also divided by Kelvin.
00:02:21.330 --> 00:02:23.070
So this is our ideal gas constant,
00:02:23.070 --> 00:02:24.850
and then we're going to multiply that
00:02:24.850 --> 00:02:27.960
times the temperature in Kelvin.
00:02:27.960 --> 00:02:30.130
Now they only gave us two
significant figures here.
00:02:30.130 --> 00:02:31.700
They're only going to the ones place.
00:02:31.700 --> 00:02:33.530
So let's only go only go to the ones place
00:02:33.530 --> 00:02:34.950
when we convert to Kelvin.
00:02:34.950 --> 00:02:37.700
So let's just add 273 to this.
00:02:37.700 --> 00:02:40.290
So this is going to be times 303 Kelvin.
00:02:43.420 --> 00:02:45.010
And let's make sure the units work out.
00:02:45.010 --> 00:02:47.880
That cancels with that,
that cancels with that,
00:02:47.880 --> 00:02:49.130
that cancels with that.
00:02:49.130 --> 00:02:52.310
And if we have a dividing
by moles in the denominator,
00:02:52.310 --> 00:02:53.960
then that's just going to become a moles
00:02:53.960 --> 00:02:55.360
eventually in the numerator.
00:02:56.231 --> 00:02:58.000
So this is going to be
approximately equal to
00:02:58.000 --> 00:03:03.000
1.22 times 1.5 divided by 0.08206.
00:03:07.880 --> 00:03:10.770
And then we're going to
also divide that whole thing
00:03:10.770 --> 00:03:13.270
by 303.
00:03:13.270 --> 00:03:15.040
Is equal to this.
00:03:15.040 --> 00:03:16.510
And let's see how many
significant figures.
00:03:16.510 --> 00:03:18.960
We have three, we have three,
00:03:18.960 --> 00:03:22.250
we have a lot more than
three right over here.
00:03:22.250 --> 00:03:24.730
And then we have three right over here.
00:03:24.730 --> 00:03:27.160
So I'm going to round to
three significant figures.
00:03:27.160 --> 00:03:29.523
So 0.0736.
00:03:33.200 --> 00:03:38.200
So 0.0736 moles
00:03:39.530 --> 00:03:43.780
of molecular oxygen is how many we need,
00:03:43.780 --> 00:03:46.060
how much we need to
produce to get this volume
00:03:46.060 --> 00:03:47.990
at this pressure at this temperature.
00:03:47.990 --> 00:03:50.780
And so we're going to need two times this
00:03:50.780 --> 00:03:53.390
number of moles of silver oxide,
00:03:53.390 --> 00:03:55.700
because notice for every one mole
00:03:55.700 --> 00:03:57.010
of molecular oxygen we produce
00:03:57.010 --> 00:03:59.890
we need twice as many
moles of silver oxide.
00:03:59.890 --> 00:04:02.190
So let's multiply this times two.
00:04:02.190 --> 00:04:04.920
So, times two gets us,
00:04:04.920 --> 00:04:08.477
and once again, three
significant figures, 0.147.
00:04:10.420 --> 00:04:15.250
So this is approximately 0.147 moles
00:04:16.320 --> 00:04:21.320
of silver oxide that we need to produce.
00:04:21.650 --> 00:04:23.330
But they're not asking us how many moles
00:04:23.330 --> 00:04:24.630
of silver oxide are needed.
00:04:24.630 --> 00:04:26.440
They're asking us how many grams.
00:04:26.440 --> 00:04:30.400
So we just have to multiply
this times the molar mass.
00:04:30.400 --> 00:04:33.480
So let's first figure out the
molar mass of silver oxide.
00:04:33.480 --> 00:04:34.380
I'll write it right over here.
00:04:34.380 --> 00:04:39.180
So silver oxide's molar
mass is going to be
00:04:39.180 --> 00:04:42.540
whatever the molar mass
of silver is times two,
00:04:42.540 --> 00:04:45.290
plus the molar mass of oxygen.
00:04:45.290 --> 00:04:48.553
And so let me get the periodic
table of elements out.
00:04:49.920 --> 00:04:54.503
Molar mass of silver is
107.87, oxygen, 16.00.
00:04:55.500 --> 00:05:00.500
So that gives us 107.87
for each of the silvers.
00:05:01.570 --> 00:05:06.150
And then plus 16.00 for
the oxygen, which gives us
00:05:08.409 --> 00:05:13.409
107.87 times two is equal to that.
00:05:14.930 --> 00:05:16.935
Let's see it goes to the hundredth place.
00:05:16.935 --> 00:05:20.440
And then plus 16.00 also
goes to the hundreds place.
00:05:20.440 --> 00:05:22.960
So we'll go to 231.74.
00:05:22.960 --> 00:05:24.030
Also going to the hundreds place.
00:05:24.030 --> 00:05:25.680
I'm just keeping track of
the significant figures
00:05:25.680 --> 00:05:26.880
when we're adding.
00:05:26.880 --> 00:05:31.880
So this is 231.74 grams
per mole of silver oxide.
00:05:35.110 --> 00:05:37.380
And so if we take the
moles of silver oxide
00:05:37.380 --> 00:05:42.380
and we multiply that times
231.74 grams per mole,
00:05:43.860 --> 00:05:45.480
and notice the moles cancel out,
00:05:45.480 --> 00:05:47.840
and we're just left with the
grams, which is what we want.
00:05:47.840 --> 00:05:49.810
This is going to be
approximately equal to,
00:05:49.810 --> 00:05:51.580
and we're going to end up
with three significant figures
00:05:51.580 --> 00:05:54.070
'cause we have three here and five here.
00:05:54.070 --> 00:05:57.863
So we're going to take that
and multiply it by 0.147.
00:06:00.890 --> 00:06:01.940
Gives us this.
00:06:01.940 --> 00:06:06.460
And three significant
figures would be 34.1.
00:06:06.460 --> 00:06:10.170
Approximately 34.1 grams
00:06:10.170 --> 00:06:15.170
of silver oxide is required
to produce this much oxygen.
|
Worked example: Calculating the amount of product formed from a limiting reactant | https://www.youtube.com/watch?v=cVqEfuJBVd8 | vtt | https://www.youtube.com/api/timedtext?v=cVqEfuJBVd8&ei=7lWUZfy9I72wp-oP1dG_2Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=05D5C87F9B957762984AF8A8D5C5D519492BA38A.0FC6F728A844479EFDEC31DB574BC4BE4BA93619&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.950 --> 00:00:02.540
- [Instructor] So right
here, we have a reaction
00:00:02.540 --> 00:00:05.265
where you can take some
carbon monoxide gas
00:00:05.265 --> 00:00:09.070
and some hydrogen gas,
and when they react,
00:00:09.070 --> 00:00:10.660
you're gonna produce methanol,
00:00:10.660 --> 00:00:11.910
and this is actually pretty interesting.
00:00:11.910 --> 00:00:13.410
Methanol has many applications.
00:00:13.410 --> 00:00:16.818
One of them it's actually race car fuel.
00:00:16.818 --> 00:00:20.210
But we're gonna do is
study how much methanol
00:00:20.210 --> 00:00:22.170
we can produce if we have a certain amount
00:00:22.170 --> 00:00:25.430
of carbon monoxide and molecular hydrogen.
00:00:25.430 --> 00:00:27.950
So let's say, we have 356
grams of carbon monoxide
00:00:27.950 --> 00:00:31.310
and 65.0 grams of molecular hydrogen.
00:00:31.310 --> 00:00:32.900
Pause this video, and based on this,
00:00:32.900 --> 00:00:37.023
figure out how many grams
of methanol will we produce?
00:00:38.130 --> 00:00:42.030
Well, a good place to start
is by converting these numbers
00:00:42.030 --> 00:00:44.277
of carbon monoxide, this
amount of carbon monoxide,
00:00:44.277 --> 00:00:48.040
and molecular hydrogen into moles.
00:00:48.040 --> 00:00:49.810
And so to do that, we can take out
00:00:49.810 --> 00:00:52.280
a periodic table of elements
00:00:52.280 --> 00:00:54.766
and the molar mass of carbon monoxide,
00:00:54.766 --> 00:00:58.490
you can look at the molar
masses of carbon and oxygen
00:00:58.490 --> 00:00:59.780
and add them together.
00:00:59.780 --> 00:01:04.780
So 12.01 plus 16, that is going
to be 28.01 grams per mole.
00:01:09.790 --> 00:01:12.860
And if we want to convert to moles,
00:01:12.860 --> 00:01:17.550
we're gonna have to multiply
this times moles per gram.
00:01:17.550 --> 00:01:19.690
And so for every one mole, we have,
00:01:19.690 --> 00:01:24.690
we just figured it out 28.01 grams.
00:01:24.790 --> 00:01:27.920
And this is going to
be approximately equal
00:01:27.920 --> 00:01:32.920
to 356 divided by 28.01
is equal to, let's see,
00:01:34.477 --> 00:01:37.520
and we have three significant
figures here and four here.
00:01:37.520 --> 00:01:42.120
So I'll round to 12.7 moles,
approximately 12.7 moles.
00:01:44.280 --> 00:01:45.578
And then we could do the same thing
00:01:45.578 --> 00:01:48.390
for the molecular hydrogen.
00:01:48.390 --> 00:01:53.050
And here we're going, for every one mole,
00:01:53.050 --> 00:01:56.288
how many grams or what's our molar mass
00:01:56.288 --> 00:01:58.360
of our molecular hydrogen?
00:01:58.360 --> 00:02:03.360
Well, each hydrogen atom
is 1.008 grams per mole,
00:02:04.150 --> 00:02:06.950
but each molecule of hydrogen
has two hydrogens in it,
00:02:06.950 --> 00:02:11.348
so it's gonna be two times six, so 2.016.
00:02:11.348 --> 00:02:16.348
2.016 grams per mole or one
mole for every 2.016 grams.
00:02:17.140 --> 00:02:19.930
And so this is going to
be approximately equal to,
00:02:19.930 --> 00:02:21.303
get the calculator out again,
00:02:21.303 --> 00:02:26.303
65 divided by 2.016 is equal is to that.
00:02:28.020 --> 00:02:29.460
And we have three significant figures,
00:02:29.460 --> 00:02:31.890
four significant figures,
so if I round to three,
00:02:31.890 --> 00:02:36.890
it's approximately 32.2
moles, so 32.2 moles.
00:02:40.180 --> 00:02:42.385
And so the first thing to think about is,
00:02:42.385 --> 00:02:46.056
in our reaction for every
one mole of carbon monoxide,
00:02:46.056 --> 00:02:49.420
we use two moles of molecular hydrogen,
00:02:49.420 --> 00:02:53.630
and then that produces one mole
of methanol right over here.
00:02:53.630 --> 00:02:56.053
And so however much
carbon monoxide we have
00:02:56.053 --> 00:02:58.970
in terms of moles, we need
twice as much hydrogen.
00:02:58.970 --> 00:03:01.350
And so we see here a molecular hydrogen.
00:03:01.350 --> 00:03:05.710
And so two times 12.7 is going to be 25.4.
00:03:05.710 --> 00:03:08.837
So we actually have more than
enough molecular hydrogen.
00:03:08.837 --> 00:03:13.833
And so we are going to use 25.4
moles of molecular hydrogen.
00:03:18.400 --> 00:03:19.420
How did I do that?
00:03:19.420 --> 00:03:20.550
Well, it's gonna be twice the number
00:03:20.550 --> 00:03:21.780
of moles of carbon monoxide,
00:03:21.780 --> 00:03:25.930
twice this number right over
here is this right over here.
00:03:25.930 --> 00:03:27.010
And we can immediately see
00:03:27.010 --> 00:03:28.760
how much we're gonna have leftover.
00:03:28.760 --> 00:03:30.483
We're going to have leftover,
00:03:31.420 --> 00:03:36.420
leftover 32.2 minus 25.4 is 6.8,
00:03:36.513 --> 00:03:40.650
6.8 moles of molecular hydrogen.
00:03:40.650 --> 00:03:43.840
And how many moles of
methanol we're gonna produce?
00:03:43.840 --> 00:03:45.220
Well, the same number of moles
00:03:45.220 --> 00:03:46.920
of carbon monoxide that we're using up.
00:03:46.920 --> 00:03:48.336
It's a one-to-one ratio.
00:03:48.336 --> 00:03:53.080
So we're going to produce
12.7 moles of methanol.
00:03:53.080 --> 00:03:54.310
And so let me write that a year.
00:03:54.310 --> 00:03:59.310
So if I have 12.7 mole of methanol, CH3OH,
00:04:02.221 --> 00:04:04.310
how do I convert this to grams?
00:04:04.310 --> 00:04:06.554
Well, I have to multiply
this times a certain number
00:04:06.554 --> 00:04:11.554
of grams per mole so that
we can cancel out the moles
00:04:12.910 --> 00:04:15.320
or essentially the molar mass of methanol,
00:04:15.320 --> 00:04:18.030
and to figure out the
molar mass of methanol,
00:04:18.030 --> 00:04:19.606
we'll get our calculator out again.
00:04:19.606 --> 00:04:22.870
So we have four hydrogens here.
00:04:22.870 --> 00:04:27.870
So four times 1.008 is going to be that.
00:04:28.920 --> 00:04:30.230
And then to that,
00:04:30.230 --> 00:04:32.970
we're going to add the
molar mass of carbon
00:04:32.970 --> 00:04:36.370
'cause we have one carbon plus 12.01,
00:04:36.370 --> 00:04:39.512
and then plus one oxygen
in that methanol molecule
00:04:39.512 --> 00:04:40.830
is equal to that.
00:04:40.830 --> 00:04:44.240
And let's see, we will
round to the hundreds place
00:04:44.240 --> 00:04:46.810
because our oxygen and carbon molar mass
00:04:46.810 --> 00:04:49.310
is only went to the hundreds
place here, so 32.04,
00:04:52.557 --> 00:04:54.307
32.04 grams per mole.
00:04:57.000 --> 00:05:02.000
So we have 12.7 moles
times 32.04 grams per mole
00:05:04.812 --> 00:05:07.810
will tell us that we are going to produce
00:05:07.810 --> 00:05:09.250
that much methanol.
00:05:09.250 --> 00:05:11.300
And let's see, we have three
significant figures, four,
00:05:11.300 --> 00:05:12.690
so I'll round to three.
00:05:12.690 --> 00:05:15.740
So approximately 407 grams of methanol,
00:05:15.740 --> 00:05:20.643
407 grams of CH3OH.
00:05:22.840 --> 00:05:24.600
Now the next question is,
00:05:24.600 --> 00:05:28.870
what's the mass of hydrogen
that we have leftover?
00:05:28.870 --> 00:05:31.620
Well, we just have to
convert our moles of hydrogen
00:05:31.620 --> 00:05:34.100
that we have leftover to grams,
00:05:34.100 --> 00:05:39.100
6.8 moles of molecular hydrogen times,
00:05:39.210 --> 00:05:41.090
the molar mass here in grams per mole
00:05:41.090 --> 00:05:43.430
is just gonna be the reciprocal
of this right over here,
00:05:43.430 --> 00:05:45.293
so times 2.016,
00:05:49.152 --> 00:05:53.150
2.016 is going to give
us this right over here.
00:05:53.150 --> 00:05:57.240
And if we were rounding to
two significant figures,
00:05:57.240 --> 00:05:59.220
which I have right over here,
00:05:59.220 --> 00:06:03.770
that is going to give us
approximately 14 grams,
00:06:03.770 --> 00:06:07.810
approximately 14 grams
of molecular hydrogen
00:06:07.810 --> 00:06:09.833
is leftover, leftover.
00:06:11.250 --> 00:06:12.440
So we used a good bit of it.
00:06:12.440 --> 00:06:16.980
We used about 51 grams and
we have 14 grams leftover
00:06:16.980 --> 00:06:18.580
and it was carbon monoxide
00:06:18.580 --> 00:06:20.830
that was actually the
limiting reactant here.
|
Worked example: Calculating amounts of reactants and products | https://www.youtube.com/watch?v=9ujy3qfa7jI | vtt | https://www.youtube.com/api/timedtext?v=9ujy3qfa7jI&ei=7lWUZc-8I5boxN8P3I-8EA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=25352EDB299199E7C1F4FE4163D8846DA53864DD.A89D2AB6DE9565C9D4F64EF22CAE1BF68A8000F2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.270 --> 00:00:02.980
- [Instructor] We're told that glucose,
00:00:02.980 --> 00:00:06.570
C6H12O6, reacts with oxygen
00:00:06.570 --> 00:00:09.960
to give carbon dioxide and water.
00:00:09.960 --> 00:00:13.100
What mass of oxygen, in grams,
00:00:13.100 --> 00:00:15.950
is required for complete reaction
00:00:15.950 --> 00:00:20.380
of 25.0 grams of glucose?
00:00:20.380 --> 00:00:22.830
What masses of carbon dioxide and water,
00:00:22.830 --> 00:00:25.190
in grams, are formed?
00:00:25.190 --> 00:00:27.340
So, pause this video and see
if you can have a go at this
00:00:27.340 --> 00:00:29.660
and then we'll work through this together.
00:00:29.660 --> 00:00:33.090
All right, now first let's
just set up the reaction.
00:00:33.090 --> 00:00:34.500
So, this is going to be,
00:00:34.500 --> 00:00:37.010
we have glucose, so that is C6H12O6,
00:00:40.370 --> 00:00:42.200
is going to react with oxygen.
00:00:42.200 --> 00:00:45.633
Now, oxygen in its molecular
form is going to be O2.
00:00:46.500 --> 00:00:51.500
And what it gives is
carbon dioxide and water.
00:00:52.640 --> 00:00:54.970
Plus water.
00:00:54.970 --> 00:00:56.890
Now the next question is are we balanced.
00:00:56.890 --> 00:00:58.710
Do we have a conservation of mass here?
00:00:58.710 --> 00:01:01.370
And let's just go element by element.
00:01:01.370 --> 00:01:03.750
So first let's focus on the carbons.
00:01:03.750 --> 00:01:05.250
So, we have six carbons
00:01:05.250 --> 00:01:07.300
on the left-hand side of this reaction.
00:01:07.300 --> 00:01:10.330
How many carbons do we have
on the right-hand side?
00:01:10.330 --> 00:01:12.800
Well, right now we only have one carbon
00:01:12.800 --> 00:01:15.130
in this carbon dioxide molecule.
00:01:15.130 --> 00:01:17.240
So if we want the carbons to be conserved
00:01:17.240 --> 00:01:20.090
we need to have six carbons on
the right-hand side as well.
00:01:20.090 --> 00:01:23.530
So let me see what'll happen
when I throw a six there.
00:01:23.530 --> 00:01:25.070
So now my carbons are balanced:
00:01:25.070 --> 00:01:27.170
six on the left, six on the right.
00:01:27.170 --> 00:01:29.690
Now let's look at the other elements.
00:01:29.690 --> 00:01:34.130
So on the left-hand side I
have 12 hydrogens in total.
00:01:34.130 --> 00:01:37.650
On the right-hand side I
only have two hydrogens.
00:01:37.650 --> 00:01:38.840
So if I want to balance that
00:01:38.840 --> 00:01:40.800
I could multiply the water molecule.
00:01:40.800 --> 00:01:44.530
Instead of just one
here, I could have six,
00:01:44.530 --> 00:01:47.800
and now this would be 12 hydrogen atoms
00:01:47.800 --> 00:01:50.560
so both the carbons and the
hydrogens are now balanced.
00:01:50.560 --> 00:01:53.110
By putting that six there I
haven't messed with the carbons.
00:01:53.110 --> 00:01:54.890
And now last, but not least,
00:01:54.890 --> 00:01:57.850
let's think about the oxygens here.
00:01:57.850 --> 00:02:01.500
So on the left, we have six oxygens there
00:02:01.500 --> 00:02:03.500
and then another two oxygens there.
00:02:03.500 --> 00:02:05.532
So that's a total of eight oxygens.
00:02:05.532 --> 00:02:10.532
And on the right, I have
six times two, I have 12
00:02:10.780 --> 00:02:13.580
plus another six oxygens.
00:02:13.580 --> 00:02:16.120
So I have 18 oxygens
on the right-hand side,
00:02:16.120 --> 00:02:19.230
and I only have eight oxygens
on the left-hand side.
00:02:19.230 --> 00:02:20.840
So I have to increase
the number of oxygens
00:02:20.840 --> 00:02:22.450
on the left-hand side.
00:02:22.450 --> 00:02:23.976
So let's see.
00:02:23.976 --> 00:02:27.060
This six you can imagine
matches up with this six.
00:02:27.060 --> 00:02:29.740
So if I could somehow
make this into 12 oxygens,
00:02:29.740 --> 00:02:31.240
I'll be good.
00:02:31.240 --> 00:02:33.260
So the best way to make
this into 12 oxygens
00:02:33.260 --> 00:02:37.610
is to multiply this by
six, so let me do that.
00:02:37.610 --> 00:02:41.920
So if I put a six right over
here, I think I'm all balanced.
00:02:41.920 --> 00:02:43.740
I have six carbons on both sides,
00:02:43.740 --> 00:02:45.750
I have 12 hydrogens on both sides,
00:02:45.750 --> 00:02:50.070
and it looks like I have
18 oxygens on both sides.
00:02:50.070 --> 00:02:52.610
So I'm a fully balanced equation here.
00:02:52.610 --> 00:02:55.360
So let me get a periodic table of elements
00:02:55.360 --> 00:02:58.060
and I only need to think about
carbon, hydrogen, and oxygen.
00:02:58.060 --> 00:03:00.960
So for the sake of space, let
me scroll down a little bit.
00:03:01.990 --> 00:03:05.690
I just need to look at
this stuff over here.
00:03:05.690 --> 00:03:07.470
And so, let's first,
00:03:07.470 --> 00:03:09.280
let's see hydrogen's right up here.
00:03:09.280 --> 00:03:12.590
And we can see in this
periodic table of elements,
00:03:12.590 --> 00:03:14.970
it gives the average atomic mass,
00:03:14.970 --> 00:03:16.800
but you can also view that number
00:03:16.800 --> 00:03:21.300
1.008, as its molar mass.
00:03:21.300 --> 00:03:26.300
So it's 1.008 grams per mole of hydrogen.
00:03:27.770 --> 00:03:30.160
Now we can move on to carbon.
00:03:30.160 --> 00:03:35.160
Carbon is 12.01, 12.01
grams per mole of carbon.
00:03:39.920 --> 00:03:43.340
And then last but not
least, oxygen over here.
00:03:43.340 --> 00:03:48.340
That is 16.00 grams per mole of oxygen.
00:03:51.600 --> 00:03:53.660
And now we can use that information.
00:03:53.660 --> 00:03:56.600
I can now remove our
periodic table of elements.
00:03:56.600 --> 00:03:58.410
We can use this information to figure out
00:03:58.410 --> 00:04:01.760
the molar masses of
each of these molecules.
00:04:01.760 --> 00:04:05.270
So for example, glucose right over here,
00:04:05.270 --> 00:04:07.903
if we're talking about C6H12O6,
00:04:11.610 --> 00:04:15.540
how many grams per mole
is that going to be?
00:04:15.540 --> 00:04:19.570
How many grams is a mole
of glucose going to be?
00:04:19.570 --> 00:04:23.320
Well, it's six carbons, 12
hydrogens, and six oxygens.
00:04:23.320 --> 00:04:24.880
So one way to think about is going to be
00:04:24.880 --> 00:04:27.398
six times this, so it's going to be
00:04:27.398 --> 00:04:29.720
six times 12.01
00:04:29.720 --> 00:04:34.640
plus we have 12 times 1.008
00:04:36.640 --> 00:04:40.473
plus six times 16.00,
00:04:42.080 --> 00:04:45.720
and then this is going
to be grams per mole.
00:04:45.720 --> 00:04:47.440
And this is going to
be equal to, let's see,
00:04:47.440 --> 00:04:52.393
72.06 plus 12.096
00:04:55.820 --> 00:04:59.903
plus six times 16 is 96.00.
00:05:02.140 --> 00:05:06.310
Of course all of this
is in grams per mole.
00:05:06.310 --> 00:05:08.720
And so this is going to
be equal to, let's see,
00:05:08.720 --> 00:05:12.180
72 plus 12 is 84
00:05:12.180 --> 00:05:15.950
plus 96 is 180,
00:05:15.950 --> 00:05:18.510
180 point, and let's see,
00:05:18.510 --> 00:05:23.140
we have 60 thousandths
plus 96 thousandths,
00:05:23.140 --> 00:05:25.760
which would be 156 thousandths,
00:05:25.760 --> 00:05:30.050
so 156 thousandths grams per mole.
00:05:30.050 --> 00:05:32.100
Let me make sure I got the
significant figures right.
00:05:32.100 --> 00:05:34.070
The six, the 12 and six are pure numbers,
00:05:34.070 --> 00:05:35.870
so I'm still good with this.
00:05:35.870 --> 00:05:40.080
And then when I add
these numbers together,
00:05:40.080 --> 00:05:44.120
I need to round to as
much precision as I have
00:05:44.120 --> 00:05:45.210
in the least one.
00:05:45.210 --> 00:05:47.920
So here I go up to the hundredths,
00:05:47.920 --> 00:05:50.060
up to the hundredths,
up to the thousandths.
00:05:50.060 --> 00:05:52.740
So I need to round this,
actually, to the hundredths place.
00:05:52.740 --> 00:05:57.740
So this is going to be 180.16
grams per mole of glucose.
00:06:02.690 --> 00:06:04.780
And now let's think about
the other molecules.
00:06:04.780 --> 00:06:06.230
If we think about oxygen,
00:06:06.230 --> 00:06:08.380
I'll do that over here to save space,
00:06:08.380 --> 00:06:10.690
oxygen, that's pretty straightforward.
00:06:10.690 --> 00:06:14.170
A molecular oxygen molecule
just has two oxygen atoms,
00:06:14.170 --> 00:06:15.410
so it's going to be two times this,
00:06:15.410 --> 00:06:20.410
so it's going to be 32.00 grams per mole.
00:06:20.440 --> 00:06:23.220
And then carbon dioxide.
00:06:23.220 --> 00:06:26.280
Carbon dioxide is going to be,
00:06:26.280 --> 00:06:28.370
it's two oxygens plus one carbon.
00:06:28.370 --> 00:06:30.620
So it's going to be this plus one carbon,
00:06:30.620 --> 00:06:32.900
so that's this plus 12.01,
00:06:32.900 --> 00:06:37.750
so that's 44.01 grams per mole.
00:06:37.750 --> 00:06:41.570
And then last but not
least we have the water.
00:06:41.570 --> 00:06:43.723
And so, H2O.
00:06:45.130 --> 00:06:47.910
This is going to be two hydrogens,
00:06:47.910 --> 00:06:49.377
so that's two times 1.008,
00:06:50.320 --> 00:06:54.730
so that's 2.016 plus an oxygen.
00:06:54.730 --> 00:06:59.600
So that's going to be 2.016 plus 16
00:06:59.600 --> 00:07:01.357
is going to be 18.016.
00:07:05.290 --> 00:07:07.770
Once again, we only go to
the hundredths place here,
00:07:07.770 --> 00:07:10.170
so I'm going to round to
the hundredths place here.
00:07:10.170 --> 00:07:15.170
So 18.02 grams per mole.
00:07:15.940 --> 00:07:18.070
Now the next step is to think about,
00:07:18.070 --> 00:07:22.600
all right we're reacting
with 25 grams of glucose.
00:07:22.600 --> 00:07:25.780
How many moles of glucose is that?
00:07:25.780 --> 00:07:28.770
So we have 25.0,
00:07:28.770 --> 00:07:33.770
25.0 grams of glucose.
00:07:34.347 --> 00:07:37.030
And we want to turn this
into moles of glucose.
00:07:37.030 --> 00:07:41.060
And we know the molar mass
is 180.16 grams per mole,
00:07:41.060 --> 00:07:43.900
or we could multiply and say that this is
00:07:43.900 --> 00:07:48.900
for every one mole, per
mole, it is 180.16 grams.
00:07:50.940 --> 00:07:53.290
All I did is take the
reciprocal of this over here.
00:07:53.290 --> 00:07:55.320
And notice, the grams
will cancel with the grams
00:07:55.320 --> 00:07:57.963
and I'll be left with moles of glucose.
00:07:58.850 --> 00:08:02.490
That's going to be equal to 25.0
00:08:02.490 --> 00:08:07.490
divided by 180.16 moles of glucose.
00:08:08.660 --> 00:08:13.660
25 divided by 180.16 is equal to this.
00:08:15.800 --> 00:08:17.820
And let's see, I have
three significant figures
00:08:17.820 --> 00:08:19.590
divided by five significant figures.
00:08:19.590 --> 00:08:21.850
So I'm going to round to
three significant figures.
00:08:21.850 --> 00:08:23.593
So 0.139.
00:08:25.740 --> 00:08:30.740
So this is approximately equal
to 0.139 mole of glucose.
00:08:34.990 --> 00:08:36.840
Now, they say the first question is
00:08:36.840 --> 00:08:39.100
what mass of oxygen is required
00:08:39.100 --> 00:08:41.360
for a complete reaction of this.
00:08:41.360 --> 00:08:43.430
Well, for every mole of glucose we need
00:08:43.430 --> 00:08:46.720
six moles of molecular oxygen.
00:08:46.720 --> 00:08:48.210
And so, we're going to need,
00:08:48.210 --> 00:08:50.410
let me just multiply that times six.
00:08:50.410 --> 00:08:53.950
So times six is equal to that.
00:08:53.950 --> 00:08:56.230
And remember, I had three
significant figures.
00:08:56.230 --> 00:08:57.903
So, 0.833.
00:09:00.660 --> 00:09:01.760
So we're going to need
00:09:04.785 --> 00:09:05.863
0.833 moles of molecular oxygen.
00:09:12.490 --> 00:09:14.070
And then I just multiply that
00:09:14.070 --> 00:09:17.220
times the molar mass of molecular oxygen.
00:09:17.220 --> 00:09:22.220
So, times 32.00 grams per
mole of molecular oxygen.
00:09:26.180 --> 00:09:28.847
0.833 times 32 is equal to that.
00:09:33.020 --> 00:09:35.208
If you go three significant figures,
00:09:35.208 --> 00:09:36.041
it's 26.7.
00:09:38.988 --> 00:09:42.488
26.7 grams of oxygen, of molecular oxygen.
00:09:47.260 --> 00:09:50.100
And so we've answered the
first part of the question.
00:09:50.100 --> 00:09:53.240
What mass of oxygen is
required for complete reaction?
00:09:53.240 --> 00:09:56.130
So, that's this right over here.
00:09:56.130 --> 00:09:58.130
And then the next question is what masses
00:09:58.130 --> 00:10:01.570
of carbon dioxide and
water in grams are formed.
00:10:01.570 --> 00:10:03.610
Remember, for every one mole of glucose,
00:10:03.610 --> 00:10:05.960
we needed six moles of molecular oxygen
00:10:05.960 --> 00:10:08.070
and we produce six moles of carbon dioxide
00:10:08.070 --> 00:10:10.940
and we produce six moles of water.
00:10:10.940 --> 00:10:13.100
So this is the number of moles of glucose
00:10:13.100 --> 00:10:15.020
we input into the reaction.
00:10:15.020 --> 00:10:16.710
Six times that was this.
00:10:16.710 --> 00:10:19.020
So this is actually
also the number of moles
00:10:19.020 --> 00:10:22.860
of carbon dioxide or water
that we're going to produce.
00:10:22.860 --> 00:10:27.007
So, if we take our original 0.833 mole
00:10:29.750 --> 00:10:32.100
of carbon dioxide and I multiply that
00:10:32.100 --> 00:10:34.060
times carbon dioxide's molar mass,
00:10:34.060 --> 00:10:38.350
44.01 grams per mole,
00:10:38.350 --> 00:10:41.173
this is going to be
approximately equal to,
00:10:41.173 --> 00:10:45.870
.833 times 44.01
00:10:45.870 --> 00:10:48.340
is equal to three significant figures,
00:10:48.340 --> 00:10:51.430
36.7 grams.
00:10:51.430 --> 00:10:55.440
36.7 grams of carbon dioxide.
00:10:55.440 --> 00:10:56.600
And once again, you can see
00:10:56.600 --> 00:10:58.796
that the moles cancel with the moles,
00:10:58.796 --> 00:11:02.110
just as they did before, to
give us grams of carbon dioxide.
00:11:02.110 --> 00:11:04.520
And then last but not least,
we can do that with the water.
00:11:04.520 --> 00:11:09.520
0.833 mole of H2O times its molar mass,
00:11:12.120 --> 00:11:17.120
times 18.02 grams per mole of water
00:11:19.370 --> 00:11:21.577
is going to give us approximately
00:11:21.577 --> 00:11:22.967
.833 times 18.02, gives us,
00:11:28.800 --> 00:11:33.800
three significant figures
is going to be 15.0.
00:11:34.060 --> 00:11:39.060
15.0 grams of water.
00:11:39.470 --> 00:11:41.040
And once again, those moles canceled out
00:11:41.040 --> 00:11:42.350
to give us the right units.
00:11:42.350 --> 00:11:44.510
And we're done, which is pretty cool.
00:11:44.510 --> 00:11:47.840
This is really useful in chemistry
to be able to understand,
00:11:47.840 --> 00:11:50.410
based on a balanced chemical equation,
00:11:50.410 --> 00:11:51.680
to be able to understand,
00:11:51.680 --> 00:11:54.750
hey, if I have a certain
mass of one of the inputs,
00:11:54.750 --> 00:11:57.000
one of the things that
are one of the reactants,
00:11:57.000 --> 00:11:58.270
how much do I need of the other?
00:11:58.270 --> 00:12:00.920
And then how much mass of the products
00:12:00.920 --> 00:12:02.610
am I actually going to produce?
00:12:02.610 --> 00:12:04.663
All of which we just figured out.
|
Physical and chemical changes | https://www.youtube.com/watch?v=3e8e0d1fWLk | vtt | https://www.youtube.com/api/timedtext?v=3e8e0d1fWLk&ei=7lWUZf2nHbuvvdIP8Yu28A8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=41707D05E8D3C4FA30967050642B6D4B4368EE6C.A636DB87860F697BE27C760910D82CFC7CE14621&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.200 --> 00:00:01.950
- [Instructor] So what we have
are three different pictures
00:00:01.950 --> 00:00:05.880
of substances undergoing
some type of change.
00:00:05.880 --> 00:00:08.230
And we're going to focus on in this video
00:00:08.230 --> 00:00:11.950
is classifying things as
either being physical changes
00:00:11.950 --> 00:00:14.050
or chemical changes.
00:00:14.050 --> 00:00:15.540
And you might already have already thought
00:00:15.540 --> 00:00:18.790
about this or seen this in
a previous science class.
00:00:18.790 --> 00:00:21.120
But when we talk about a physical change,
00:00:21.120 --> 00:00:23.500
we're talking about where
there could be a change
00:00:23.500 --> 00:00:25.900
in properties but we're
not having a change
00:00:25.900 --> 00:00:29.140
in the actual composition
of what we're talking about,
00:00:29.140 --> 00:00:32.820
while in a chemical change
you actually do have a change
00:00:32.820 --> 00:00:36.210
in composition, how the
different constituent atoms
00:00:36.210 --> 00:00:39.420
and elements match up or
connect or bond to each other
00:00:39.420 --> 00:00:41.680
might be different.
00:00:41.680 --> 00:00:43.970
So my first question to
you is pause this video
00:00:43.970 --> 00:00:45.670
and we have some ice melting here.
00:00:45.670 --> 00:00:49.060
We have some propane
combusting or burning here,
00:00:49.060 --> 00:00:52.400
and we have some iron rusting here.
00:00:52.400 --> 00:00:53.233
And I want you to think
00:00:53.233 --> 00:00:54.970
about which of these are physical changes,
00:00:54.970 --> 00:00:57.370
and which of these are
chemical changes and why.
00:00:58.700 --> 00:01:01.550
All right, now let's first
think about this water,
00:01:01.550 --> 00:01:02.940
this ice melting.
00:01:02.940 --> 00:01:06.285
And if we wanted to write it
in fancy chemical language,
00:01:06.285 --> 00:01:09.920
or chemistry language, we
could write this as H2O,
00:01:09.920 --> 00:01:14.920
going from its solid form to
H2O going into its liquid form.
00:01:16.890 --> 00:01:19.500
Now, we don't have a
change in composition,
00:01:19.500 --> 00:01:21.010
in either state whether you're looking
00:01:21.010 --> 00:01:22.430
at this liquid water here,
00:01:22.430 --> 00:01:25.000
or whether you're looking
at the solid water there,
00:01:25.000 --> 00:01:29.240
you'll see a bunch of water molecules.
00:01:29.240 --> 00:01:33.490
Each oxygen is still
bonded to two hydrogens.
00:01:33.490 --> 00:01:36.450
And so you're not having
a change in composition.
00:01:36.450 --> 00:01:41.410
And so this over here is a
physical, physical change.
00:01:41.410 --> 00:01:42.890
And if we kept heating that water up
00:01:42.890 --> 00:01:44.330
and it started to vaporize
00:01:44.330 --> 00:01:46.710
that would also be a physical change.
00:01:46.710 --> 00:01:49.010
Whereas it turns into water vapor.
00:01:49.010 --> 00:01:52.150
You have your intermolecular
forces being overcome
00:01:52.150 --> 00:01:53.660
but the covalent bonds
00:01:53.660 --> 00:01:55.630
between the oxygens and the hydrogens,
00:01:55.630 --> 00:01:58.720
those aren't breaking
or forming in some way.
00:01:58.720 --> 00:02:01.010
So once again, when you
go from ice to water,
00:02:01.010 --> 00:02:02.900
physical change, from water to vapor
00:02:02.900 --> 00:02:04.840
or you could say from liquid to gas
00:02:04.840 --> 00:02:08.350
that is also going to
be a physical change.
00:02:08.350 --> 00:02:10.872
One general rule of thumb
when you think about
00:02:10.872 --> 00:02:13.000
what's going on on a microscopic level,
00:02:13.000 --> 00:02:14.100
and this is a general rule of thumb.
00:02:14.100 --> 00:02:15.120
It doesn't always apply.
00:02:15.120 --> 00:02:17.230
And we'll think about an
edge case in a little bit
00:02:17.230 --> 00:02:21.340
is when you're overcoming
intermolecular forces
00:02:21.340 --> 00:02:23.930
that tends to be a physical change.
00:02:23.930 --> 00:02:27.351
But if you have chemical
bonds forming or breaking
00:02:27.351 --> 00:02:30.564
that would be a chemical change.
00:02:30.564 --> 00:02:33.840
Now let's think about what's
going on here with the propane.
00:02:33.840 --> 00:02:35.980
If you were to write the
chemical reaction here
00:02:35.980 --> 00:02:40.700
it would be propane C3H8 in gas form.
00:02:40.700 --> 00:02:43.020
It needs oxygen to combust.
00:02:43.020 --> 00:02:44.350
So for every mole of propane
00:02:44.350 --> 00:02:48.880
we have five moles of
molecular oxygen in gas form.
00:02:48.880 --> 00:02:51.760
And then when it combusts
00:02:51.760 --> 00:02:54.770
you're going to produce
three for every one mole
00:02:54.770 --> 00:02:57.320
of propane and five moles
of molecular oxygen,
00:02:57.320 --> 00:03:02.140
you're gonna produce three
moles of carbon dioxide gas
00:03:02.140 --> 00:03:07.140
and four moles of water
in vapor form as well.
00:03:07.790 --> 00:03:10.170
And so what you actually have is the bonds
00:03:10.170 --> 00:03:11.900
in those molecules are actually breaking
00:03:11.900 --> 00:03:13.900
and then re forming.
00:03:13.900 --> 00:03:16.960
So you don't just have
physical change going on here.
00:03:16.960 --> 00:03:21.670
You have chemical change, chemical change.
00:03:21.670 --> 00:03:22.520
One way to think about it.
00:03:22.520 --> 00:03:25.860
You had propane here before, C3 H8,
00:03:25.860 --> 00:03:29.223
after the reaction you no
longer have the propane here.
00:03:29.223 --> 00:03:32.300
When you actually see as
fire, which is fascinating.
00:03:32.300 --> 00:03:34.487
This is just very hot gas,
00:03:34.487 --> 00:03:36.540
and that very hot air that you're seeing,
00:03:36.540 --> 00:03:38.600
and there's gonna be some
carbon dioxide in there
00:03:38.600 --> 00:03:41.190
and there's gonna be some
water vapor in there.
00:03:41.190 --> 00:03:42.900
The reason why it's getting so hot
00:03:42.900 --> 00:03:46.480
is because this releases a lot of energy.
00:03:46.480 --> 00:03:50.370
Now let's think about what's
going on here with this iron.
00:03:50.370 --> 00:03:53.640
If I were to write this
as a chemical reaction,
00:03:53.640 --> 00:03:57.100
for every four moles of iron in solid form
00:03:57.100 --> 00:04:01.160
plus three moles of
molecular oxygen in gas form,
00:04:01.160 --> 00:04:04.160
and that would just be the
ambient oxygen around this iron.
00:04:04.160 --> 00:04:09.160
It is going to produce two
moles of iron oxide as a solid
00:04:13.740 --> 00:04:15.750
and that's what you see
there in the orange.
00:04:15.750 --> 00:04:17.190
That is the iron oxide.
00:04:17.190 --> 00:04:21.030
So notice this reaction
is forming new ionic bonds
00:04:21.030 --> 00:04:22.920
in that ferrous oxide.
00:04:22.920 --> 00:04:24.810
And to undergo the reaction we had to
00:04:24.810 --> 00:04:28.280
break the metallic bonds of the solid iron
00:04:28.280 --> 00:04:31.710
and the covalent bonds
in the molecular oxygen.
00:04:31.710 --> 00:04:36.130
So anytime we are breaking and
making these chemical bonds
00:04:36.130 --> 00:04:38.160
we have a chemical change.
00:04:38.160 --> 00:04:40.150
Now, let me give you an
interesting question.
00:04:40.150 --> 00:04:44.260
What about the dissolving of
sodium chloride or table salt?
00:04:44.260 --> 00:04:48.010
So you have NaCl in its solid form,
00:04:48.010 --> 00:04:50.100
when you place it into water,
00:04:50.100 --> 00:04:54.330
you get sodium chloride in aqueous form.
00:04:54.330 --> 00:04:57.160
And how does that look when this happens?
00:04:57.160 --> 00:04:59.430
Well, sodium chloride in solid form,
00:04:59.430 --> 00:05:02.580
you know it forms this lattice
00:05:02.580 --> 00:05:04.810
because they have these ionic bonds.
00:05:04.810 --> 00:05:06.660
I'll try to draw a few of them.
00:05:06.660 --> 00:05:08.910
So it looks something like this,
00:05:08.910 --> 00:05:10.640
where we've seen this multiple times,
00:05:10.640 --> 00:05:13.940
chlorine nabs electrons becomes
chloride, becomes negative.
00:05:13.940 --> 00:05:18.170
Sodium loses electron
becomes a positive ion.
00:05:18.170 --> 00:05:19.790
And so they get attracted to each other
00:05:19.790 --> 00:05:21.600
and then they can form this
00:05:21.600 --> 00:05:23.760
three-dimensional lattice structure,
00:05:23.760 --> 00:05:25.860
when it is in solid form.
00:05:25.860 --> 00:05:27.410
And I'm trying my best to draw it
00:05:27.410 --> 00:05:30.300
in three dimensions over here.
00:05:30.300 --> 00:05:33.720
And actually I could put one
right over here like this,
00:05:33.720 --> 00:05:35.900
but when you dissolve it into water
00:05:35.900 --> 00:05:38.400
the ions get split apart.
00:05:38.400 --> 00:05:40.780
You get the ions that all get dissolved,
00:05:40.780 --> 00:05:42.810
they get split apart in the water.
00:05:42.810 --> 00:05:47.810
And so the ionic bonds
themselves are being broken.
00:05:48.210 --> 00:05:49.810
Now you could argue that, hey, you know
00:05:49.810 --> 00:05:52.280
the constituent ions are
just being separated.
00:05:52.280 --> 00:05:54.720
So maybe this is a physical change
00:05:54.720 --> 00:05:56.360
or you could say, no, ionic bonds.
00:05:56.360 --> 00:05:57.810
Those are legit bonds.
00:05:57.810 --> 00:06:01.550
Those are strong bonds, and
those are getting broken.
00:06:01.550 --> 00:06:04.020
And so you're also
getting chemical change.
00:06:04.020 --> 00:06:07.670
And it actually turns out
that this is a gray area
00:06:07.670 --> 00:06:10.770
when you're talking about
dissolving a salt like this
00:06:10.770 --> 00:06:13.511
into water, whether you're
talking about a physical change
00:06:13.511 --> 00:06:16.180
or you're talking about a chemical change.
00:06:16.180 --> 00:06:18.620
And actually just this past
weekend, I was at the beach
00:06:18.620 --> 00:06:21.780
and we ran out of salt
and I did this in reverse.
00:06:21.780 --> 00:06:25.140
I went to the ocean and I
got a pot full of salt water.
00:06:25.140 --> 00:06:27.460
And it actually took me
about 30 minutes to boil it.
00:06:27.460 --> 00:06:30.630
And I was able to evaporate
all of the water out of it.
00:06:30.630 --> 00:06:33.200
And essentially the salt
in that water was able
00:06:33.200 --> 00:06:35.550
to reform these ionic bonds.
00:06:35.550 --> 00:06:39.240
And so one could debate whether
I was creating a physical
00:06:39.240 --> 00:06:40.880
or a chemical change.
00:06:40.880 --> 00:06:44.360
I was definitely doing a
physical change with the water.
00:06:44.360 --> 00:06:48.670
I was evaporating it, but I was
actually forming ionic bonds
00:06:48.670 --> 00:06:49.840
between the sodium and chloride.
00:06:49.840 --> 00:06:51.690
So one could argue that
that was maybe a physical
00:06:51.690 --> 00:06:53.283
and a chemical change.
|
Drawing particulate models of reaction mixtures | https://www.youtube.com/watch?v=kCkyk4YNUyY | vtt | https://www.youtube.com/api/timedtext?v=kCkyk4YNUyY&ei=7lWUZezeI9m-mLAPrqqEgA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=504FD6B5876C50203679279D05640EDA198CCE89.2A1C47C75181834317A62C2BC0310EF744A2EE8F&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.260 --> 00:00:01.400
- [Instructor] In a previous video,
00:00:01.400 --> 00:00:04.000
we used a particulate model like this
00:00:04.000 --> 00:00:05.310
to understand a reaction,
00:00:05.310 --> 00:00:07.477
not just to understand the reaction,
00:00:08.490 --> 00:00:11.120
but to balance the
chemical reaction as well.
00:00:11.120 --> 00:00:14.390
And when I hand drew these particles,
00:00:14.390 --> 00:00:17.300
the atoms in this particulate model here,
00:00:17.300 --> 00:00:19.190
I tried to draw it pretty close
00:00:19.190 --> 00:00:21.620
to their actual relative sizes.
00:00:21.620 --> 00:00:24.140
Carbon atoms are a little
bit bigger than oxygen atoms,
00:00:24.140 --> 00:00:27.220
and they're both a lot
bigger than hydrogen atoms.
00:00:27.220 --> 00:00:28.360
What we're gonna do in this video
00:00:28.360 --> 00:00:32.190
is extend our understanding
using a particulate model
00:00:32.190 --> 00:00:35.000
to start to visualize
what actually might go on
00:00:35.000 --> 00:00:36.220
in a mixture
00:00:36.220 --> 00:00:40.860
of some of these reactant molecules.
00:00:40.860 --> 00:00:43.320
So what I have here on the left-hand side
00:00:43.320 --> 00:00:45.120
are the various molecules.
00:00:45.120 --> 00:00:47.530
I have two methane molecules here.
00:00:47.530 --> 00:00:49.500
I have three water molecules.
00:00:49.500 --> 00:00:51.670
And what I wanna do with you
00:00:51.670 --> 00:00:56.360
is draw what we would expect
to see after the reaction.
00:00:56.360 --> 00:00:58.790
And I encourage you, like
always, pause this video
00:00:58.790 --> 00:01:00.190
and see if you can have a go at that,
00:01:00.190 --> 00:01:01.200
maybe with a pencil and paper,
00:01:01.200 --> 00:01:03.210
at least just try to
imagine it in your head,
00:01:03.210 --> 00:01:04.693
before I do this with you.
00:01:05.550 --> 00:01:07.700
All right, now, let's do this together.
00:01:07.700 --> 00:01:11.410
Now, we know that for every
methane and every water,
00:01:11.410 --> 00:01:15.060
we're going to produce one carbon monoxide
00:01:15.060 --> 00:01:17.610
and three molecular hydrogens.
00:01:17.610 --> 00:01:19.470
And each of those molecules of hydrogen
00:01:19.470 --> 00:01:21.280
have two hydrogens in them.
00:01:21.280 --> 00:01:26.280
So let's just say that this
one and this one react.
00:01:26.320 --> 00:01:28.980
They're going to produce
one carbon monoxide.
00:01:28.980 --> 00:01:31.660
I'm gonna try to draw the
relative sizes roughly, right?
00:01:31.660 --> 00:01:35.150
So one carbon monoxide.
00:01:35.150 --> 00:01:38.770
And then they're gonna
produce six hydrogen atoms
00:01:38.770 --> 00:01:41.530
that are going to be in
three hydrogen molecules.
00:01:41.530 --> 00:01:43.200
So let's do,
00:01:43.200 --> 00:01:47.700
that's two and four,
00:01:47.700 --> 00:01:50.020
and then I'll just do one here
00:01:50.020 --> 00:01:53.270
and then six.
00:01:53.270 --> 00:01:56.370
All right, so I took care
of this one and this one.
00:01:56.370 --> 00:02:00.700
And now we can imagine that
maybe this water molecule
00:02:00.700 --> 00:02:03.400
reacts with this methane molecule,
00:02:03.400 --> 00:02:07.080
and so that would produce
another carbon monoxide.
00:02:07.080 --> 00:02:08.280
Let me draw that
00:02:08.280 --> 00:02:09.800
roughly at the right size.
00:02:09.800 --> 00:02:14.030
Another carbon monoxide molecule
00:02:15.660 --> 00:02:19.340
and three more hydrogen molecules
00:02:19.340 --> 00:02:21.130
for a total of six more hydrogens.
00:02:21.130 --> 00:02:25.740
So that's one and two
00:02:26.770 --> 00:02:28.830
and three.
00:02:28.830 --> 00:02:31.810
And now we have this water right over here
00:02:31.810 --> 00:02:34.560
that had no one to react
with in this situation,
00:02:34.560 --> 00:02:35.850
had no partner.
00:02:35.850 --> 00:02:40.100
And so that's just going to be
a leftover reactant molecule.
00:02:40.100 --> 00:02:42.220
So let me just draw it right over here.
00:02:42.220 --> 00:02:45.885
So that water could be
00:02:45.885 --> 00:02:49.830
right over right over here.
00:02:49.830 --> 00:02:51.660
And so this was a useful way
00:02:51.660 --> 00:02:53.880
of starting to visualize
what might be going on.
00:02:53.880 --> 00:02:55.610
Remember, this is happening
at a very high temperature.
00:02:55.610 --> 00:02:58.060
They're all bouncing around, et cetera.
00:02:58.060 --> 00:03:00.220
And then when they react,
you might get this,
00:03:00.220 --> 00:03:02.640
but then this water molecule
has no one to react to,
00:03:02.640 --> 00:03:05.840
so it is, you could view it as a leftover
00:03:05.840 --> 00:03:07.453
after the reaction.
|
Visualizing chemical equations using particulate models | https://www.youtube.com/watch?v=3UoxWEZuwp8 | vtt | https://www.youtube.com/api/timedtext?v=3UoxWEZuwp8&ei=7lWUZduxHfS4mLAPlPu4uA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EC231F86AFADE2266811880F78A6606D48387A33.6CBCB12C7F42B1B575A795740AEA8842A97683E2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.260 --> 00:00:02.180
- [Instructor] A question that
some of you might have asked,
00:00:02.180 --> 00:00:05.560
or maybe haven't asked is where
do we get our hydrogen from?
00:00:05.560 --> 00:00:09.030
Because molecular hydrogen,
if it was just in the air,
00:00:09.030 --> 00:00:12.050
it is lighter than the other
things that make up the air,
00:00:12.050 --> 00:00:14.540
so it would just float to
the top of the atmosphere.
00:00:14.540 --> 00:00:16.120
So how would we get it?
00:00:16.120 --> 00:00:18.660
Well, this reaction right over here
00:00:18.660 --> 00:00:21.860
is actually one of the
most cost-effective ways
00:00:21.860 --> 00:00:24.660
of getting molecular hydrogen,
00:00:24.660 --> 00:00:27.600
which you can see right
over here on the right.
00:00:27.600 --> 00:00:29.740
What do you do at a very high temperature?
00:00:29.740 --> 00:00:31.120
What I would consider a high temperature,
00:00:31.120 --> 00:00:34.880
roughly between 700 and
1,000 degrees Celsius,
00:00:34.880 --> 00:00:38.620
you get some methane gas
in the presence of water.
00:00:38.620 --> 00:00:39.453
And of course,
00:00:39.453 --> 00:00:41.820
water at that temperature
is going to be a gas,
00:00:41.820 --> 00:00:43.370
we're talking about steam.
00:00:43.370 --> 00:00:47.210
And then they will react
to produce carbon monoxide
00:00:47.210 --> 00:00:50.410
and molecular hydrogen.
00:00:50.410 --> 00:00:53.180
Now something might be
feeling a little off
00:00:53.180 --> 00:00:55.770
when I wrote this reaction like this.
00:00:55.770 --> 00:00:58.900
So pause this video and
think about what is off here.
00:00:58.900 --> 00:01:00.710
And I'll give you a little bit of a hint.
00:01:00.710 --> 00:01:02.850
Think about what are we inputting?
00:01:02.850 --> 00:01:04.890
What are the atoms and the number of atoms
00:01:04.890 --> 00:01:06.650
that we're inputting into the reaction?
00:01:06.650 --> 00:01:09.290
And then what are the number
and the types of atoms
00:01:09.290 --> 00:01:10.470
that we are outputting?
00:01:10.470 --> 00:01:13.110
For example, we have one
carbon that we are inputting
00:01:13.110 --> 00:01:14.670
between the methane and the water.
00:01:14.670 --> 00:01:17.210
And we have one carbon
that we are getting out
00:01:17.210 --> 00:01:18.300
on the other side.
00:01:18.300 --> 00:01:20.490
Think about that for the
oxygen and the hydrogens,
00:01:20.490 --> 00:01:23.223
and see whether it all makes sense.
00:01:24.210 --> 00:01:26.980
All right, now let's work
through this together.
00:01:26.980 --> 00:01:29.210
And actually to help us visualize,
00:01:29.210 --> 00:01:31.350
instead of just writing it in this form,
00:01:31.350 --> 00:01:34.650
I'm also gonna try to visualize
the various molecules.
00:01:34.650 --> 00:01:36.860
So this right over here
is a methane molecule.
00:01:36.860 --> 00:01:40.190
You have one carbon that is
bonded to four hydrogens.
00:01:40.190 --> 00:01:42.993
You can see that up there, CH4, CH4.
00:01:43.990 --> 00:01:45.620
Here we have a water molecule.
00:01:45.620 --> 00:01:49.800
You have an oxygen that is
bonded to two hydrogens.
00:01:49.800 --> 00:01:51.520
And then they react.
00:01:51.520 --> 00:01:53.400
You get a carbon monoxide molecule,
00:01:53.400 --> 00:01:55.300
or this is how I've visualized it.
00:01:55.300 --> 00:01:57.690
So you have a carbon and an oxygen.
00:01:57.690 --> 00:01:59.760
And then I draw the molecular hydrogen.
00:01:59.760 --> 00:02:03.080
Molecular hydrogen has two
hydrogens bonded to each other.
00:02:03.080 --> 00:02:05.790
And that is what I have depicted here.
00:02:05.790 --> 00:02:07.940
Now based on the hint I gave you before
00:02:07.940 --> 00:02:10.090
I asked you to pause the video,
00:02:10.090 --> 00:02:14.260
you will notice that we have
a carbon on the input side,
00:02:14.260 --> 00:02:15.340
you have it right there.
00:02:15.340 --> 00:02:17.510
And we have one carbon on the output side.
00:02:17.510 --> 00:02:21.450
So that seems to obey
conservation of mass.
00:02:21.450 --> 00:02:23.830
Now what about for the oxygens?
00:02:23.830 --> 00:02:28.410
Well, we have one oxygen between
the methane and the water
00:02:28.410 --> 00:02:30.170
that we're inputting into the reaction
00:02:30.170 --> 00:02:31.780
and we have it drawn right over here.
00:02:31.780 --> 00:02:35.094
And then we have one oxygen
that we are outputting
00:02:35.094 --> 00:02:39.410
on the output side of our
reaction right over here.
00:02:39.410 --> 00:02:40.880
Now what about the hydrogens?
00:02:40.880 --> 00:02:43.330
Well, on the left side of our
reaction, right over here,
00:02:43.330 --> 00:02:47.210
we have four hydrogens plus
another two or six hydrogens.
00:02:47.210 --> 00:02:48.580
You can also count them here:
00:02:48.580 --> 00:02:52.430
one, two, three, four,
five, six hydrogens.
00:02:52.430 --> 00:02:53.640
While on the right hand side,
00:02:53.640 --> 00:02:55.630
we only have two hydrogens,
00:02:55.630 --> 00:02:57.850
and they're in one hydrogen molecules.
00:02:57.850 --> 00:03:00.010
So what happen to the
other four hydrogens?
00:03:00.010 --> 00:03:01.790
They can't just disappear.
00:03:01.790 --> 00:03:04.520
We have to have conservation of mass.
00:03:04.520 --> 00:03:07.280
So we need to have another four hydrogens
00:03:07.280 --> 00:03:09.890
on the right-hand side of this equation.
00:03:09.890 --> 00:03:12.490
Well, how can we have
another four hydrogens?
00:03:12.490 --> 00:03:16.340
Well, that's if we have two
more molecules of hydrogen.
00:03:16.340 --> 00:03:19.960
So that's one, and then that is two.
00:03:19.960 --> 00:03:24.290
So instead of just having one
molecule of molecular hydrogen
00:03:24.290 --> 00:03:27.550
that has two hydrogen atoms
in it, we now have three.
00:03:27.550 --> 00:03:30.930
So to balance this chemical equation,
00:03:30.930 --> 00:03:32.640
all we have to do is say, okay,
00:03:32.640 --> 00:03:36.020
we don't just have one, one
molecule of hydrogen here,
00:03:36.020 --> 00:03:39.660
we have three molecules of hydrogen.
00:03:39.660 --> 00:03:42.870
And what I have just done is
balance the chemical equation.
00:03:42.870 --> 00:03:45.930
It's just making sure that we
have a conservation of mass,
00:03:45.930 --> 00:03:49.160
that we don't have constituent
atoms on the left-hand side
00:03:49.160 --> 00:03:52.420
that somehow disappear
on the right hand side,
00:03:52.420 --> 00:03:55.080
or we don't have constituent atoms
00:03:55.080 --> 00:03:57.290
that somehow appear on the right hand side
00:03:57.290 --> 00:04:00.663
without ever being
input into the reaction.
|
Khan Academy Needs Your Help To Keep Going | https://www.youtube.com/watch?v=gqSgo6PUn40 | vtt | https://www.youtube.com/api/timedtext?v=gqSgo6PUn40&ei=7lWUZaXhHKqBp-oP5-KFgAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=96710C552B64F6C21A02E0E45884F9885905A981.608D9FD31E05C849EA1AB6C4C60ABDE2BB486968&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.250 --> 00:00:02.780
- Hi, Sal Khan here from Khan Academy.
00:00:02.780 --> 00:00:04.550
And I'm just here to remind everyone
00:00:04.550 --> 00:00:06.830
that Khan Academy is a
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And we can only do that work
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that there's actually a good
body of scientific research
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that one of the top ways
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And when you give to Khan Academy,
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the social return on investment
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is really one of the highest
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that you can do.
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So when you give those dollars,
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not only will it help
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as we go through the back
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To make it even better,
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every dollar you give will
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00:01:00.670 --> 00:01:03.260
So, as we make our way to the end of 2020,
00:01:03.260 --> 00:01:04.560
which has been a tough year,
00:01:04.560 --> 00:01:07.440
and more folks are
dependent on Khan Academy
00:01:07.440 --> 00:01:10.230
and being able to keep
learning than ever before,
00:01:10.230 --> 00:01:12.210
I hope you seriously consider
00:01:12.210 --> 00:01:15.650
thinking about how powerful
a donation to Khan Academy
00:01:15.650 --> 00:01:18.763
can be, and how happy
that's going to make you.
|
Limits of composite functions: internal limit doesn't exist | https://www.youtube.com/watch?v=XYaZgRQdV3g | vtt | https://www.youtube.com/api/timedtext?v=XYaZgRQdV3g&ei=7lWUZeG_HLy_mLAP-peosAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=4203DD8D929D515D4B8A0FA8FC23CFD0A3B29613.C4F06EA17B8F2922CBA1473EC86FB15616C061F2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.566 --> 00:00:01.500
- [Instructor] All right, let's get
00:00:01.500 --> 00:00:03.140
a little bit more practice taking limits
00:00:03.140 --> 00:00:04.890
of composite functions.
00:00:04.890 --> 00:00:06.980
Here, we want to figure
out what is the limit
00:00:06.980 --> 00:00:11.740
as x approaches negative
one of g of h of x?
00:00:11.740 --> 00:00:14.300
The function g, we see
it defined graphically
00:00:14.300 --> 00:00:15.800
here on the left, and the function h,
00:00:15.800 --> 00:00:18.140
we see it defined graphically
here on the right.
00:00:18.140 --> 00:00:20.090
Pause this video and have a go at this.
00:00:21.060 --> 00:00:23.790
All right, now your first
temptation might be to say,
00:00:23.790 --> 00:00:26.780
all right, what is the limit
as x approaches negative one
00:00:26.780 --> 00:00:31.780
of h of x, and if that limit
exists, then input that into g.
00:00:32.250 --> 00:00:34.710
If you take the limit as
x approaches negative one
00:00:34.710 --> 00:00:37.430
of h of x, you see that
you have a different limit
00:00:37.430 --> 00:00:39.350
as you approach from the right
00:00:39.350 --> 00:00:41.830
than when you approach from the left.
00:00:41.830 --> 00:00:45.560
So your temptation might be
to give up at this point,
00:00:45.560 --> 00:00:47.870
but what we'll do in
this video is to realize
00:00:47.870 --> 00:00:51.030
that this composite limit actually exists
00:00:51.030 --> 00:00:53.660
even though the limit as
x approaches negative one
00:00:53.660 --> 00:00:56.920
of h of x does not exist.
00:00:56.920 --> 00:00:58.900
How do we figure this out?
00:00:58.900 --> 00:01:00.990
Well, what we could do
is take right-handed
00:01:00.990 --> 00:01:02.920
and left-handed limits.
00:01:02.920 --> 00:01:06.180
Let's first figure out what is the limit
00:01:07.110 --> 00:01:11.940
as x approaches negative
one from the right hand side
00:01:11.940 --> 00:01:14.937
of g of h of x?
00:01:19.600 --> 00:01:22.380
Well, to think about that,
what is the limit of h
00:01:22.380 --> 00:01:25.280
as x approaches negative one
from the right hand side?
00:01:25.280 --> 00:01:28.640
As we approach negative one
from the right hand side,
00:01:28.640 --> 00:01:32.140
it looks like h is
approaching negative two.
00:01:32.140 --> 00:01:35.359
Another way to think about
it is this is going to be
00:01:35.359 --> 00:01:40.359
equal to the limit as h of
x approaches negative two,
00:01:42.580 --> 00:01:45.630
and what direction is it
approaching negative two from?
00:01:45.630 --> 00:01:47.820
Well, it's approaching
negative two from values
00:01:47.820 --> 00:01:49.470
larger than negative two.
00:01:49.470 --> 00:01:52.820
H of x is decreasing down to negative two
00:01:52.820 --> 00:01:55.730
as x approaches negative
one from the right.
00:01:55.730 --> 00:01:59.910
So it's approaching from
values larger than negative two
00:01:59.910 --> 00:02:02.380
of g of h of x.
00:02:02.380 --> 00:02:05.960
G of h of x.
00:02:05.960 --> 00:02:09.100
I'm color coding it to be
able to keep track of things.
00:02:09.100 --> 00:02:12.050
This is analogous to
saying what is the limit,
00:02:12.050 --> 00:02:16.010
if you think about it as
x approaches negative two
00:02:16.010 --> 00:02:18.630
from the positive direction of g?
00:02:18.630 --> 00:02:21.810
Here, h is just the input into g.
00:02:21.810 --> 00:02:25.430
So the input into g is
approaching negative two
00:02:25.430 --> 00:02:28.610
from above, from the right I should say,
00:02:28.610 --> 00:02:30.010
from values larger than negative two,
00:02:30.010 --> 00:02:32.890
and we can see that g
is approaching three.
00:02:32.890 --> 00:02:36.930
So this right over here is
going to be equal to three.
00:02:36.930 --> 00:02:41.443
Now, let's take the limit
as x approaches negative one
00:02:44.580 --> 00:02:49.580
from the left of g of h of x.
00:02:51.720 --> 00:02:54.490
What we could do is first think
about what is h approaching
00:02:54.490 --> 00:02:57.830
as x approaches negative
one from the left?
00:02:57.830 --> 00:03:00.800
As x approaches negative
one from the left,
00:03:00.800 --> 00:03:03.860
it looks like h is
approaching negative three.
00:03:03.860 --> 00:03:06.000
We could say this is the limit
00:03:07.060 --> 00:03:11.660
as h of x is approaching negative three,
00:03:11.660 --> 00:03:13.620
and it is approaching negative three
00:03:13.620 --> 00:03:15.860
from values greater than negative three.
00:03:15.860 --> 00:03:20.200
H of x is approaching
negative three from above,
00:03:20.200 --> 00:03:23.850
or we could say from values
greater than negative three,
00:03:23.850 --> 00:03:28.850
and then of g of h of x.
00:03:31.340 --> 00:03:32.173
Another way to think about it,
00:03:32.173 --> 00:03:34.790
what is the limit as the input to g
00:03:34.790 --> 00:03:38.550
approaches negative three from the right?
00:03:38.550 --> 00:03:42.600
As we approach negative
three from the right,
00:03:42.600 --> 00:03:46.300
g is right here at three,
00:03:46.300 --> 00:03:51.230
so this is going to be
equal to three again.
00:03:51.230 --> 00:03:54.890
So notice the right hand
limit and the left hand limit
00:03:54.890 --> 00:03:58.100
in this case are both equal to three.
00:03:58.100 --> 00:03:59.850
So when the right hand
and the left hand limit
00:03:59.850 --> 00:04:02.450
is equal to the same thing,
we know that the limit
00:04:02.450 --> 00:04:04.540
is equal to that thing.
00:04:04.540 --> 00:04:06.480
This is a pretty cool example,
00:04:06.480 --> 00:04:09.830
because the limit of, you
could say the internal function
00:04:09.830 --> 00:04:12.520
right over here of h of x, did not exist,
00:04:12.520 --> 00:04:16.293
but the limit of the composite
function still exists.
|
Limits of composite functions: external limit doesn't exist | https://www.youtube.com/watch?v=VAk50-zIes8 | vtt | https://www.youtube.com/api/timedtext?v=VAk50-zIes8&ei=7lWUZfLKLvC_mLAPgvCW0AE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D25A26D75324C2286422F93A405285EF99F395AD.23DE4FEB6FA9037AB5160063EF5DCE7C56C8593A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:01.580
- [Instructor] So over
here I have two functions
00:00:01.580 --> 00:00:03.950
that have been visually
or graphically defined.
00:00:03.950 --> 00:00:06.950
On the left here I have
the graph of g of x,
00:00:06.950 --> 00:00:09.920
and on the right here I
have the graph of h of x.
00:00:09.920 --> 00:00:11.760
And what I want to do is figure out
00:00:11.760 --> 00:00:16.760
what is the limit of g of
h of x as x approaches one.
00:00:17.690 --> 00:00:20.783
Pause this video and see
if you can figure that out.
00:00:21.690 --> 00:00:23.030
All right, now let's do this together.
00:00:23.030 --> 00:00:24.950
Now the first thing that
you might try to say is,
00:00:24.950 --> 00:00:27.530
all right, let's just figure out first,
00:00:27.530 --> 00:00:32.530
the limit as x approaches one of h of x.
00:00:33.180 --> 00:00:35.310
And when you look at that,
what is that going to be?
00:00:35.310 --> 00:00:38.210
Well, as we approach one from the left,
00:00:38.210 --> 00:00:40.650
it looks like h of x is approaching two.
00:00:40.650 --> 00:00:42.100
And as we approach from the right,
00:00:42.100 --> 00:00:44.260
it looks like h of x is approaching two.
00:00:44.260 --> 00:00:46.680
So it looks like this
is just going to be two.
00:00:46.680 --> 00:00:47.513
And let me see, okay,
00:00:47.513 --> 00:00:50.510
well maybe we can then
just input that into g.
00:00:50.510 --> 00:00:52.120
So what is g of two?
00:00:52.120 --> 00:00:54.830
Well, g of two is zero,
00:00:54.830 --> 00:00:56.870
but the limit doesn't seem defined.
00:00:56.870 --> 00:00:58.870
It looks like when we
approach two from the right,
00:00:58.870 --> 00:01:00.280
we're approaching zero.
00:01:00.280 --> 00:01:01.640
And when we approach two from the left,
00:01:01.640 --> 00:01:03.440
we're approaching negative two.
00:01:03.440 --> 00:01:06.400
So maybe this limit doesn't exist.
00:01:06.400 --> 00:01:07.800
But if you're thinking that,
00:01:07.800 --> 00:01:10.120
we haven't fully thought through it,
00:01:10.120 --> 00:01:12.550
because what we could do
is think about this limit
00:01:12.550 --> 00:01:16.190
in terms of both the left-handed
and right-handed limits.
00:01:16.190 --> 00:01:17.940
So let's think of it this way.
00:01:17.940 --> 00:01:21.540
First, let's think about what is the limit
00:01:22.420 --> 00:01:27.420
as x approaches one from the
left-hand side of g of h of x.
00:01:31.180 --> 00:01:32.980
All right, when you
think about it this way,
00:01:32.980 --> 00:01:37.520
if we're approaching one from
the left right over here,
00:01:37.520 --> 00:01:41.380
we see that we are
approaching two from the left,
00:01:41.380 --> 00:01:44.620
I guess you could say, we're
approaching two from below.
00:01:44.620 --> 00:01:48.360
And so the thing that we
are inputting into g of x
00:01:48.360 --> 00:01:51.180
is approaching two from below.
00:01:51.180 --> 00:01:54.270
So the thing that we are inputting into g
00:01:54.270 --> 00:01:56.730
is approaching two from below.
00:01:56.730 --> 00:01:59.220
So if you approach two from below,
00:01:59.220 --> 00:02:01.000
right over here, what is g approaching?
00:02:01.000 --> 00:02:04.290
It looks like g is
approaching negative two.
00:02:04.290 --> 00:02:07.450
So this looks like it is going
to be equal to negative two,
00:02:07.450 --> 00:02:09.620
at least this left-handed limit.
00:02:09.620 --> 00:02:11.460
Now let's do a right-handed limit.
00:02:11.460 --> 00:02:14.960
What is the limit as x approaches one
00:02:14.960 --> 00:02:19.670
from the right hand of g of h of x?
00:02:19.670 --> 00:02:21.670
Well, we can do the same exercise.
00:02:21.670 --> 00:02:24.480
As we approach one from the right,
00:02:24.480 --> 00:02:28.050
it looks like h is
approaching two from below,
00:02:28.050 --> 00:02:30.660
from values less than two.
00:02:30.660 --> 00:02:33.820
And so if we are
approaching two from below,
00:02:33.820 --> 00:02:34.730
because remember,
00:02:34.730 --> 00:02:38.110
whatever h is outputting
is the input into g.
00:02:38.110 --> 00:02:40.900
So if the thing that
we're inputting g into g
00:02:40.900 --> 00:02:43.190
is approaching two from below,
00:02:43.190 --> 00:02:45.640
that means that g, once again,
00:02:45.640 --> 00:02:49.130
is going to be approaching negative two.
00:02:49.130 --> 00:02:52.370
So this is a really, really,
really interesting case,
00:02:52.370 --> 00:02:57.370
where the limit of g of
x as x approaches two
00:02:57.470 --> 00:02:59.010
does not exist.
00:02:59.010 --> 00:03:00.440
But because on h of x,
00:03:00.440 --> 00:03:03.220
when we approach from both the
left and the right hand side,
00:03:03.220 --> 00:03:05.490
h is approaching two from below.
00:03:05.490 --> 00:03:07.770
We just have to think
about the left-handed limit
00:03:07.770 --> 00:03:11.900
as we approach two from
below or from the left on g,
00:03:11.900 --> 00:03:15.210
because in both situations, we
are approaching negative two.
00:03:15.210 --> 00:03:17.930
And so that is going to be our limit.
00:03:17.930 --> 00:03:19.860
When the left-handed and
the right-handed limit
00:03:19.860 --> 00:03:22.150
are the same, that is
going to be your limit.
00:03:22.150 --> 00:03:24.163
It is equal to negative two.
|
Finding decreasing interval given the function | https://www.youtube.com/watch?v=Fk4pn8ZOy1w | vtt | https://www.youtube.com/api/timedtext?v=Fk4pn8ZOy1w&ei=7lWUZZ3kL4u1vdIPqpKNEA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D32230C503504448ADC38D1AAB73FFA6E5D2C0F5.88E4D22CF949D8E94A012D2FF9B574663979056C&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.510 --> 00:00:02.330
- [Instructor] Let's
say we have the function
00:00:02.330 --> 00:00:06.080
F of X is equal to X to the sixth,
00:00:06.080 --> 00:00:08.540
minus three X to the fifth.
00:00:08.540 --> 00:00:10.630
And my question to you
00:00:10.630 --> 00:00:13.740
is using only what we
know about derivatives.
00:00:13.740 --> 00:00:16.670
Try to figure out over
what interval or intervals
00:00:16.670 --> 00:00:18.930
is this function decreasing?
00:00:18.930 --> 00:00:21.480
Pause the video and
try to figure that out.
00:00:21.480 --> 00:00:24.130
All right, now let's do this together.
00:00:24.130 --> 00:00:26.650
So we know that a function is decreasing
00:00:26.650 --> 00:00:28.530
when its derivative is negative.
00:00:28.530 --> 00:00:29.780
Or another way to say it,
00:00:29.780 --> 00:00:30.990
It's going to be decreasing
00:00:30.990 --> 00:00:33.560
when F prime of X
00:00:33.560 --> 00:00:36.800
is less than zero.
00:00:36.800 --> 00:00:39.010
So what is F prime of X?
00:00:39.010 --> 00:00:40.770
Well, we could use the derivative rules
00:00:40.770 --> 00:00:42.420
and drew the properties we know.
00:00:42.420 --> 00:00:45.000
We apply the power rule
to X, to the sixth,
00:00:45.000 --> 00:00:46.300
We bring the six out front
00:00:46.300 --> 00:00:48.430
or multiply the one coefficient here,
00:00:48.430 --> 00:00:51.510
times six, to get six,
00:00:51.510 --> 00:00:54.000
X to the fifth
00:00:54.000 --> 00:00:55.570
detriment that exponent,
00:00:55.570 --> 00:00:58.550
minus bring the five times the three
00:00:58.550 --> 00:01:01.040
minus 15, X to the,
00:01:01.040 --> 00:01:02.330
we detriment the five,
00:01:02.330 --> 00:01:04.410
so X to the fourth.
00:01:04.410 --> 00:01:05.940
And we need to figure out
00:01:05.940 --> 00:01:10.310
over what intervals is this
going to be less than zero.
00:01:10.310 --> 00:01:13.160
And now let's see how we can
simplify this a little bit.
00:01:13.160 --> 00:01:16.730
Both of these terms are
divisible by X to the fourth,
00:01:16.730 --> 00:01:19.160
and they're both divisible by three.
00:01:19.160 --> 00:01:23.480
So let's factor out a
three X to the fourth
00:01:23.480 --> 00:01:25.830
times, you factor out of
three X to the fourth year,
00:01:25.830 --> 00:01:29.090
you're left with a two X,
00:01:29.090 --> 00:01:32.060
and then over here you have minus five
00:01:32.060 --> 00:01:34.650
has to be less than zero.
00:01:34.650 --> 00:01:36.240
Any interval where this is true,
00:01:36.240 --> 00:01:38.570
we are going to be decreasing.
00:01:38.570 --> 00:01:40.710
Now, how do we get this
to be less than zero?
00:01:40.710 --> 00:01:42.580
Well, if I take the product of two things
00:01:42.580 --> 00:01:43.970
and it's less than zero,
00:01:43.970 --> 00:01:46.530
that means that they have
to have different signs,
00:01:46.530 --> 00:01:48.250
either one's positive
and the other's negative
00:01:48.250 --> 00:01:50.390
or one's negative and
the other's positive.
00:01:50.390 --> 00:01:52.030
So we have two situations.
00:01:52.030 --> 00:01:54.200
So we could say either,
00:01:54.200 --> 00:01:57.810
either, three X to the fourth
00:01:57.810 --> 00:01:59.600
is greater than zero
00:01:59.600 --> 00:02:04.260
and, and two X minus five
00:02:04.260 --> 00:02:06.200
is less than zero.
00:02:06.200 --> 00:02:07.870
So that's one situation.
00:02:07.870 --> 00:02:09.520
I'll do some in a different color,
00:02:09.520 --> 00:02:12.700
or I'll do this one in a different color,
00:02:12.700 --> 00:02:16.920
three X to the fourth is less than zero
00:02:16.920 --> 00:02:20.620
and two X minus five
00:02:20.620 --> 00:02:22.810
is greater than zero.
00:02:22.810 --> 00:02:25.170
Actually let me stay on
the second case first.
00:02:25.170 --> 00:02:26.420
Are there any situations
00:02:26.420 --> 00:02:29.270
where three X to the fourth
can be less than zero?
00:02:29.270 --> 00:02:30.320
You take any number,
00:02:30.320 --> 00:02:31.480
you take it to the fourth power
00:02:31.480 --> 00:02:32.480
even if it's a negative,
00:02:32.480 --> 00:02:33.940
it's going to become a positive.
00:02:33.940 --> 00:02:37.310
So you can't get a negative
expression right over here.
00:02:37.310 --> 00:02:40.790
So actually the second condition
is impossible to obtain.
00:02:40.790 --> 00:02:43.190
You can't get any situation for any X
00:02:43.190 --> 00:02:45.410
where three X to the
fourth is less than zero.
00:02:45.410 --> 00:02:47.330
So we can rule this one out.
00:02:47.330 --> 00:02:49.310
And so this is our best hope.
00:02:49.310 --> 00:02:52.170
So under what conditions
is three X to the fourth,
00:02:52.170 --> 00:02:54.630
greater than zero.
00:02:54.630 --> 00:02:56.570
Well, if you divide both sides by three,
00:02:56.570 --> 00:03:01.530
you get X to the fourth
is greater than zero.
00:03:01.530 --> 00:03:02.950
And if you think about it,
00:03:02.950 --> 00:03:05.930
this is gonna be true for any X value
00:03:05.930 --> 00:03:08.110
that is not equal to zero.
00:03:08.110 --> 00:03:09.410
Even if you have a negative value there,
00:03:09.410 --> 00:03:10.243
if you have a negative one,
00:03:10.243 --> 00:03:11.980
you take it to the fourth
power becomes a positive one.
00:03:11.980 --> 00:03:14.100
Only zero will be equal to zero
00:03:14.100 --> 00:03:15.570
when you take it to the fourth power.
00:03:15.570 --> 00:03:16.510
So one way we could say this
00:03:16.510 --> 00:03:19.090
is going to be true for any non zero X,
00:03:19.090 --> 00:03:22.130
or we could just say,
X does not equal zero,
00:03:22.130 --> 00:03:25.140
and, this is a little
bit more straightforward,
00:03:25.140 --> 00:03:26.750
we add five to both sides
00:03:26.750 --> 00:03:29.240
we get two X is less than five,
00:03:29.240 --> 00:03:31.380
divide both sides by two,
00:03:31.380 --> 00:03:35.250
you get X is less than five halves.
00:03:35.250 --> 00:03:37.180
So it might be tempting to say, all right,
00:03:37.180 --> 00:03:38.860
the intervals that matter are
00:03:38.860 --> 00:03:41.930
all the exes less than five halves,
00:03:41.930 --> 00:03:45.710
but X cannot be equal to zero.
00:03:45.710 --> 00:03:48.210
Now, is that the entire interval
00:03:48.210 --> 00:03:50.540
where our function is decreasing?
00:03:50.540 --> 00:03:53.370
Well, let's think about
what happens at zero itself.
00:03:53.370 --> 00:03:57.990
We're decreasing over the
interval from negative infinity
00:03:57.990 --> 00:03:59.710
all the way up to zero.
00:03:59.710 --> 00:04:03.920
And we're also decreasing
from zero to five halves.
00:04:03.920 --> 00:04:06.220
And so for decreasing
right to the left of zero,
00:04:06.220 --> 00:04:07.940
we're decreasing right
to the right of zero,
00:04:07.940 --> 00:04:10.020
we're actually going to
be decreasing at zero
00:04:10.020 --> 00:04:14.010
at we're also gonna be
decreasing at zero as well.
00:04:14.010 --> 00:04:15.640
So there's something interesting here,
00:04:15.640 --> 00:04:18.800
even though the derivative
at X equals zero,
00:04:18.800 --> 00:04:20.950
is going to be equal to zero,
00:04:20.950 --> 00:04:23.510
we are still decreasing.
00:04:23.510 --> 00:04:25.810
And so the interval that we care about
00:04:25.810 --> 00:04:27.550
the interval over which we're decreasing
00:04:27.550 --> 00:04:31.090
is just X is less than five halves.
00:04:31.090 --> 00:04:33.340
And we can see that by
graphing the function,
00:04:33.340 --> 00:04:35.790
I graphed it on Desmos,
00:04:35.790 --> 00:04:37.620
and you can see here
00:04:37.620 --> 00:04:40.580
that the function is decreasing
from negative infinity,
00:04:40.580 --> 00:04:42.710
it's decreasing at a
slower and slower rate
00:04:42.710 --> 00:04:45.790
we get to zero still
decreasing to the left of zero,
00:04:45.790 --> 00:04:48.410
and then it continues to
decrease to the right of zero.
00:04:48.410 --> 00:04:51.570
So any, any value, any X
value to the left of zero
00:04:51.570 --> 00:04:52.940
the value of the function is going to be
00:04:52.940 --> 00:04:54.980
larger than F of zero,
00:04:54.980 --> 00:04:56.610
and X to the right of zero.
00:04:56.610 --> 00:04:57.770
The value of the function is going to be
00:04:57.770 --> 00:04:59.760
less than the function at zero.
00:04:59.760 --> 00:05:02.180
So it's actually decreasing through zero,
00:05:02.180 --> 00:05:06.110
even though the slope of the
tangent line at zero is zero,
00:05:06.110 --> 00:05:07.800
even though it's non negative
00:05:07.800 --> 00:05:09.530
and then we keep decreasing
00:05:09.530 --> 00:05:11.970
so we're decreasing for all values of X,
00:05:11.970 --> 00:05:14.890
less than five halves,
00:05:14.890 --> 00:05:16.693
which you can see visually here.
|
Example: Graphing y=-cos(π⋅x)+1.5 | https://www.youtube.com/watch?v=9XtCWJmKF28 | vtt | https://www.youtube.com/api/timedtext?v=9XtCWJmKF28&ei=7lWUZYG7I-u4mLAPtuOK8AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=92DF96A1F5EB5DC3C9CE0CDDA9AB2F1680400CAE.6AD53271A49D1A4EEBEDFA87B637B40EDFD98BE4&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.740 --> 00:00:01.710
- [Instructor] We're told to graph
00:00:01.710 --> 00:00:05.850
y is equal to negative
cosine of pi times x plus 1.5
00:00:06.998 --> 00:00:09.190
in the interactive widget.
00:00:09.190 --> 00:00:11.810
So, pause this video and think
about how you would do that.
00:00:11.810 --> 00:00:13.980
And just to explain how this widget works
00:00:13.980 --> 00:00:15.780
if you're trying to do it on Khan Academy,
00:00:15.780 --> 00:00:19.610
this dot right over here
helps define the midline.
00:00:19.610 --> 00:00:21.180
You can move that up and down.
00:00:21.180 --> 00:00:23.090
And then this one right over here
00:00:23.090 --> 00:00:25.070
is a neighboring extreme point.
00:00:25.070 --> 00:00:28.850
So either a minimum or a maximum point.
00:00:28.850 --> 00:00:32.240
So, there's a couple of ways
that we could approach this.
00:00:32.240 --> 00:00:33.073
First of all,
00:00:33.073 --> 00:00:37.420
let's just think about what
would cosine of pi x look like,
00:00:37.420 --> 00:00:38.881
and then we'll think about
what the negative does
00:00:38.881 --> 00:00:40.740
and the plus 1.5.
00:00:40.740 --> 00:00:42.900
So, cosine of pi x.
00:00:42.900 --> 00:00:45.390
When x is equal zero,
00:00:45.390 --> 00:00:48.500
pi times zero, is just going to be zero,
00:00:48.500 --> 00:00:51.750
cosine of zero is equal to one.
00:00:51.750 --> 00:00:54.010
And if we're just talking
about cosine of pi x,
00:00:54.010 --> 00:00:56.570
that's going to be a maximum
point when you hit one.
00:00:56.570 --> 00:00:58.320
Just cosine of pi x would oscillate
00:00:58.320 --> 00:01:00.550
between one and negative one.
00:01:00.550 --> 00:01:02.130
And then what would its period be
00:01:02.130 --> 00:01:05.190
if we're talking about cosine of pi x?
00:01:05.190 --> 00:01:06.300
Well, you might remember,
00:01:06.300 --> 00:01:09.530
one way to think about the
period is to take two pi
00:01:09.530 --> 00:01:12.730
and divide it by whatever
the coefficient is
00:01:12.730 --> 00:01:14.530
on the x right over here.
00:01:14.530 --> 00:01:17.850
So two pi divided by pi would tell us
00:01:17.850 --> 00:01:20.940
that we have a period of two.
00:01:20.940 --> 00:01:23.770
And so how do we construct
a period of two here?
00:01:23.770 --> 00:01:27.420
Well, that means that as we
start here at x equals zero,
00:01:27.420 --> 00:01:30.500
we're at one, we want to get
back to that maximum point
00:01:30.500 --> 00:01:33.830
by the time x is equal to two.
00:01:33.830 --> 00:01:36.180
So let me see how I can do that.
00:01:36.180 --> 00:01:38.660
If I were to squeeze it a little bit,
00:01:38.660 --> 00:01:40.120
that looks pretty good.
00:01:40.120 --> 00:01:42.100
And the reason why I worked
on this midline point
00:01:42.100 --> 00:01:45.020
is I liked having this
maximum point at one
00:01:45.020 --> 00:01:47.440
when x is equal to zero,
00:01:47.440 --> 00:01:49.550
because we said cosine of pi times zero
00:01:49.550 --> 00:01:50.670
should be equal to one.
00:01:50.670 --> 00:01:53.480
So that's why I'm just
manipulating this other point
00:01:53.480 --> 00:01:55.620
in order to set the period right.
00:01:55.620 --> 00:01:56.510
But this looks right.
00:01:56.510 --> 00:01:58.100
We're going from this maximum point
00:01:58.100 --> 00:01:59.420
and we're going all the way down
00:01:59.420 --> 00:02:01.120
and then back to that maximum point,
00:02:01.120 --> 00:02:03.800
and it looks like our
period is indeed two.
00:02:03.800 --> 00:02:07.600
So this is what the graph of
cosine of pi x would look like.
00:02:07.600 --> 00:02:09.920
Now, what about this negative sign?
00:02:09.920 --> 00:02:12.650
Well, the negative would
essentially flip it around.
00:02:12.650 --> 00:02:14.820
So, instead of whenever
we're equaling one,
00:02:14.820 --> 00:02:15.940
we should be equal to negative one.
00:02:15.940 --> 00:02:17.510
And every time we're
equal to negative one,
00:02:17.510 --> 00:02:18.670
we should be equal to one.
00:02:18.670 --> 00:02:20.100
So what I could is I could just take that
00:02:20.100 --> 00:02:21.520
and then bring it down here,
00:02:21.520 --> 00:02:23.300
and there you have it,
I flipped it around.
00:02:23.300 --> 00:02:27.090
So this is the graph of y
equals negative cosine of pi x.
00:02:27.090 --> 00:02:29.773
And then last but not least,
we have this plus 1.5.
00:02:30.669 --> 00:02:33.840
So that's just going to
shift everything up by 1.5.
00:02:33.840 --> 00:02:36.670
So I'm just going to
shift everything up by,
00:02:36.670 --> 00:02:41.660
shift it up by 1.5 and shift it up by 1.5.
00:02:43.530 --> 00:02:44.700
And there you have it.
00:02:44.700 --> 00:02:49.700
That is the graph of negative
cosine of pi x plus 1.5.
00:02:49.710 --> 00:02:53.170
And you can validate
that that's our midline.
00:02:53.170 --> 00:02:56.560
We're still oscillating
one above and one below.
00:02:56.560 --> 00:02:59.940
The negative sign, when
cosine of pi time zero,
00:02:59.940 --> 00:03:01.800
that should be one, but then
you take the negative that,
00:03:01.800 --> 00:03:03.340
we get to negative one.
00:03:03.340 --> 00:03:07.050
You add 1.5 to that,
you get to positive .5.
00:03:07.050 --> 00:03:09.593
And so this is all looking quite good.
|
Example: Graphing y=3⋅sin(½⋅x)-2 | https://www.youtube.com/watch?v=-Si4W4KyeMw | vtt | https://www.youtube.com/api/timedtext?v=-Si4W4KyeMw&ei=7lWUZeOwLsq0vdIPtOmh2A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=369CEFE51262A4DC584655F12CDE9D0B079D501A.0793E16A5B2C9178ECB09E619FDBFF9735D199D9&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.220 --> 00:00:01.450
- [Instructor] So we're asked to graph
00:00:01.450 --> 00:00:04.440
y is equal to three times sine of 1/2x
00:00:04.440 --> 00:00:06.900
minus 2 in the interactive widget.
00:00:06.900 --> 00:00:08.250
And this is the interactive widget
00:00:08.250 --> 00:00:10.460
that you would find on Khan Academy.
00:00:10.460 --> 00:00:14.410
And it first bears mentioning
how this widget works.
00:00:14.410 --> 00:00:16.330
So this point right over here,
00:00:16.330 --> 00:00:19.670
it helps you define the midline,
00:00:19.670 --> 00:00:20.800
the thing that you could imagine
00:00:20.800 --> 00:00:23.540
your sine or cosine
function oscillates around,
00:00:23.540 --> 00:00:26.400
and then you also define a
neighboring extreme point,
00:00:26.400 --> 00:00:29.240
either a maximum or a minimum point
00:00:29.240 --> 00:00:32.060
to graph your function.
00:00:32.060 --> 00:00:33.700
So let's think about how we would do this,
00:00:33.700 --> 00:00:35.470
and like always, I encourage
you to pause this video
00:00:35.470 --> 00:00:37.810
and think about how you
would do it yourself.
00:00:37.810 --> 00:00:39.510
But the first way I like to think about it
00:00:39.510 --> 00:00:42.010
is what would a regular,
just, if this just said
00:00:42.010 --> 00:00:45.370
y is equal to sine of x,
how would I graph that?
00:00:45.370 --> 00:00:47.560
Well, sine of 0 is 0.
00:00:47.560 --> 00:00:52.560
Sine of pi over 2 is 1.
00:00:52.770 --> 00:00:55.530
And then sine of pi is 0, again.
00:00:55.530 --> 00:00:59.550
And so this is what just regular
sine of x would look like.
00:00:59.550 --> 00:01:01.770
But let's think about
how this is different.
00:01:01.770 --> 00:01:04.300
Well, first of all,
it's not just sine of x,
00:01:04.300 --> 00:01:06.820
it's sine of 1/2x.
00:01:06.820 --> 00:01:10.730
So what would be the graph
of just sine of 1/2x?
00:01:10.730 --> 00:01:11.940
Well, one way to think about it,
00:01:11.940 --> 00:01:13.660
there's actually two
ways to think about it,
00:01:13.660 --> 00:01:16.720
is a coefficient right
over here on your x term
00:01:16.720 --> 00:01:19.160
that tells you how fast
00:01:19.160 --> 00:01:22.070
the thing that's being
inputted into sine is growing.
00:01:22.070 --> 00:01:24.720
And now it's going to grow half as fast.
00:01:24.720 --> 00:01:26.680
And so one way to think about it is
00:01:26.680 --> 00:01:29.920
your period is now going
to be twice as long.
00:01:29.920 --> 00:01:31.210
So one way to think about it is
00:01:31.210 --> 00:01:33.940
instead of getting to this next
maximum point at pi over 2,
00:01:33.940 --> 00:01:35.620
you're going to get there at pi.
00:01:35.620 --> 00:01:36.770
And you could test that.
00:01:36.770 --> 00:01:39.210
If you at, when x is equal to pi,
00:01:39.210 --> 00:01:42.120
this will be 1/2 pi, sine of 1/2 pi,
00:01:42.120 --> 00:01:44.930
is indeed equal to 1.
00:01:44.930 --> 00:01:47.100
Another way to think about it is
00:01:47.100 --> 00:01:48.640
you might be familiar with the formula,
00:01:48.640 --> 00:01:49.920
although I always like you to think
00:01:49.920 --> 00:01:51.790
about where these formulas come from,
00:01:51.790 --> 00:01:55.490
that to figure out the period
of a sine or cosine function,
00:01:55.490 --> 00:01:57.080
you take 2 pi and you divide it
00:01:57.080 --> 00:01:59.370
by whatever this coefficient is.
00:01:59.370 --> 00:02:02.040
So 2 pi divided by 1/2
is going to be 4 pi.
00:02:02.040 --> 00:02:03.160
And you could see the period here,
00:02:03.160 --> 00:02:07.440
we go up, down, and back
to where we were over 4 pi.
00:02:07.440 --> 00:02:08.400
And that makes sense,
00:02:08.400 --> 00:02:10.360
because if you just had
a 1 coefficient here,
00:02:10.360 --> 00:02:12.950
your period would be 2 pi, 2 pi radians.
00:02:12.950 --> 00:02:15.820
You make one circle around the unit circle
00:02:15.820 --> 00:02:17.430
is one way to think about it.
00:02:17.430 --> 00:02:21.670
So right here we have the
graph of sine of 1/2x.
00:02:21.670 --> 00:02:23.370
Now what if we wanted to, instead,
00:02:23.370 --> 00:02:27.180
think about 3 times the
graph of sine of 1/2x,
00:02:27.180 --> 00:02:29.560
or 3 sine 1/2x?
00:02:29.560 --> 00:02:31.010
Well then our amplitude's just going to be
00:02:31.010 --> 00:02:32.450
three times as much.
00:02:32.450 --> 00:02:35.450
And so instead of our
maximum point going from,
00:02:35.450 --> 00:02:37.030
instead of our maximum point being at 1,
00:02:37.030 --> 00:02:38.910
it will now be at 3.
00:02:38.910 --> 00:02:40.500
Or another way to think about it is
00:02:40.500 --> 00:02:44.500
we're going 3 above the midline
and 3 below the midline.
00:02:44.500 --> 00:02:48.560
So this right over here is
the graph of 3 sine of 1/2x.
00:02:48.560 --> 00:02:50.620
Now we have one thing left to do,
00:02:50.620 --> 00:02:52.330
and this is this minus 2.
00:02:52.330 --> 00:02:55.960
So this minus 2 is just going
to shift everything down by 2.
00:02:55.960 --> 00:02:57.810
So we just have to shift everything down.
00:02:57.810 --> 00:02:59.780
So let me shift this one down by 2
00:02:59.780 --> 00:03:01.760
and let me shift it this one down by 2.
00:03:01.760 --> 00:03:03.460
And so there you have it.
00:03:03.460 --> 00:03:07.250
Notice our period is still 4 pi.
00:03:07.250 --> 00:03:09.770
Our amplitude, how much we oscillate
00:03:09.770 --> 00:03:12.670
above or below the midline, is still 3.
00:03:12.670 --> 00:03:14.600
And now we have this minus 2.
00:03:14.600 --> 00:03:17.180
Another way to think about
it, when x is equal to 0,
00:03:17.180 --> 00:03:19.140
this whole first term is going to be 0,
00:03:19.140 --> 00:03:21.530
and y should be equal to negative 2?
00:03:21.530 --> 00:03:22.563
And we're done.
|
GoodBoy3000 | https://www.youtube.com/watch?v=tD1e_BaOA4U | vtt | https://www.youtube.com/api/timedtext?v=tD1e_BaOA4U&ei=7lWUZc_CJK_oxN8PkpOn4A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B3E16EE7BFA022B0EBBFEDAE78941AAFC7AC0F14.AA4B1C89D818D8E49E749106F0369C71C39E5D4E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.485 --> 00:00:01.650
(soft music)
00:00:01.650 --> 00:00:03.580
- [Narrator] Every morning,
your neural chip alarm
00:00:03.580 --> 00:00:07.170
goes off at 5:00 a.m.
Metropoluxe standard time.
00:00:07.170 --> 00:00:09.000
You'd prefer to be woken up by the Sun,
00:00:09.000 --> 00:00:11.560
but nobody in your sector
of the city is allowed
00:00:11.560 --> 00:00:15.740
to venture to the upper levels
to experience real sunlight.
00:00:15.740 --> 00:00:19.300
Oh well, chip-regulated
hormones and artificial sunlight
00:00:19.300 --> 00:00:22.000
work well enough for the likes of us.
00:00:22.000 --> 00:00:23.400
Even at this early hour,
00:00:23.400 --> 00:00:26.730
you hear the hum of
Metropoluxe all around you.
00:00:26.730 --> 00:00:29.820
The artificial sun lamps
warming up their bulbs,
00:00:29.820 --> 00:00:32.010
the garbage bots circling the city floor
00:00:32.010 --> 00:00:34.010
to sweep up the trash,
00:00:34.010 --> 00:00:37.670
the workers trudging to
expresselator terminals,
00:00:37.670 --> 00:00:38.800
you roll out of your cot
00:00:38.800 --> 00:00:42.120
and switch on the tiny sunlamp
over the tiny workbench
00:00:42.120 --> 00:00:44.870
you crammed into the corner of your room.
00:00:44.870 --> 00:00:48.710
As you approach the
table, GB3 whirs awake.
00:00:48.710 --> 00:00:51.100
You greet him fondly as you pat his head.
00:00:51.100 --> 00:00:53.300
The robot nuzzles up next to you.
00:00:53.300 --> 00:00:55.890
Its metal fur is cold this morning.
00:00:55.890 --> 00:00:57.670
But you don't really mind.
00:00:57.670 --> 00:01:01.170
The GoodBoy3000 is a
canine companion robot,
00:01:01.170 --> 00:01:03.430
the most advanced technology of its kind.
00:01:03.430 --> 00:01:05.150
Well, except for the fact
00:01:05.150 --> 00:01:07.543
that they're up to the 7,000 series now,
00:01:08.610 --> 00:01:10.690
and this isn't the real deal.
00:01:10.690 --> 00:01:13.740
Those costs hundreds of
thousands of credits.
00:01:13.740 --> 00:01:17.070
You found a good as new
GoodBoy3000 neuro coil
00:01:17.070 --> 00:01:19.380
at the scrap yard a few years back,
00:01:19.380 --> 00:01:21.840
and figured you could
learn how to build one.
00:01:21.840 --> 00:01:24.560
Years of tinkering and
experimenting later,
00:01:24.560 --> 00:01:26.710
you built your best friend.
00:01:26.710 --> 00:01:29.560
Speaking of the scrapyard,
you glance at the nano clock
00:01:29.560 --> 00:01:32.060
from the corner of your heads up display.
00:01:32.060 --> 00:01:35.860
You have about 45 more
minutes left to work on GB3
00:01:35.860 --> 00:01:37.970
before you have to head
to the expresselators
00:01:37.970 --> 00:01:39.950
to get to work on time.
00:01:39.950 --> 00:01:42.160
Just thinking about your
dead circuit of a boss
00:01:42.160 --> 00:01:44.150
makes you grumble to yourself.
00:01:44.150 --> 00:01:47.080
If you're even a second
late, you're fired.
00:01:47.080 --> 00:01:48.780
You shiver at the thought.
00:01:48.780 --> 00:01:51.190
Losing your job would
mean that your parents
00:01:51.190 --> 00:01:52.770
would be furious.
00:01:52.770 --> 00:01:56.350
And what little credits you
did have would quickly dry up.
00:01:56.350 --> 00:02:00.050
You motion for GB3 to sit in
front of you on the workbench.
00:02:00.050 --> 00:02:01.830
You flip on his maintenance switch
00:02:01.830 --> 00:02:05.810
and start to examine his
auxiliary memory backup subsystem.
00:02:05.810 --> 00:02:07.630
You've been getting up
early for months now
00:02:07.630 --> 00:02:09.360
to spend time on this.
00:02:09.360 --> 00:02:11.240
It's not a feature that these robots have,
00:02:11.240 --> 00:02:13.510
but that hasn't stopped
you from taking the time
00:02:13.510 --> 00:02:16.400
and effort to figure out
the mechanics on your own.
00:02:16.400 --> 00:02:19.380
Everything from the hour
spent trolling the holodecks
00:02:19.380 --> 00:02:21.360
to study robot manuals,
00:02:21.360 --> 00:02:24.310
to showing up to your
workbench every day to tinker
00:02:24.310 --> 00:02:26.240
and experiment with parts.
00:02:26.240 --> 00:02:29.940
If you can solve it, GB3 will
be the only dog in Metropoluxe
00:02:29.940 --> 00:02:31.440
with this tech.
00:02:31.440 --> 00:02:33.230
Your hard work has paid off.
00:02:33.230 --> 00:02:36.240
Your GB3 is as good as
the newest 7,000 series
00:02:36.240 --> 00:02:38.820
they keep showing on the telebeam.
00:02:38.820 --> 00:02:39.820
You shake your head.
00:02:40.670 --> 00:02:44.650
You can't even imagine owning
something that expensive.
00:02:44.650 --> 00:02:47.070
Who even has that many credits?
00:02:47.070 --> 00:02:49.910
A solar in the upper levels, you guess.
00:02:49.910 --> 00:02:51.870
You've been trying to make a memory input
00:02:51.870 --> 00:02:54.270
of GB3 for weeks now.
00:02:54.270 --> 00:02:56.840
If something were to happen with GB3,
00:02:56.840 --> 00:02:58.950
you could initiate a restoration process
00:02:58.950 --> 00:03:00.840
that would bring him back to life.
00:03:00.840 --> 00:03:04.390
The thought of losing
him, his memory data,
00:03:04.390 --> 00:03:06.800
well, it's unthinkable.
00:03:06.800 --> 00:03:08.810
You have a promise you made to yourself
00:03:08.810 --> 00:03:10.920
that you take very seriously.
00:03:10.920 --> 00:03:13.770
Some progress, just any little thing
00:03:13.770 --> 00:03:16.880
everyday while working on GB3.
00:03:16.880 --> 00:03:19.460
But the last week or so has been rough.
00:03:19.460 --> 00:03:20.760
You check the clock again.
00:03:21.650 --> 00:03:24.030
You're running low on time for today.
00:03:24.030 --> 00:03:26.760
And while everything seems
to be connected properly,
00:03:26.760 --> 00:03:28.810
it just hasn't been working.
00:03:28.810 --> 00:03:31.300
Still, your promise.
00:03:31.300 --> 00:03:35.083
You find an empty power connection
on one of the components.
00:03:36.110 --> 00:03:38.730
That component's already
connected to the main feed.
00:03:38.730 --> 00:03:41.210
So you're not quite sure
why there's another lead
00:03:41.210 --> 00:03:44.600
going to it, but hey, it's something.
00:03:44.600 --> 00:03:48.090
You wire it up, put a dab
of sotter on the connection,
00:03:48.090 --> 00:03:50.673
and start closing the
access panels you'd opened.
00:03:52.560 --> 00:03:54.920
You even use an upgraded replacement panel
00:03:54.920 --> 00:03:58.890
over your custom enclosure
to ensure progress for today,
00:03:58.890 --> 00:04:01.270
in case the power thing was a dead end?
00:04:01.270 --> 00:04:03.160
You flip the maintenance switch back off
00:04:03.160 --> 00:04:06.740
and grab your satchel as GB3
whirs to life behind you.
00:04:06.740 --> 00:04:09.210
He greets you by rubbing
the whole length of his body
00:04:09.210 --> 00:04:11.660
along your leg, shoulder to tail,
00:04:11.660 --> 00:04:15.510
his signature move which
you taught him on your own.
00:04:15.510 --> 00:04:17.610
You give him a few quick paths on the head
00:04:17.610 --> 00:04:18.803
and hurry out the door.
00:04:19.680 --> 00:04:21.830
You check the data pad and immediately
00:04:21.830 --> 00:04:24.910
see the alerts you've been
missing while tinkering.
00:04:24.910 --> 00:04:28.047
Expresselator's out again.
00:04:28.047 --> 00:04:29.400
(upbeat music)
00:04:29.400 --> 00:04:31.130
It's not the end of the world.
00:04:31.130 --> 00:04:32.880
You only take it one stop anyhow,
00:04:32.880 --> 00:04:35.260
but the alternative is a hyper cycle path
00:04:35.260 --> 00:04:37.670
you always try to avoid.
00:04:37.670 --> 00:04:40.810
You hate showing up to
work already caked in dirt.
00:04:40.810 --> 00:04:43.030
You sigh, run to your bike,
00:04:43.030 --> 00:04:45.361
and head out to the edge of Metropoluxe.
00:04:45.361 --> 00:04:47.550
(cosmic whir)
00:04:47.550 --> 00:04:50.250
This is probably the
closest you've ever cut it.
00:04:50.250 --> 00:04:52.420
It looks like you'll
arrive just a minute or two
00:04:52.420 --> 00:04:54.340
before the start of your shift.
00:04:54.340 --> 00:04:56.650
And that's if nothing else goes wrong.
00:04:56.650 --> 00:04:58.680
Thankfully, nothing does.
00:04:58.680 --> 00:05:02.120
And a short while later you're
hopping off your hyper cycle
00:05:02.120 --> 00:05:04.750
and sprinting to the
gate of the rusty rodeo.
00:05:04.750 --> 00:05:07.830
Your satchel slapping
at the top of your leg,
00:05:07.830 --> 00:05:11.060
you skid through the door,
just as the hourly reminder
00:05:11.060 --> 00:05:14.860
blares across the telobeam
from the Metropoluxe council.
00:05:14.860 --> 00:05:17.170
- You are in sector 22
00:05:17.170 --> 00:05:20.980
of the Metropoluxe
Industrial Reclamation Zone.
00:05:20.980 --> 00:05:24.240
Travel is prohibited to solar levels.
00:05:24.240 --> 00:05:29.030
Do not attempt to interact
with the solar, thank you.
00:05:29.030 --> 00:05:32.160
- You hate being reminded how
stuck you are in this place,
00:05:32.160 --> 00:05:33.930
but since you just swiped in on time,
00:05:33.930 --> 00:05:37.620
you've still got a job
and you've got GB3 too.
00:05:37.620 --> 00:05:39.550
The scrap bot at the gate chirps.
00:05:39.550 --> 00:05:44.140
- Dangerous debris detected,
rerouting to crusher.
00:05:44.140 --> 00:05:45.270
- That's odd.
00:05:45.270 --> 00:05:48.660
You usually don't get new scrap
until later in your shift.
00:05:48.660 --> 00:05:50.580
You turn to look at
what came into the yard,
00:05:50.580 --> 00:05:54.000
but for now, all you see is
the massive magnet engaged
00:05:54.000 --> 00:05:55.850
in front of the gate.
00:05:55.850 --> 00:05:58.220
When it lifts, you drop your wrench
00:05:58.220 --> 00:06:03.220
as you see GB3 stuck to the
underside, his visor dim.
00:06:03.330 --> 00:06:07.260
A GoodBoy3000 can't survive
a magnetic field like that.
00:06:07.260 --> 00:06:09.910
They're still working on
that for the 8,000 line.
00:06:09.910 --> 00:06:11.360
And they're not even out yet.
00:06:12.340 --> 00:06:15.820
No, no, no, you must
have accidentally enabled
00:06:15.820 --> 00:06:18.470
guardian mode as you gave
him one last pat on the head
00:06:18.470 --> 00:06:19.860
out the door.
00:06:19.860 --> 00:06:21.780
Dutifully, he followed you
00:06:21.780 --> 00:06:23.840
and you took him right
to the biggest magnet
00:06:23.840 --> 00:06:25.850
you've ever seen in your life.
00:06:25.850 --> 00:06:28.350
You run over to the scrap
bot and shove it aside,
00:06:28.350 --> 00:06:31.020
overriding the controls
for the scrap magnet.
00:06:31.020 --> 00:06:33.420
Gently, you lower it
back in front of the gate
00:06:33.420 --> 00:06:36.080
and disengage the magnetic field.
00:06:36.080 --> 00:06:38.580
You hear GB3 collapse to the dirt
00:06:38.580 --> 00:06:40.870
and you start to choke up a bit.
00:06:40.870 --> 00:06:43.890
You hoist the magnet back
to its resting position
00:06:43.890 --> 00:06:45.323
and sprint over to the gate.
00:06:46.350 --> 00:06:48.110
GB3 is lifeless
00:06:48.110 --> 00:06:50.690
as you roll him over to
flip the maintenance switch
00:06:50.690 --> 00:06:52.990
and open the access panel.
00:06:52.990 --> 00:06:55.640
The upgraded panel you use
today feels like it weighs
00:06:55.640 --> 00:06:58.123
10 times as much as it
did when you put it on.
00:06:59.560 --> 00:07:04.100
Oh wow, a small amber LED glows
00:07:04.100 --> 00:07:06.660
inside the custom memory enclosure.
00:07:06.660 --> 00:07:09.610
You glance over and see a
symbol on the access panel
00:07:09.610 --> 00:07:11.640
that you didn't recognize.
00:07:11.640 --> 00:07:14.180
It feels like lightning
tearing through your brain
00:07:14.180 --> 00:07:15.890
as you make the connection.
00:07:15.890 --> 00:07:19.210
That's the symbol for magnetic shielding.
00:07:19.210 --> 00:07:21.430
You learned about it
while studying the parts
00:07:21.430 --> 00:07:24.650
you needed back when you first built GB3.
00:07:24.650 --> 00:07:27.050
Excitedly, you run for a volt pack.
00:07:27.050 --> 00:07:30.330
GB3 still out and you need to
bring in some outside power
00:07:30.330 --> 00:07:32.800
to see if this thing's going to work.
00:07:32.800 --> 00:07:34.860
You slide back next to
him on your knee pads
00:07:34.860 --> 00:07:36.430
and make the connection.
00:07:36.430 --> 00:07:38.680
The LED flashes green twice,
00:07:38.680 --> 00:07:41.060
then turns back to solid amber.
00:07:41.060 --> 00:07:44.300
You hear a click from
inside his main access.
00:07:44.300 --> 00:07:47.050
You jump up and without
even bothering to reattach
00:07:47.050 --> 00:07:49.050
the panels, you squint your eyes shut
00:07:49.050 --> 00:07:50.693
and flip the maintenance switch.
00:07:51.889 --> 00:07:52.850
(robot beeps)
00:07:52.850 --> 00:07:53.880
It worked.
00:07:53.880 --> 00:07:57.480
GB3 blinks to life, writes
himself, and displays a message
00:07:57.480 --> 00:07:59.757
in block letters across his visor,
00:07:59.757 --> 00:08:02.880
"I knew you could fix me."
00:08:02.880 --> 00:08:04.440
He wags his whole body
00:08:04.440 --> 00:08:07.960
then rubs his shoulder down
to his tail against your leg.
00:08:07.960 --> 00:08:09.383
It's really him.
00:08:10.580 --> 00:08:12.690
You knew you could fix him too.
00:08:12.690 --> 00:08:15.250
You whisper as much as you kneel back down
00:08:15.250 --> 00:08:16.970
and wrap him in your arms.
00:08:16.970 --> 00:08:19.040
You think back on everything you learned,
00:08:19.040 --> 00:08:23.360
everything you did to get to
this moment with your dog.
00:08:23.360 --> 00:08:27.010
Each one of those hours you
put in have played their part.
00:08:27.010 --> 00:08:30.030
You look lovingly into GB3's visor,
00:08:30.030 --> 00:08:32.860
and you swell with a bit
of well-earned pride.
00:08:32.860 --> 00:08:34.780
GB3 might not have all the features
00:08:34.780 --> 00:08:36.800
that the newer models come with,
00:08:36.800 --> 00:08:40.379
but he's got something even better, you.
00:08:40.379 --> 00:08:43.296
(electronic music)
|
The Lighthouse Keeper | https://www.youtube.com/watch?v=kEJRG-xuHi0 | vtt | https://www.youtube.com/api/timedtext?v=kEJRG-xuHi0&ei=7lWUZbe0Lo-KmLAPrsmr8Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C5D15C3AC50DEDB292197A98EB7A77714B7F099D.216DB4889DD397A9AA41263DDC4524BF77107404&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.125 --> 00:00:02.500
(gentle music)
00:00:02.500 --> 00:00:06.120
- You wake to the sound of
crashing waves, swelling
00:00:06.120 --> 00:00:09.093
and breaking against the
breakwaters outside your home.
00:00:09.930 --> 00:00:11.370
They have a rhythm to them,
00:00:11.370 --> 00:00:14.393
a rhythm you've grown
accustomed to, like a heartbeat.
00:00:15.340 --> 00:00:18.770
They build, swell, and crash.
00:00:18.770 --> 00:00:22.530
Build, swell and crash again and again,
00:00:22.530 --> 00:00:24.803
splashing at the foundations of your home.
00:00:25.930 --> 00:00:29.350
This is normal, of course, after all
00:00:29.350 --> 00:00:30.700
you're a lighthouse keeper.
00:00:31.710 --> 00:00:34.290
The sun has not yet risen and it's cold
00:00:34.290 --> 00:00:37.200
in every part of the lighthouse
except your quarters.
00:00:37.200 --> 00:00:40.270
Your day begins as you throw
on your heaviest sweater,
00:00:40.270 --> 00:00:42.180
your knit cap, and the gloves
00:00:42.180 --> 00:00:44.680
your aunt knit for you this spring.
00:00:44.680 --> 00:00:47.290
This is how every day starts for you.
00:00:47.290 --> 00:00:50.240
Trudging up the stairs in
the dim pre-dawn light.
00:00:50.240 --> 00:00:52.110
You make your way to the observation room
00:00:52.110 --> 00:00:54.330
in it's grand wide windows
00:00:54.330 --> 00:00:56.670
to take weather readings
from the equipment.
00:00:56.670 --> 00:00:59.870
Your hands trace the old
pitted iron railings.
00:00:59.870 --> 00:01:02.290
As you make your way up
the tight spiral staircase
00:01:02.290 --> 00:01:04.870
in the center of the lighthouse tower.
00:01:04.870 --> 00:01:07.690
You're starting to memorize
the way the railings feel.
00:01:07.690 --> 00:01:08.920
You can tell how far up you are
00:01:08.920 --> 00:01:10.710
based on the pits in the metal,
00:01:10.710 --> 00:01:13.020
because you do this every day.
00:01:13.020 --> 00:01:14.910
Every day the same.
00:01:14.910 --> 00:01:17.300
You could do this with your eyes closed.
00:01:17.300 --> 00:01:18.840
Why do you do it?
00:01:18.840 --> 00:01:20.280
Wake up in darkness,
00:01:20.280 --> 00:01:23.480
type on an old laptop
with cold numbed fingers.
00:01:23.480 --> 00:01:25.880
Tell the weather office
that the horizons clear
00:01:25.880 --> 00:01:29.710
or that there's good visibility,
that there's heavy fog,
00:01:29.710 --> 00:01:31.860
rapidly decreasing barometric pressure,
00:01:31.860 --> 00:01:33.390
a big storm, actually.
00:01:33.390 --> 00:01:36.380
Wow, that's a huge storm,
if you're being honest.
00:01:36.380 --> 00:01:38.490
You snap out of your
reverie as the sun crests
00:01:38.490 --> 00:01:41.240
over the horizon and new readings come in.
00:01:41.240 --> 00:01:44.150
Red sky morning, sailor take warning.
00:01:44.150 --> 00:01:46.410
It's your job to keep
the bright shining lamp
00:01:46.410 --> 00:01:48.210
atop the lighthouse tower lit,
00:01:48.210 --> 00:01:50.650
to let the ships at sea
know where the ocean ends
00:01:50.650 --> 00:01:53.580
and the sharp rocks and
reefs of the coast begin.
00:01:53.580 --> 00:01:56.140
It's most important when
the visibility is bad.
00:01:56.140 --> 00:01:58.290
And right now a fog is rolling in.
00:01:58.290 --> 00:02:02.230
In an hour's time, it'll be
thick as pea soup out there.
00:02:02.230 --> 00:02:03.570
They won't be able to see a thing
00:02:03.570 --> 00:02:06.860
except for the bright beacon
of the lighthouse itself
00:02:06.860 --> 00:02:09.450
that cuts through the fog
like nothing else can.
00:02:09.450 --> 00:02:10.790
That's why you do it.
00:02:10.790 --> 00:02:14.180
People are counting on
you to keep that lamp lit.
00:02:14.180 --> 00:02:15.600
And you know what?
00:02:15.600 --> 00:02:17.280
You've got this.
00:02:17.280 --> 00:02:19.020
It's checklist time.
00:02:19.020 --> 00:02:21.610
In the supply room, you
check up on your supplies.
00:02:21.610 --> 00:02:23.760
You've got plenty of
batteries for your flashlight,
00:02:23.760 --> 00:02:28.610
spare fuses for the fuse box,
and crucially, lots of snacks.
00:02:28.610 --> 00:02:30.390
You hurry down to the basement
00:02:30.390 --> 00:02:32.200
where your diesel generator is.
00:02:32.200 --> 00:02:33.550
It's humming away.
00:02:33.550 --> 00:02:36.300
The fuel tank is full, you just checked.
00:02:36.300 --> 00:02:37.560
This is your ritual.
00:02:37.560 --> 00:02:41.700
You do this every 12
hours, every single day.
00:02:41.700 --> 00:02:44.783
It's boring, but there's
also a kind of comfort in it.
00:02:44.783 --> 00:02:48.343
A comfort in the consistency
of a simple job done well.
00:02:49.420 --> 00:02:50.810
The generator keeps the light on
00:02:50.810 --> 00:02:52.940
in the lamp at the top of the lighthouse,
00:02:52.940 --> 00:02:54.890
and it also powers the
heater in your bedroom.
00:02:54.890 --> 00:02:56.173
So there's that too.
00:02:57.110 --> 00:03:00.260
You make yourself some breakfast
and a mug of hot cocoa.
00:03:00.260 --> 00:03:02.830
The kind from a packet with
the raspberry flavoring,
00:03:02.830 --> 00:03:06.070
and you sit in your favorite
chair in the observation room,
00:03:06.070 --> 00:03:07.833
just watching the storm build.
00:03:08.690 --> 00:03:13.343
Big gray clouds, fat and heavy
with rain, swell in the sky.
00:03:14.180 --> 00:03:15.740
The wind picks up.
00:03:15.740 --> 00:03:18.670
Whitecap start blossoming
on the crests of waves.
00:03:18.670 --> 00:03:21.610
And those clouds start
moving in faster and faster,
00:03:21.610 --> 00:03:24.220
blotting out the already dim sunlight.
00:03:24.220 --> 00:03:26.650
You start to see those
sideways lightning strikes
00:03:26.650 --> 00:03:30.790
that grasp between clouds,
anvil crawlers, they call them.
00:03:30.790 --> 00:03:32.950
The sign of a really big storm.
00:03:32.950 --> 00:03:35.900
It begins to rain, and you
can just make out the rumble
00:03:35.900 --> 00:03:37.475
of the approaching storm.
00:03:37.475 --> 00:03:39.430
(thunder rumbling)
00:03:39.430 --> 00:03:41.580
You radio with some of
the bigger container ships
00:03:41.580 --> 00:03:43.610
within distance and
urge them to get to port
00:03:43.610 --> 00:03:46.410
as soon as possible, because
the radar is telling you
00:03:46.410 --> 00:03:49.283
that the really nasty
weather is coming, and fast.
00:03:50.120 --> 00:03:52.150
The wind picks up, and as the rain begins
00:03:52.150 --> 00:03:54.820
to batter the lighthouse, it
starts to get harder and harder
00:03:54.820 --> 00:03:57.507
to hear what people are
saying over the radio.
00:03:57.507 --> 00:03:59.130
(heavy rain pouring)
00:03:59.130 --> 00:04:00.560
Back on the observation deck,
00:04:00.560 --> 00:04:02.630
the sea swells are getting bigger.
00:04:02.630 --> 00:04:03.700
The winds whipping them up
00:04:03.700 --> 00:04:06.010
into these big gray blue mountains.
00:04:06.010 --> 00:04:07.260
And now they're starting to beat
00:04:07.260 --> 00:04:09.220
against the upper windows
of the lighthouse.
00:04:09.220 --> 00:04:11.280
So we're talking at least 80 feet here.
00:04:11.280 --> 00:04:13.690
Huge geysers of sea spray foaming up
00:04:13.690 --> 00:04:16.170
and splashing against the walls.
00:04:16.170 --> 00:04:18.480
When you send your weather
report into central,
00:04:18.480 --> 00:04:20.780
the satellite connection
drops out in the rain
00:04:20.780 --> 00:04:21.613
and you have to switch
00:04:21.613 --> 00:04:23.552
to the low frequency radio transmission.
00:04:23.552 --> 00:04:25.480
(dramatic music)
00:04:25.480 --> 00:04:28.170
The rain on the windows
sounds like hammer blows.
00:04:28.170 --> 00:04:31.840
The waves and the thunder are
coming so fast and so loud now
00:04:31.840 --> 00:04:34.180
that you have difficulty
telling them apart.
00:04:34.180 --> 00:04:36.640
A prodigious bolt of
lightning splits the sky
00:04:36.640 --> 00:04:39.440
and shows you the armada
of clouds on approach
00:04:39.440 --> 00:04:41.090
for just a second.
00:04:41.090 --> 00:04:42.870
It's time to check on the lamp.
00:04:42.870 --> 00:04:44.550
It's an extremely bright light
00:04:44.550 --> 00:04:48.540
refracted through this delicate,
enormous multifaceted lens
00:04:48.540 --> 00:04:50.760
that vastly increases its output,
00:04:50.760 --> 00:04:53.760
making it visible for many miles at sea.
00:04:53.760 --> 00:04:55.067
The motor's going underneath the lamp
00:04:55.067 --> 00:04:58.210
and it's rotating the
whole thing very slowly.
00:04:58.210 --> 00:05:00.843
Sending a searchlight beam
out into the gloomy dark.
00:05:02.220 --> 00:05:05.810
Modern lighthouses use LEDs,
but this definitely isn't
00:05:05.810 --> 00:05:07.380
a modern lighthouse.
00:05:07.380 --> 00:05:10.080
Plus you've grown accustomed
to the rhythmic groaning.
00:05:11.890 --> 00:05:14.170
It almost hurts to look at,
that's how bright it is,
00:05:14.170 --> 00:05:15.610
but you're glad it's there
00:05:15.610 --> 00:05:17.800
as the waves beat against the walls,
00:05:17.800 --> 00:05:20.430
as a beacon in the darkening fog.
00:05:20.430 --> 00:05:23.690
Winter brings the night on
quickly and it's growing dark.
00:05:23.690 --> 00:05:25.560
It's a good thing the light is on.
00:05:25.560 --> 00:05:29.180
At least you're not out in one
of those ships on the water.
00:05:29.180 --> 00:05:30.460
The light suddenly goes out
00:05:30.460 --> 00:05:32.610
and you are plunged into darkness.
00:05:32.610 --> 00:05:34.400
It was so bright in the lamp room, in fact
00:05:34.400 --> 00:05:36.163
that you feel completely blind.
00:05:37.090 --> 00:05:39.590
The lamp didn't burn
out, the power is gone.
00:05:39.590 --> 00:05:42.210
The motor that rotated the
lamp has stopped moving.
00:05:42.210 --> 00:05:45.713
All you can hear now is the
terrible storm and the waves.
00:05:46.550 --> 00:05:48.490
You've got to see if
the generator gave out.
00:05:48.490 --> 00:05:50.100
You grab for your sturdy flashlight,
00:05:50.100 --> 00:05:51.970
but a lightning bolt
strikes the lighthouse
00:05:51.970 --> 00:05:53.147
at the same moment.
00:05:54.480 --> 00:05:55.400
You're safe.
00:05:55.400 --> 00:05:57.060
It must've caught the lightening rod.
00:05:57.060 --> 00:05:59.100
You notice that even the roar of the storm
00:05:59.100 --> 00:06:02.470
sounds muffled and distant due
to the ringing in your ears.
00:06:02.470 --> 00:06:03.760
And it takes you a beat to realize
00:06:03.760 --> 00:06:07.240
you've dropped the
flashlight down the stairs,
00:06:07.240 --> 00:06:09.943
which you will now have to
traverse in total darkness.
00:06:10.860 --> 00:06:14.080
The wind howls, the waves
batter the lighthouse,
00:06:14.080 --> 00:06:17.680
and yet a feeling of
confidence washes over you.
00:06:17.680 --> 00:06:22.330
As soon as your hand touches
that pitted cold iron railing.
00:06:22.330 --> 00:06:24.910
You know this building
backwards and forwards.
00:06:24.910 --> 00:06:26.800
You know every inch of the stairwell
00:06:26.800 --> 00:06:29.230
based on the feel of the railing alone.
00:06:29.230 --> 00:06:31.670
You make this climb many times each day,
00:06:31.670 --> 00:06:35.100
when the sun blazes and
when it's completely dark.
00:06:35.100 --> 00:06:36.670
Every day the same.
00:06:36.670 --> 00:06:39.348
You could do this with your eyes closed.
00:06:39.348 --> 00:06:40.610
(bright music)
00:06:40.610 --> 00:06:43.210
Halfway down the stairs, you
stop off in the supply room
00:06:43.210 --> 00:06:44.730
and root around in the darkness
00:06:44.730 --> 00:06:47.030
until you find one of everything.
00:06:47.030 --> 00:06:48.580
A fuse for the fuse box,
00:06:48.580 --> 00:06:51.270
extra batteries for the
flashlight just in case,
00:06:51.270 --> 00:06:55.230
and for you a bar of chocolate,
because you'll need it.
00:06:55.230 --> 00:06:58.923
Every item was exactly in
the place you knew it'd be.
00:06:59.800 --> 00:07:01.810
On the landing just
outside the supply room,
00:07:01.810 --> 00:07:03.010
you find the flashlight.
00:07:03.010 --> 00:07:06.040
Dented, sure, but it still works.
00:07:06.040 --> 00:07:08.470
Now that you can see again,
you run down to the generator
00:07:08.470 --> 00:07:11.370
to find that it's still running,
but all the lights are out.
00:07:11.370 --> 00:07:12.870
A fuse must've broken.
00:07:12.870 --> 00:07:15.030
You hit the emergency
stop on the generator,
00:07:15.030 --> 00:07:16.450
turn off the switch that connects it
00:07:16.450 --> 00:07:17.996
to the Lighthouse's power system.
00:07:17.996 --> 00:07:20.360
Knock open the fuse box, and there it is.
00:07:20.360 --> 00:07:22.490
A blackened busted fuse.
00:07:22.490 --> 00:07:23.540
You don't know how it happened,
00:07:23.540 --> 00:07:25.040
but you've got a fresh fuse in there
00:07:25.040 --> 00:07:28.670
and replaced before you even
have time to think about it.
00:07:28.670 --> 00:07:32.180
You close the fusebox, you
turn the generator back on
00:07:32.180 --> 00:07:34.763
and you pull that switch.
00:07:34.763 --> 00:07:35.596
(flicks switch on)
00:07:35.596 --> 00:07:37.460
And the lights are on again.
00:07:37.460 --> 00:07:38.378
Up the stairs, let's go.
00:07:38.378 --> 00:07:39.250
(intense music)
00:07:39.250 --> 00:07:41.150
The lights along the
stairwell light your path,
00:07:41.150 --> 00:07:42.980
and by the time you
make it up to the lamp,
00:07:42.980 --> 00:07:45.410
you know what you'll see
before you even get there.
00:07:45.410 --> 00:07:47.030
A beacon in the darkness,
00:07:47.030 --> 00:07:49.733
sweeping out into that
rain streaked Indigo night.
00:07:50.670 --> 00:07:53.470
You did it, you were
prepared for this moment
00:07:53.470 --> 00:07:57.400
and you met it because you
were consistent and careful.
00:07:57.400 --> 00:07:59.110
That bar of chocolate tastes better
00:07:59.110 --> 00:08:01.560
than anything you've eaten in years.
00:08:01.560 --> 00:08:04.123
Because more than anything, you earned it.
00:08:05.300 --> 00:08:07.190
Your radio crackles to life,
00:08:07.190 --> 00:08:09.740
and the grateful captain of
a container ship thanks you
00:08:09.740 --> 00:08:11.260
for keeping the light on.
00:08:11.260 --> 00:08:12.590
She can see it now.
00:08:12.590 --> 00:08:14.400
And she and her navigator are using it
00:08:14.400 --> 00:08:15.863
to plot a course to shore.
00:08:17.050 --> 00:08:19.853
Remember this moment and
remember this feeling.
00:08:22.820 --> 00:08:24.370
You are a lantern (indistinct),
00:08:25.765 --> 00:08:27.690
a light for others to see by.
00:08:27.690 --> 00:08:30.893
You can do this because
you have done this.
00:08:32.160 --> 00:08:33.373
And you'll keep going.
00:08:34.232 --> 00:08:36.899
(intense music)
|
Theorem for limits of composite functions: when conditions aren't met | https://www.youtube.com/watch?v=eK8T3CcSvwE | vtt | https://www.youtube.com/api/timedtext?v=eK8T3CcSvwE&ei=7lWUZavMJ86cp-oPt42ayAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245342&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9CE1F7497FAAB4D86DCA11C044A433C1B109B52F.98011DB603E4D7BE03374DEB2A61B0832BCEB807&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:02.810
- [Tutor] In a previous
video we used this theorem
00:00:02.810 --> 00:00:05.580
to evaluate certain types
of composite functions.
00:00:05.580 --> 00:00:07.126
In this video we'll do
a few more examples,
00:00:07.126 --> 00:00:09.486
that get a little bit more involved.
00:00:09.486 --> 00:00:11.820
So let's say we wanted
to figure out the limit
00:00:11.820 --> 00:00:14.210
as x approaches zero
00:00:14.210 --> 00:00:19.210
of f of g of x,
00:00:19.270 --> 00:00:21.300
f of g of x.
00:00:21.300 --> 00:00:22.606
First of all, pause this video
00:00:22.606 --> 00:00:25.706
and think about whether
this theorem even applies.
00:00:25.706 --> 00:00:27.450
Well, the first thing to think about
00:00:27.450 --> 00:00:32.330
is what is the limit as x
approaches zero of g of x
00:00:32.330 --> 00:00:35.650
to see if we meet this first condition.
00:00:35.650 --> 00:00:37.810
So if we look at g of x, right over here
00:00:37.810 --> 00:00:40.010
as x approaches zero from the left,
00:00:40.010 --> 00:00:42.150
it looks like g is approaching two,
00:00:42.150 --> 00:00:44.310
as x approaches zero from the right,
00:00:44.310 --> 00:00:46.610
it looks like g is approaching two
00:00:46.610 --> 00:00:50.560
and so it looks like this
is going to be equal to two.
00:00:50.560 --> 00:00:51.967
So that's a check.
00:00:51.967 --> 00:00:53.820
Now let's see the second condition,
00:00:53.820 --> 00:00:57.620
is f continuous at that limit at two.
00:00:57.620 --> 00:00:59.380
So when x is equal to two,
00:00:59.380 --> 00:01:02.490
it does not look like f is continuous.
00:01:02.490 --> 00:01:05.455
So we do not meet this second
condition right over here,
00:01:05.455 --> 00:01:08.920
so we can't just directly
apply this theorem.
00:01:08.920 --> 00:01:11.490
But just because you
can't apply the theorem
00:01:11.490 --> 00:01:15.900
does not mean that the limit
doesn't necessarily exist.
00:01:15.900 --> 00:01:17.430
For example, in this situation
00:01:17.430 --> 00:01:20.410
the limit actually does exist.
00:01:20.410 --> 00:01:21.420
One way to think about it,
00:01:21.420 --> 00:01:25.380
when x approaches zero from the left,
00:01:25.380 --> 00:01:30.380
it looks like g is
approaching two from above
00:01:31.890 --> 00:01:34.530
and so that's going to be the input into f
00:01:34.530 --> 00:01:38.290
and so if we are now
approaching two from above here
00:01:38.290 --> 00:01:39.920
as the input into f,
00:01:39.920 --> 00:01:43.890
it looks like our function
is approaching zero
00:01:43.890 --> 00:01:45.830
and then we can go the other way.
00:01:45.830 --> 00:01:50.830
If we are approaching zero from
the right, right over here,
00:01:51.850 --> 00:01:54.103
it looks like the value of our function
00:01:54.103 --> 00:01:58.150
is approaching two from below.
00:01:58.150 --> 00:02:01.590
Now if we approach two from below,
00:02:01.590 --> 00:02:05.800
it looks like the value
of f is approaching zero.
00:02:05.800 --> 00:02:07.590
So in both of these scenarios,
00:02:07.590 --> 00:02:11.330
our value of our function
f is approaching zero.
00:02:11.330 --> 00:02:13.340
So I wasn't able to use this theorem,
00:02:13.340 --> 00:02:14.750
but I am able to figure out
00:02:14.750 --> 00:02:16.752
that this is going to be equal to zero.
00:02:16.752 --> 00:02:19.340
Now let me give you another example.
00:02:19.340 --> 00:02:21.660
Let's say we wanted to
figure out the limit
00:02:21.660 --> 00:02:24.180
as x approaches two
00:02:24.180 --> 00:02:28.453
of f of g of x.
00:02:29.321 --> 00:02:30.610
Pause this video,
00:02:30.610 --> 00:02:32.860
we'll first see if this
theorem even applies.
00:02:33.750 --> 00:02:36.180
Well, we first wanna see what is the limit
00:02:36.180 --> 00:02:39.619
as x approaches two of g of x.
00:02:39.619 --> 00:02:42.696
When we look at approaching
two from the left,
00:02:42.696 --> 00:02:45.363
it looks like g is
approaching negative two.
00:02:45.363 --> 00:02:48.530
When we approach x equals
two from the right,
00:02:48.530 --> 00:02:50.910
it looks like g is approaching zero.
00:02:50.910 --> 00:02:53.310
So our right and left hand
limits are not the same here,
00:02:53.310 --> 00:02:58.310
so this thing does not
exist, does not exist
00:02:59.855 --> 00:03:02.890
and so we don't meet this
condition right over here,
00:03:02.890 --> 00:03:04.622
so we can't apply the theorem.
00:03:04.622 --> 00:03:06.070
But as we've already seen,
00:03:06.070 --> 00:03:08.090
just because you can't apply the theorem
00:03:08.090 --> 00:03:11.253
does not mean that the
limit does not exist.
00:03:11.253 --> 00:03:13.240
But if you like pondering things,
00:03:13.240 --> 00:03:16.190
I encourage you to see that
this limit doesn't exist
00:03:16.190 --> 00:03:18.410
by doing very similar analysis
00:03:18.410 --> 00:03:21.453
to the one that I did
for our first example.
|
Theorem for limits of composite functions | https://www.youtube.com/watch?v=9Z3ngNi-12k | vtt | https://www.youtube.com/api/timedtext?v=9Z3ngNi-12k&ei=8VWUZbHDEvy2mLAP-d-m2Ac&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E2CF9A1318B27E8B1807E98A829EE2E48552C5A9.5ACFF1857BDEEAB7602621A05772604377B80107&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:02.350
- [Tutor] In this video, we're
going to try to understand
00:00:02.350 --> 00:00:04.705
limits of composite
functions, or at least a way
00:00:04.705 --> 00:00:07.230
of thinking about limits
of composite functions
00:00:07.230 --> 00:00:08.917
and in particular, we're
gonna think about the case
00:00:08.917 --> 00:00:12.360
where we're trying to find
the limit as x approaches a,
00:00:12.360 --> 00:00:16.128
of f of g of x
00:00:16.128 --> 00:00:19.680
and we're going to see
under certain circumstances,
00:00:19.680 --> 00:00:24.680
this is going to be
equal to f of the limit,
00:00:25.990 --> 00:00:30.990
the limit as x approaches a of g of x
00:00:31.610 --> 00:00:34.510
and what are those
circumstances you are asking?
00:00:34.510 --> 00:00:35.760
Well, this is going to be true
00:00:35.760 --> 00:00:38.170
if and only if two things are true,
00:00:38.170 --> 00:00:41.140
first of all, this limit needs to exist.
00:00:41.140 --> 00:00:46.140
So the limit as x approaches
a of g of x needs to exist,
00:00:48.410 --> 00:00:52.220
so that needs to exist
and then on top of that,
00:00:52.220 --> 00:00:56.000
the function f needs to be
continuous at this point
00:00:56.000 --> 00:01:00.500
and f continuous at L.
00:01:03.740 --> 00:01:05.120
So let's look at some examples
00:01:05.120 --> 00:01:07.180
and see if we can apply this idea
00:01:07.180 --> 00:01:08.603
or see if we can't apply it.
00:01:09.450 --> 00:01:12.340
So here I have two functions,
00:01:12.340 --> 00:01:15.446
that are graphically
represented right over here,
00:01:15.446 --> 00:01:18.360
let me make sure I have
enough space for them
00:01:18.360 --> 00:01:23.360
and what we see on the
left-hand side is our function f
00:01:23.780 --> 00:01:28.780
and what we see on the right-hand
side is our function g.
00:01:28.920 --> 00:01:33.060
So first let's figure
out what is the limit
00:01:33.060 --> 00:01:35.860
as x approaches negative three
00:01:35.860 --> 00:01:39.840
of f of g of x.
00:01:39.840 --> 00:01:41.630
Pause this video and see,
00:01:41.630 --> 00:01:44.440
first of all, does this theorem apply?
00:01:44.440 --> 00:01:47.517
And if it does apply, what is this limit?
00:01:47.517 --> 00:01:49.250
So the first thing we need to see
00:01:49.250 --> 00:01:51.810
is does this theorem apply?
00:01:51.810 --> 00:01:54.870
So first of all, if we
were to find the limit
00:01:54.870 --> 00:01:59.870
as x approaches negative
three of g of x, what is that?
00:02:00.150 --> 00:02:03.022
Well, when we're approaching
negative three from the right,
00:02:03.022 --> 00:02:06.522
it looks like our function
is actually at three
00:02:06.522 --> 00:02:08.770
and it looks like when we're
approaching negative three
00:02:08.770 --> 00:02:11.580
from the left, it looks like
our function is at three.
00:02:11.580 --> 00:02:13.760
So it looks like this limit is three,
00:02:13.760 --> 00:02:17.395
even though the value g of
negative three is negative two,
00:02:17.395 --> 00:02:19.940
but it's a point discontinuity.
00:02:19.940 --> 00:02:21.710
As we approach it from either side,
00:02:21.710 --> 00:02:23.790
the value of the function is at three.
00:02:23.790 --> 00:02:25.920
So this thing is going to be three,
00:02:25.920 --> 00:02:28.343
so it exists, so we meet
that first condition
00:02:28.343 --> 00:02:32.470
and then the second question
is is our function f
00:02:32.470 --> 00:02:35.750
continuous at this limit,
continuous at three?
00:02:35.750 --> 00:02:39.820
So when x equals three, yeah,
it looks like at that point,
00:02:39.820 --> 00:02:43.010
our function is definitely continuous
00:02:43.010 --> 00:02:45.400
and so we could say that this limit
00:02:45.400 --> 00:02:46.900
is going to be the same thing
00:02:46.900 --> 00:02:51.280
as this equals f of the limit
00:02:52.420 --> 00:02:56.883
as x approaches negative three of g of x,
00:02:58.020 --> 00:02:59.930
close the parentheses
00:02:59.930 --> 00:03:03.080
and we know that this is equal to three
00:03:03.080 --> 00:03:04.950
and we know that f of three
00:03:04.950 --> 00:03:07.650
is going to be equal to negative one.
00:03:07.650 --> 00:03:09.254
So this met the conditions
for this theorem
00:03:09.254 --> 00:03:10.700
and we were able to use the theorem
00:03:10.700 --> 00:03:12.150
to actually solve this limit.
|
Geometric series as a function | https://www.youtube.com/watch?v=OzH735zyTWs | vtt | https://www.youtube.com/api/timedtext?v=OzH735zyTWs&ei=8VWUZdb9D4mQhcIPgPiFiAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=18721430D346FA4222C1BB48EB9317CB4A375FC8.0EEFF36D537634CD81741C930C24492A1714C121&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.170 --> 00:00:01.270
- [Instructor] So we have this function
00:00:01.270 --> 00:00:03.450
that's equal to 2 minus 8x squared
00:00:03.450 --> 00:00:07.000
plus 32x to the fourth
minus 128x to the sixth.
00:00:07.000 --> 00:00:08.610
And it just keeps going and going.
00:00:08.610 --> 00:00:11.170
So it's defined as an infinite series.
00:00:11.170 --> 00:00:13.130
And what I want to explore in this video,
00:00:13.130 --> 00:00:16.360
is there another way
to write this function
00:00:16.360 --> 00:00:19.800
so it's not expressed
as an infinite series?
00:00:19.800 --> 00:00:21.790
Well, some of you might be thinking,
00:00:21.790 --> 00:00:24.360
well, this looks like a geometric series
00:00:24.360 --> 00:00:26.730
on the right hand side, an
infinite geometric series,
00:00:26.730 --> 00:00:30.320
and we know what the sun of an
infinite geometric series is
00:00:30.320 --> 00:00:31.970
if it converges.
00:00:31.970 --> 00:00:34.710
So maybe that's a way
that we can express this.
00:00:34.710 --> 00:00:35.543
So let's try to do that.
00:00:35.543 --> 00:00:36.710
So first let's just confirm
00:00:36.710 --> 00:00:38.680
that this is an infinite geometric series.
00:00:38.680 --> 00:00:41.200
And in order for it to
be a geometric series,
00:00:41.200 --> 00:00:44.680
each successive term has
to be some common ratio
00:00:44.680 --> 00:00:46.220
times the previous term.
00:00:46.220 --> 00:00:48.930
So to go from 2 to negative 8x squared,
00:00:48.930 --> 00:00:50.560
what do you have to multiply by?
00:00:50.560 --> 00:00:55.560
Well you have to multiply
by negative 4x squared.
00:00:55.600 --> 00:00:57.500
Now let's see if you
multiply negative 8x squared
00:00:57.500 --> 00:00:59.700
times negative 4x
squared, what do you get?
00:00:59.700 --> 00:01:02.360
Well, negative 4 times
negative 8 is positive 32.
00:01:02.360 --> 00:01:04.220
x squared times x squared
is x to the fourth.
00:01:04.220 --> 00:01:05.130
So that works.
00:01:05.130 --> 00:01:08.200
And then you multiply that
times negative 4x squared,
00:01:08.200 --> 00:01:11.670
and you indeed would get
negative 128x to the sixth.
00:01:11.670 --> 00:01:15.540
So this indeed looks like
an infinite geometric series
00:01:15.540 --> 00:01:16.430
on the right-hand side.
00:01:16.430 --> 00:01:19.430
In fact, we can rewrite f of x
00:01:19.430 --> 00:01:21.840
as being equal to the sum
00:01:22.750 --> 00:01:27.390
from n equals 0 to infinity of,
00:01:27.390 --> 00:01:28.880
you have your first term,
00:01:28.880 --> 00:01:30.520
and then you have your common ratio,
00:01:30.520 --> 00:01:33.400
negative 4x squared
00:01:33.400 --> 00:01:35.610
to the nth power.
00:01:35.610 --> 00:01:37.890
Let's confirm that works when n equals 0
00:01:37.890 --> 00:01:39.130
this is going to be 1.
00:01:39.130 --> 00:01:43.010
So 2 times 1 is 2, and that
indeed is our first term there.
00:01:43.010 --> 00:01:44.760
And then to that, you're gonna add it
00:01:44.760 --> 00:01:46.700
to when n is equal to 1.
00:01:46.700 --> 00:01:48.690
So that's just going to be
two times negative 4X squared,
00:01:48.690 --> 00:01:52.110
which is indeed this second
term right over here.
00:01:52.110 --> 00:01:54.810
And so this looks like it works.
00:01:54.810 --> 00:01:57.350
Now what is the sum
00:01:57.350 --> 00:02:01.120
of an infinite geometric series like this?
00:02:01.120 --> 00:02:02.760
Well it's going to be a finite value,
00:02:02.760 --> 00:02:06.930
assuming the absolute
value of your common ratio
00:02:06.930 --> 00:02:09.200
is less than 1.
00:02:09.200 --> 00:02:10.680
So first of all, let's just think about
00:02:10.680 --> 00:02:12.740
under what conditions
is the absolute value
00:02:12.740 --> 00:02:14.500
of our common ratio less than 1?
00:02:14.500 --> 00:02:15.460
And then we could say, okay,
00:02:15.460 --> 00:02:19.060
that helps us to find a
radius of convergence.
00:02:19.060 --> 00:02:23.250
And then if x is in that zone,
00:02:23.250 --> 00:02:24.920
or if it's in that interval,
00:02:24.920 --> 00:02:28.860
then we can figure out a
non-infinite geometric series way
00:02:28.860 --> 00:02:31.040
of expressing this function.
00:02:31.040 --> 00:02:33.670
So if we just think about
under what circumstances
00:02:33.670 --> 00:02:36.650
will this converge, will it
come out to a finite value?
00:02:36.650 --> 00:02:39.360
That's a situation in
which the absolute value
00:02:39.360 --> 00:02:42.890
of your common ratio is less than 1.
00:02:42.890 --> 00:02:45.613
And so let's see if we can
simplify this a little bit.
00:02:46.820 --> 00:02:49.070
No matter what x is, it's
always going to be not,
00:02:49.070 --> 00:02:51.570
x squared is always
going to be non-negative.
00:02:51.570 --> 00:02:54.980
And so the only, so this entire expression
00:02:54.980 --> 00:02:56.810
is always going to be negative.
00:02:56.810 --> 00:02:59.000
And so if you take the
absolute value of it,
00:02:59.000 --> 00:03:02.840
this is going to be
evaluate as 4x squared,
00:03:02.840 --> 00:03:04.530
which is always going to be positive.
00:03:04.530 --> 00:03:07.020
So this is equivalent to 4x squared,
00:03:07.020 --> 00:03:08.980
which needs to be less than 1.
00:03:08.980 --> 00:03:13.560
Or we could say that x squared
needs to be less than 1/4.
00:03:13.560 --> 00:03:18.530
Or we could say that x needs to be
00:03:18.530 --> 00:03:20.890
less than 1/2
00:03:20.890 --> 00:03:24.180
and greater than negative 1/2.
00:03:24.180 --> 00:03:27.290
One way to think about it is
anywhere in this interval,
00:03:27.290 --> 00:03:30.350
if you square it, you're
going to be less than 1/4.
00:03:30.350 --> 00:03:33.730
At 1/2, if you square
it, it's equal to 1/4.
00:03:33.730 --> 00:03:37.150
And at negative 1/2, if you
square it, it's equal to 1/4.
00:03:37.150 --> 00:03:39.570
But for lower absolute values,
00:03:39.570 --> 00:03:41.540
it's going to be less than 1/4.
00:03:41.540 --> 00:03:43.590
And so that's what this
interval right here says.
00:03:43.590 --> 00:03:46.400
Another way to think about
it is the absolute value of x
00:03:46.400 --> 00:03:48.830
needs to be less than 1/2.
00:03:48.830 --> 00:03:51.440
And so we've just defined an interval
00:03:51.440 --> 00:03:55.680
over which this infinite
geometric series will converge.
00:03:55.680 --> 00:03:58.880
You could say this has a
radius of convergence of,
00:03:58.880 --> 00:04:02.853
let me write it this way,
radius of convergence,
00:04:04.130 --> 00:04:07.240
convergence of 1/2,
00:04:07.240 --> 00:04:11.220
you can go 1/2 above 0 and 1/2 below 0.
00:04:11.220 --> 00:04:13.460
But now that we've set the conditions
00:04:13.460 --> 00:04:16.370
under which this would
converge, let's rewrite it.
00:04:16.370 --> 00:04:19.230
So this function is going to be equal to,
00:04:19.230 --> 00:04:22.450
we know what the sum of an
infinite geometric series is.
00:04:22.450 --> 00:04:24.670
It's going to be equal to the first term
00:04:24.670 --> 00:04:29.070
over 1 minus your common ratio,
00:04:29.070 --> 00:04:32.480
1 minus negative 4x squared.
00:04:32.480 --> 00:04:35.730
And so we can rewrite
our function as f of x
00:04:35.730 --> 00:04:39.780
is equal to 2 over 1,
subtract a negative 1
00:04:39.780 --> 00:04:43.040
plus 4x squared for
00:04:43.920 --> 00:04:47.910
the absolute value of x is less than 1/2.
00:04:47.910 --> 00:04:50.900
We have the interval
over which we converge
00:04:50.900 --> 00:04:52.260
and there you have it.
00:04:52.260 --> 00:04:55.443
We are done.
|
Sampling distribution of the difference in sample proportions | https://www.youtube.com/watch?v=oThlns-qBaI | vtt | https://www.youtube.com/api/timedtext?v=oThlns-qBaI&ei=8VWUZcnQEp3oxN8PuM-RwAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2A8F538D912FA04750F13532A5559A6FB514BA32.089CDF01B08DC21243D7A2FCFABD3EED5F155BF4&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.480 --> 00:00:02.710
- [Instructor] We're told, suppose that 8%
00:00:02.710 --> 00:00:06.840
of all cars produced at plant
A have a certain defect,
00:00:06.840 --> 00:00:11.840
and 6% of all cars produced
at plant B have this defect.
00:00:12.670 --> 00:00:15.340
Each month, a quality control manager
00:00:15.340 --> 00:00:18.640
takes separate random samples of 200
00:00:18.640 --> 00:00:22.520
of the over 3000 cars
produced from each plant.
00:00:22.520 --> 00:00:24.490
The manager looks at the difference
00:00:24.490 --> 00:00:27.640
between the proportions
of cars with the defect
00:00:27.640 --> 00:00:29.100
in each sample.
00:00:29.100 --> 00:00:30.640
So they're looking at the difference
00:00:30.640 --> 00:00:32.810
of sample proportions every month.
00:00:32.810 --> 00:00:34.300
Describe the distribution
00:00:34.300 --> 00:00:36.240
of the difference of sample proportions
00:00:36.240 --> 00:00:40.410
in terms of its mean
standard deviation and shape.
00:00:40.410 --> 00:00:42.330
So let's take these step-by-step.
00:00:42.330 --> 00:00:45.980
So first, let's think about
the mean of the difference
00:00:45.980 --> 00:00:48.160
of our sample proportions.
00:00:48.160 --> 00:00:48.993
Pause this video
00:00:48.993 --> 00:00:51.190
and try to figure out
what that's going to be.
00:00:52.150 --> 00:00:54.990
Well, we have seen this
in previous videos,
00:00:54.990 --> 00:00:57.260
that if we have the mean of the difference
00:00:57.260 --> 00:00:59.040
of two random variables,
00:00:59.040 --> 00:01:01.380
that's the same as the
difference of the means
00:01:01.380 --> 00:01:03.110
or another way to think about it is
00:01:03.110 --> 00:01:07.210
if we wanna figure out the mean of this,
00:01:07.210 --> 00:01:10.560
so sample proportion from plant A
00:01:10.560 --> 00:01:13.460
minus sample proportion from plant B,
00:01:13.460 --> 00:01:16.020
this is just going to be equal to the mean
00:01:16.020 --> 00:01:19.270
of the sample proportion from plant A,
00:01:19.270 --> 00:01:23.970
minus the mean of the sample
proportion from plant B.
00:01:23.970 --> 00:01:26.390
Now, what are these going to be equal to?
00:01:26.390 --> 00:01:30.273
Well, what's the mean of the
sample proportion of plant A.
00:01:31.220 --> 00:01:34.620
Is just going to be the
true population proportion
00:01:34.620 --> 00:01:35.453
for plant A.
00:01:35.453 --> 00:01:36.400
And they tell us that.
00:01:36.400 --> 00:01:39.750
They tell us that 8% of all
cars produced at plant A
00:01:39.750 --> 00:01:41.030
have a certain defect.
00:01:41.030 --> 00:01:44.663
So this could be 8% or we
could write it as 0.08.
00:01:46.140 --> 00:01:47.340
And then from that,
00:01:47.340 --> 00:01:52.340
we are going to subtract the
mean of the sample proportion
00:01:52.610 --> 00:01:53.950
from plant B.
00:01:53.950 --> 00:01:55.680
And we know what that mean's going to be.
00:01:55.680 --> 00:01:58.160
The mean of a sample proportion
00:01:58.160 --> 00:02:02.120
is going to be the population proportion.
00:02:02.120 --> 00:02:03.850
The parameter of the population,
00:02:03.850 --> 00:02:08.850
which we know for plant B is 6%, 0.06,
00:02:09.450 --> 00:02:13.590
and then that gets us a
mean of the difference
00:02:13.590 --> 00:02:16.990
of 0.02 or 2%
00:02:19.569 --> 00:02:24.040
or 2% difference in defect
rate would be the mean.
00:02:24.040 --> 00:02:28.280
Now let's think about
the standard deviation.
00:02:28.280 --> 00:02:30.420
So instead of thinking in
terms of standard deviation,
00:02:30.420 --> 00:02:33.210
let's think about the square
of the standard deviation,
00:02:33.210 --> 00:02:34.110
which is variance.
00:02:34.110 --> 00:02:36.760
And from there, we can go
back to standard deviation
00:02:36.760 --> 00:02:38.610
by taking a square root.
00:02:38.610 --> 00:02:41.320
So if we're looking at the variance,
00:02:41.320 --> 00:02:42.800
lemme write it this way,
00:02:42.800 --> 00:02:45.000
if we're looking at the variance
00:02:45.000 --> 00:02:48.450
of the difference of
the sample proportions,
00:02:48.450 --> 00:02:50.610
so the sample proportion from plant A
00:02:50.610 --> 00:02:53.420
minus the sample proportion from plant B,
00:02:53.420 --> 00:02:54.720
but just as a review,
00:02:54.720 --> 00:02:57.500
if you assume that we're
sampling independently
00:02:57.500 --> 00:02:58.710
from each of the plants.
00:02:58.710 --> 00:03:00.760
So what we're sampling from plant A
00:03:00.760 --> 00:03:03.040
does not affect what we're
sampling from plant B
00:03:03.040 --> 00:03:08.040
or vice versa, then we
can add the variances.
00:03:08.398 --> 00:03:11.188
So this is going to be
equal to the variance
00:03:11.188 --> 00:03:13.582
of the sample proportion from plant A
00:03:13.582 --> 00:03:18.030
plus the variance of the
sample proportion from plant B.
00:03:18.030 --> 00:03:18.863
Some of you might be saying,
00:03:18.863 --> 00:03:20.440
"Wait, aren't we taking the difference
00:03:20.440 --> 00:03:21.630
of sample proportions here?
00:03:21.630 --> 00:03:22.720
Why are we adding?"
00:03:22.720 --> 00:03:24.420
And the reminder is,
00:03:24.420 --> 00:03:27.500
remember, variance is
a measure of a spread.
00:03:27.500 --> 00:03:29.920
And whether you're now
taking the difference
00:03:29.920 --> 00:03:33.150
of random variables or you're
taking the sum of them,
00:03:33.150 --> 00:03:34.160
when you have more variables,
00:03:34.160 --> 00:03:35.710
you're going to have more spread.
00:03:35.710 --> 00:03:37.330
So regardless of whether
this is a negative
00:03:37.330 --> 00:03:40.640
or positive over here, this
is going to be a positive.
00:03:40.640 --> 00:03:42.660
So what is this going to be equal to.
00:03:42.660 --> 00:03:44.620
We can take each of these terms,
00:03:44.620 --> 00:03:45.730
what's going to be the variance
00:03:45.730 --> 00:03:48.430
of the sample proportion from plant A?
00:03:48.430 --> 00:03:52.610
Well, if every time we
looked at one of the cars,
00:03:52.610 --> 00:03:55.470
we looked at it and then we
put it back into the mix.
00:03:55.470 --> 00:03:57.600
So if we were sampling with replacement,
00:03:57.600 --> 00:03:59.730
which means that each of our observations
00:03:59.730 --> 00:04:03.130
are independent of the other
ones, we have a formula.
00:04:03.130 --> 00:04:04.360
We know that this variance
00:04:04.360 --> 00:04:07.410
would be the population
proportion of plant A
00:04:07.410 --> 00:04:10.680
times one minus the population
proportion of plant A
00:04:10.680 --> 00:04:13.850
divided by the number that
we sampled from plant A.
00:04:13.850 --> 00:04:15.930
Now, in the scenario that
we are talking about,
00:04:15.930 --> 00:04:17.810
we didn't sample with replacement,
00:04:17.810 --> 00:04:20.210
we just took 200 at a
time and looked at them.
00:04:20.210 --> 00:04:21.530
We didn't take one at a time
00:04:21.530 --> 00:04:24.080
and replace it and do that 200 times.
00:04:24.080 --> 00:04:27.210
But we also know that this is
a pretty good approximation,
00:04:27.210 --> 00:04:30.040
even when you are not
sampling with replacement.
00:04:30.040 --> 00:04:34.930
If your sample is less
than 10% of the population,
00:04:34.930 --> 00:04:38.820
and 200 is less than 10% of 3000.
00:04:38.820 --> 00:04:41.070
So this is a pretty good approximation,
00:04:41.070 --> 00:04:43.970
what you would use in a
first year statistics class.
00:04:43.970 --> 00:04:46.270
And of course, we can use the same logic.
00:04:46.270 --> 00:04:47.470
This is going to be equal
00:04:47.470 --> 00:04:49.870
to the population proportion plant B
00:04:49.870 --> 00:04:52.760
times one minus the population
proportion in plant B,
00:04:52.760 --> 00:04:55.680
all of that over your
sample size from plant B.
00:04:55.680 --> 00:04:58.270
And we know all of these things.
00:04:58.270 --> 00:05:01.490
We know that your population
proportion in plant A
00:05:01.490 --> 00:05:05.530
is 8% or 0.08.
00:05:05.530 --> 00:05:10.490
One minus that is 0.92.
00:05:10.490 --> 00:05:14.060
We're taking samples of
200 at a time from plant A.
00:05:14.060 --> 00:05:17.090
And then in plant B, we know
the population proportion,
00:05:17.090 --> 00:05:20.950
they told us is 6% or 0.06.
00:05:20.950 --> 00:05:24.253
One minus that is 0.94.
00:05:25.680 --> 00:05:28.810
And then the sample size from plant B
00:05:28.810 --> 00:05:30.670
is also going to be 200.
00:05:30.670 --> 00:05:32.260
It's going to be 200.
00:05:32.260 --> 00:05:37.260
We get 0.08 times 0.92
divided by 200 and then plus,
00:05:42.360 --> 00:05:44.510
let's open parentheses here,
00:05:44.510 --> 00:05:49.510
we get 0.06 times 0.94 divided by 200,
00:05:52.190 --> 00:05:54.950
and then actually let me
close the parentheses,
00:05:54.950 --> 00:05:57.030
and that equals this business.
00:05:57.030 --> 00:05:58.203
So 0.00065.
00:06:00.750 --> 00:06:05.220
So 0.00065.
00:06:05.220 --> 00:06:06.240
And then from this,
00:06:06.240 --> 00:06:08.440
we can figure out what the
standard is going to be.
00:06:08.440 --> 00:06:11.140
The standard deviation of the difference
00:06:11.140 --> 00:06:14.330
between our sample proportions
00:06:15.240 --> 00:06:18.090
is going to be just the
square root of this.
00:06:18.090 --> 00:06:22.463
It's going to be the
square root of 0.00065.
00:06:24.180 --> 00:06:27.410
And that is approximately equal to,
00:06:27.410 --> 00:06:31.097
let's just take the square
root, and we get this, 0.025.
00:06:34.178 --> 00:06:36.750
0.025.
00:06:36.750 --> 00:06:37.630
And there you have it,
00:06:37.630 --> 00:06:39.600
we have thought about
the standard deviation.
00:06:39.600 --> 00:06:43.430
And then last but not least,
let's think about the shape.
00:06:43.430 --> 00:06:47.200
So just as a review, we just
have to remind ourselves
00:06:47.200 --> 00:06:50.560
that the distribution of
each sample proportion
00:06:50.560 --> 00:06:52.050
is going to be normal
00:06:52.050 --> 00:06:57.050
as long as we expect at least
10 successes and 10 failures.
00:06:57.870 --> 00:06:59.010
Well, let's look at each of these.
00:06:59.010 --> 00:07:01.230
How many successes you expect
00:07:01.230 --> 00:07:03.680
where a success would
actually be a defect?
00:07:03.680 --> 00:07:04.760
But let's think about this.
00:07:04.760 --> 00:07:09.600
8% of in each case of a sample of 200,
00:07:09.600 --> 00:07:10.860
that's going to be 16.
00:07:10.860 --> 00:07:13.380
So you would expect 16 defects,
00:07:13.380 --> 00:07:15.550
and then you would expect 200 minus 16,
00:07:15.550 --> 00:07:18.490
which is a lot larger
than 10 of no defects.
00:07:18.490 --> 00:07:21.570
So both of those are
greater than or equal to 10.
00:07:21.570 --> 00:07:24.130
And then if you did the
same thing for plant B,
00:07:24.130 --> 00:07:25.050
you get the same idea.
00:07:25.050 --> 00:07:27.940
6% of 200 is 12.
00:07:27.940 --> 00:07:30.360
And then if you say the
ones that have no defects,
00:07:30.360 --> 00:07:33.660
that's 200 minus 12,
which is way more than 10,
00:07:33.660 --> 00:07:35.170
and especially in that latter case.
00:07:35.170 --> 00:07:36.760
But in every situation,
00:07:36.760 --> 00:07:40.570
we expect to have at least
10 successes and 10 failures.
00:07:40.570 --> 00:07:44.520
And so we can assume that the
distributions of each of these
00:07:44.520 --> 00:07:45.810
are going to be normal.
00:07:45.810 --> 00:07:47.250
And we also know that the difference
00:07:47.250 --> 00:07:51.820
of two normally distributed
variables is also normal,
00:07:51.820 --> 00:07:54.930
so long as they pass that
large count condition
00:07:54.930 --> 00:07:56.130
that we just talked about.
00:07:56.130 --> 00:08:00.400
And so let's draw what this
distribution might look like.
00:08:00.400 --> 00:08:02.360
It might look something like this.
00:08:02.360 --> 00:08:04.700
It's going to be a normal distribution
00:08:05.810 --> 00:08:10.293
where you have a mean right over here.
00:08:11.430 --> 00:08:12.860
I'll do that in that same color.
00:08:12.860 --> 00:08:17.740
A mean of 0.02.
00:08:17.740 --> 00:08:19.780
You can definitely take on negative values
00:08:19.780 --> 00:08:21.630
because there are some situations
00:08:21.630 --> 00:08:25.180
in which your sample
proportion from plan B
00:08:25.180 --> 00:08:27.540
actually could be larger
just by random chance
00:08:27.540 --> 00:08:28.960
than it is from plant A.
00:08:28.960 --> 00:08:31.410
So you can definitely
take on negative values.
00:08:31.410 --> 00:08:33.430
But if I wanted to show where zero is,
00:08:33.430 --> 00:08:36.300
maybe zero is right over here,
00:08:36.300 --> 00:08:39.490
so we could draw an axes right over here.
00:08:39.490 --> 00:08:42.110
And then we know what the
standard deviation is.
00:08:42.110 --> 00:08:44.730
It's 0.025 or it's approximately that.
00:08:44.730 --> 00:08:47.000
So if we were to go one
standard deviation down,
00:08:47.000 --> 00:08:48.930
we would go right about there,
00:08:48.930 --> 00:08:50.510
and if we were to go one
standard deviation up,
00:08:50.510 --> 00:08:51.650
we would go right about there.
00:08:51.650 --> 00:08:54.360
And obviously, we could go more
than one standard deviation
00:08:54.360 --> 00:08:56.573
above or below that mean.
|
Sampling distribution of the difference in sample proportions -Probability example | https://www.youtube.com/watch?v=-Sg3F-vK_cY | vtt | https://www.youtube.com/api/timedtext?v=-Sg3F-vK_cY&ei=8VWUZfubJ6vBhcIPqN640AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9BDF51F523A957B337417BE62F4EEA0640F4691F.7BC6571827C51860553590CF6825FFBEAD73E0B9&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.360 --> 00:00:01.280
- [Instructor] In a previous video,
00:00:01.280 --> 00:00:04.080
we explored the sampling distribution
00:00:04.080 --> 00:00:06.320
that we got when we took the difference
00:00:06.320 --> 00:00:08.590
between sample proportions.
00:00:08.590 --> 00:00:11.010
And in that video, we
described the distribution
00:00:11.010 --> 00:00:13.960
in terms of its mean,
standard deviation, and shape.
00:00:13.960 --> 00:00:15.030
What we're going to do in this video
00:00:15.030 --> 00:00:17.210
is build on that example and try to answer
00:00:17.210 --> 00:00:18.910
a little bit more about it.
00:00:18.910 --> 00:00:20.880
So in this situation, what we wanna do
00:00:20.880 --> 00:00:22.720
is find the probability given that we,
00:00:22.720 --> 00:00:27.210
what we already know about this
sampling distribution's mean
00:00:27.210 --> 00:00:29.440
and standard deviation and shape.
00:00:29.440 --> 00:00:32.490
We wanna find the probability
that the sample proportion
00:00:32.490 --> 00:00:36.200
of defects from Plant B is greater
00:00:36.200 --> 00:00:39.480
than the sample proportion from Plant A.
00:00:39.480 --> 00:00:42.593
So pause this video and see
if you can figure this out.
00:00:43.980 --> 00:00:45.510
All right, now let's do this together.
00:00:45.510 --> 00:00:47.690
So first of all, let's just
interpret what this is.
00:00:47.690 --> 00:00:49.640
The probability that the sample proportion
00:00:49.640 --> 00:00:52.210
of defects from Plant B is greater
00:00:52.210 --> 00:00:55.090
than the sample proportion from Plant A.
00:00:55.090 --> 00:00:57.800
So the sample proportion from Plant B
00:00:57.800 --> 00:01:00.450
is greater than the
proportion from Plant A.
00:01:00.450 --> 00:01:03.390
Then the difference between
the sample proportions
00:01:03.390 --> 00:01:05.380
is going to be negative.
00:01:05.380 --> 00:01:08.100
So this is equivalent to the probability
00:01:08.100 --> 00:01:12.820
that the difference of
the sample proportions,
00:01:12.820 --> 00:01:15.210
so the sample proportion from A minus
00:01:15.210 --> 00:01:17.050
the sample proportion from B
00:01:17.050 --> 00:01:21.060
is going to be less than zero.
00:01:21.060 --> 00:01:22.570
Or another way to think about it,
00:01:22.570 --> 00:01:27.040
that's going to be this
area right over here.
00:01:27.040 --> 00:01:28.180
Now, there's a bunch of ways
00:01:28.180 --> 00:01:29.770
that we can figure out this area,
00:01:29.770 --> 00:01:31.390
but the easiest or one of the easiest,
00:01:31.390 --> 00:01:33.450
I guess there's many
different ways to do it,
00:01:33.450 --> 00:01:35.850
is to figure out, well, how many,
00:01:35.850 --> 00:01:37.330
this is up to and including
00:01:37.330 --> 00:01:40.990
how many standard
deviations below the mean,
00:01:40.990 --> 00:01:43.200
and then we could use a Z table.
00:01:43.200 --> 00:01:48.150
So we just have to do is figure
out what is the Z value here
00:01:49.410 --> 00:01:51.350
and the Z value here we just have to say,
00:01:51.350 --> 00:01:55.160
well, how many standard
deviations below the mean is this?
00:01:55.160 --> 00:01:56.690
And I'll do it up here.
00:01:56.690 --> 00:01:58.330
Let me square this off.
00:01:58.330 --> 00:02:00.500
So I don't make it too messy.
00:02:00.500 --> 00:02:02.690
Z is going to be equal to,
00:02:02.690 --> 00:02:07.690
so we are negative 0.02 from the mean
00:02:08.640 --> 00:02:10.810
or we're 0.02 to the left of the mean.
00:02:10.810 --> 00:02:13.023
So I'll just do negative 0.02,
00:02:14.060 --> 00:02:18.307
and then over the standard
deviation, which is 0.025,
00:02:20.310 --> 00:02:22.590
which is going to be equal to,
00:02:22.590 --> 00:02:24.053
I'll get a calculator here.
00:02:25.570 --> 00:02:30.570
We get 0.02 divided by
0.025 is equal to that.
00:02:33.780 --> 00:02:38.760
And we are, of course, going
to be to the left of the mean.
00:02:38.760 --> 00:02:42.910
So our Z is going to be
approximately negative 0.8 or 0.8.
00:02:42.910 --> 00:02:44.900
I'm saying approximately
'cause this was approximate
00:02:44.900 --> 00:02:47.470
over here when we figured
out the standard deviation.
00:02:47.470 --> 00:02:52.470
So it is negative 0.8 and
then we just have to use
00:02:53.810 --> 00:02:56.610
a Z lookup table.
00:02:56.610 --> 00:02:59.060
And so if we look at a Z lookup table,
00:02:59.060 --> 00:03:02.930
we see here is if we're
going to negative 0.8,
00:03:02.930 --> 00:03:07.930
negative 0.8 is right over
here, so negative 0.8.
00:03:08.300 --> 00:03:10.610
And then we have zeros after that.
00:03:10.610 --> 00:03:12.810
So we're looking at this right over here.
00:03:12.810 --> 00:03:14.780
The area under the normal curve
00:03:14.780 --> 00:03:17.020
up to and including that Z value.
00:03:17.020 --> 00:03:17.920
So we always have to make sure
00:03:17.920 --> 00:03:19.560
that we're looking at the right thing
00:03:19.560 --> 00:03:23.220
on this standard normal
probabilities table right over here.
00:03:23.220 --> 00:03:25.840
That gives us 0.21 or we could say
00:03:25.840 --> 00:03:29.130
this is approximately 21%.
00:03:29.130 --> 00:03:31.500
So let me get rid of this.
00:03:31.500 --> 00:03:33.820
And so we know that this right over here
00:03:33.820 --> 00:03:38.820
is approximately 21% or we could say 0.21.
00:03:41.010 --> 00:03:42.680
So the probability that
the sample proportion
00:03:42.680 --> 00:03:45.000
of defects from Plant B is greater
00:03:45.000 --> 00:03:47.200
than the sample proportion from Plant A.
00:03:47.200 --> 00:03:50.743
It's, give or take, it's
roughly one in five.
|
Path independence for line integrals | https://www.youtube.com/watch?v=H5WNQfDSWrE | vtt | https://www.youtube.com/api/timedtext?v=H5WNQfDSWrE&ei=8VWUZb_ZEI_Mp-oPtqKaqAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=23B812897CBD8B99EBA93CB8A0C37230D983CE7A.2E46B360B604386E32866D76A8D20F88A6237DDD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.030 --> 00:00:02.600
- [Instructor] What I wanna
do in this video is establish
00:00:02.600 --> 00:00:06.480
a reasonably powerful condition
in which we can establish
00:00:06.480 --> 00:00:09.150
that a vector field or that align integral
00:00:09.150 --> 00:00:11.660
of a vector field is path independent.
00:00:11.660 --> 00:00:13.720
And when I say that,
I mean that let's say,
00:00:13.720 --> 00:00:15.970
I were to take this line integral
00:00:15.970 --> 00:00:20.653
along the path c of f dot dr,
00:00:21.500 --> 00:00:25.360
and let's say my path looks like this.
00:00:25.360 --> 00:00:28.220
Let's say my path looks like this.
00:00:28.220 --> 00:00:33.000
that's my x and y axis, y and x,
00:00:33.000 --> 00:00:35.260
and let's say my path
looks something like this.
00:00:35.260 --> 00:00:39.840
I start there and I go over
there to point c just like
00:00:39.840 --> 00:00:43.020
or to my end point, the curve here is.
00:00:43.020 --> 00:00:45.750
And so I would evaluate
this line integral,
00:00:45.750 --> 00:00:48.740
this vector field along this path.
00:00:48.740 --> 00:00:52.310
This would be a path
independent vector field
00:00:52.310 --> 00:00:55.993
or we call that a
conservative vector field if,
00:00:57.110 --> 00:01:02.110
if this thing is equal
to the same integral,
00:01:02.890 --> 00:01:06.160
the same integral over a different path,
00:01:06.160 --> 00:01:07.360
that has the same end point.
00:01:07.360 --> 00:01:11.340
So let's call this c1 so
this is c1, and this is c2.
00:01:11.340 --> 00:01:15.140
This vector field is conservative if,
00:01:15.140 --> 00:01:17.640
if I start at the same point,
but I take a different path,
00:01:17.640 --> 00:01:20.223
let's say I go something like that.
00:01:21.340 --> 00:01:24.490
If I take a different
path and this is my c2,
00:01:24.490 --> 00:01:26.740
I still get the same value.
00:01:26.740 --> 00:01:28.430
these integrals, what's this telling me,
00:01:28.430 --> 00:01:30.900
is it all it cares about
to evaluate these integrals
00:01:30.900 --> 00:01:34.070
is my starting point and my ending point.
00:01:34.070 --> 00:01:36.040
It doesn't care what I do in between.
00:01:36.040 --> 00:01:38.490
It doesn't care how I get
from my starting point
00:01:38.490 --> 00:01:39.373
to my end point.
00:01:40.232 --> 00:01:42.120
These two integrals have
the same start point
00:01:42.120 --> 00:01:45.200
and same end point, so
irregardless of their actual path,
00:01:45.200 --> 00:01:46.430
they're going to be the same.
00:01:46.430 --> 00:01:49.810
that's what it means for f
to be a conservative field
00:01:49.810 --> 00:01:52.710
or what it means to be for this integral
00:01:52.710 --> 00:01:54.810
to be path independent.
00:01:54.810 --> 00:01:57.730
So before I prove or I
show you the conditions,
00:01:57.730 --> 00:02:00.620
let's build up our toolkit a little bit.
00:02:00.620 --> 00:02:04.680
And so you may or may
not have already seen
00:02:04.680 --> 00:02:08.950
the multivariable chain rule,
multivariable chain rule.
00:02:11.310 --> 00:02:13.563
And I'm not gonna prove it in this video,
00:02:14.410 --> 00:02:16.490
but I think it'll be
pretty intuitive for you,
00:02:16.490 --> 00:02:18.670
so maybe it doesn't need to have a proof
00:02:18.670 --> 00:02:19.530
or I'll prove it eventually,
00:02:19.530 --> 00:02:21.670
but I really just wanna
give you the intuition.
00:02:21.670 --> 00:02:24.400
And all that says is that
if I have some function,
00:02:24.400 --> 00:02:29.270
let's say I have f of x and y
but x and y are then functions
00:02:29.270 --> 00:02:34.270
of, let's say 1/3
variable t so f of x of t
00:02:34.290 --> 00:02:39.290
and y of t, that the derivative
of f with respect to t,
00:02:40.270 --> 00:02:45.270
the derivative of f with
respect to t, is multivariable.
00:02:45.820 --> 00:02:48.120
I have two variables here an x and y.
00:02:48.120 --> 00:02:49.240
this is going to be equal
00:02:49.240 --> 00:02:52.440
to the partial of f with respect to x,
00:02:52.440 --> 00:02:56.200
how fast does f change as exchanges,
00:02:56.200 --> 00:02:59.530
times the derivative
of x with respect to t.
00:02:59.530 --> 00:03:02.420
This is a single variable
function right here.
00:03:02.420 --> 00:03:04.890
So you just can take a regular derivative.
00:03:04.890 --> 00:03:09.250
So times how fast x
changes with respect to t.
00:03:09.250 --> 00:03:11.780
This is a standard derivative,
this is partial derivative,
00:03:11.780 --> 00:03:14.760
because at that level we're
dealing with two variables
00:03:14.760 --> 00:03:17.790
and we're not done plus how fast f changes
00:03:17.790 --> 00:03:19.270
with respect to y.
00:03:19.270 --> 00:03:23.470
How fast the partial of
f with respect to y times
00:03:23.470 --> 00:03:26.050
the derivative of y with respect to t.
00:03:26.050 --> 00:03:26.883
So dy, dt.
00:03:29.340 --> 00:03:30.210
I'm not gonna prove it,
00:03:30.210 --> 00:03:32.820
but I think it makes
pretty good intuition.
00:03:32.820 --> 00:03:35.810
This is saying, as I move a little bit dt,
00:03:35.810 --> 00:03:37.390
how much of a df do I get
00:03:37.390 --> 00:03:40.340
or how fast does f
change with respect to t?
00:03:40.340 --> 00:03:42.300
It says, well, there's two
ways that f can change.
00:03:42.300 --> 00:03:43.850
It can change with respect to x,
00:03:43.850 --> 00:03:45.840
and it can change with respect to y.
00:03:45.840 --> 00:03:48.310
So why don't I add those
two things together
00:03:48.310 --> 00:03:51.090
as they are both changing
with respect to t?
00:03:51.090 --> 00:03:53.840
That's all it's saying and
if you kind of imagined
00:03:53.840 --> 00:03:56.570
that you could cancel out
this partial x with this dx
00:03:56.570 --> 00:03:58.590
and this partial y with this dy,
00:03:58.590 --> 00:03:59.450
you could have kind of imagined
00:03:59.450 --> 00:04:03.360
the partial of f with respect
to t on the x side of things,
00:04:03.360 --> 00:04:06.460
and that plus the partial
of f with respect to t
00:04:06.460 --> 00:04:08.730
on the y in the y dimension,
00:04:08.730 --> 00:04:11.070
and then that'll give
you the total change of f
00:04:11.070 --> 00:04:12.250
with respect to t.
00:04:12.250 --> 00:04:15.443
Kind of a hand wavy argument
there, but at least to me,
00:04:15.443 --> 00:04:17.010
this is a pretty intuitive formula.
00:04:17.010 --> 00:04:18.400
So that's our toolkit right there,
00:04:18.400 --> 00:04:20.590
the multivariable chain rule.
00:04:20.590 --> 00:04:23.140
We're gonna put that aside for a second.
00:04:23.140 --> 00:04:27.970
Now, let's say I have some vector field f
00:04:28.920 --> 00:04:30.010
and this is a different than this f,
00:04:30.010 --> 00:04:32.290
so I'll do it in a
different color, magenta.
00:04:32.290 --> 00:04:36.800
I have some vector field f
that is a function of x and y,
00:04:36.800 --> 00:04:39.010
and let's say that it happens to be
00:04:39.010 --> 00:04:42.260
the gradient of some scalar field.
00:04:42.260 --> 00:04:47.000
Let's say it equals the
gradient of some scalar field
00:04:47.000 --> 00:04:49.410
I'll call that capital F.
00:04:49.410 --> 00:04:50.740
And this is gradient which means,
00:04:50.740 --> 00:04:54.580
and this is capital f is
also a function of x and y.
00:04:54.580 --> 00:04:58.400
So I could write f is
also, let me write it,
00:04:58.400 --> 00:05:00.190
I don't wanna write it on a new line,
00:05:00.190 --> 00:05:01.690
I could also write up here.
00:05:01.690 --> 00:05:04.890
Capital F is also a function of x and y
00:05:04.890 --> 00:05:08.630
and the gradient, all
that means is that f,
00:05:08.630 --> 00:05:12.520
the vector field f of
x, y lowercase f of x, y
00:05:12.520 --> 00:05:16.850
is equal to the partial
derivative of uppercase F
00:05:16.850 --> 00:05:21.070
with respect to x times
the eye unit vector,
00:05:21.070 --> 00:05:25.020
plus the partial of
uppercase F with respect
00:05:25.020 --> 00:05:27.810
to y times the j unit vector.
00:05:27.810 --> 00:05:30.640
This is the definition
of a gradient right here.
00:05:30.640 --> 00:05:32.300
This is the definition of a gradient,
00:05:32.300 --> 00:05:36.690
and if you imagine that uppercase
F is some type of surface,
00:05:36.690 --> 00:05:41.130
so if uppercase F is some
type of surface like that,
00:05:41.130 --> 00:05:46.130
just trying to do my, so
this is uppercase F of x, y
00:05:46.560 --> 00:05:49.900
the gradient of f of x, y is
going to be a vector field
00:05:49.900 --> 00:05:51.330
that tells you the direction
00:05:51.330 --> 00:05:53.500
of steepest ascent at any point.
00:05:53.500 --> 00:05:56.730
So it'll be defined on the x, y plane.
00:05:56.730 --> 00:05:59.890
So on the x, y plane, it'll
tell you, so let me draw.
00:05:59.890 --> 00:06:03.130
That's the vertical axis,
maybe that's the x axis,
00:06:03.130 --> 00:06:04.870
that's the y axis.
00:06:04.870 --> 00:06:05.892
So the gradient of it,
00:06:05.892 --> 00:06:08.150
if you take any point on the x, y plane
00:06:08.150 --> 00:06:10.280
it'll tell you the direction
you need to travel to go
00:06:10.280 --> 00:06:12.850
into this deepest descent
and for this gradient field
00:06:12.850 --> 00:06:15.610
it's going to be something like this.
00:06:15.610 --> 00:06:18.119
It's going to be something like this
00:06:18.119 --> 00:06:20.640
and maybe over here it starts
going in that direction
00:06:20.640 --> 00:06:22.600
'cause you would descend towards
00:06:22.600 --> 00:06:24.310
this little minimum point right here,
00:06:24.310 --> 00:06:25.587
anyway I don't wanna get
too involved in that.
00:06:25.587 --> 00:06:28.970
And the whole point of this
isn't to really you get
00:06:28.970 --> 00:06:30.340
the intuition behind ingredients
00:06:30.340 --> 00:06:32.070
there are other videos on this.
00:06:32.070 --> 00:06:34.780
The point of this is to get a a test
00:06:34.780 --> 00:06:37.990
to see whether something
is path independent
00:06:37.990 --> 00:06:39.620
whether a vector field
is path independent,
00:06:39.620 --> 00:06:42.160
whether it's conservative and it turns out
00:06:42.160 --> 00:06:45.720
that if this exists and
I'm gonna prove it now.
00:06:45.720 --> 00:06:50.720
If this exists, if f is the
gradient of some scalar field
00:06:51.850 --> 00:06:56.850
if f is equal to the
gradient of some scalar field
00:06:57.370 --> 00:07:02.370
then, then f is conservative, conservative
00:07:04.700 --> 00:07:07.780
or you could say it doesn't
matter what path we follow
00:07:07.780 --> 00:07:10.320
when we take a line integral over f,
00:07:10.320 --> 00:07:12.920
it just matters about our starting point
00:07:12.920 --> 00:07:14.980
and our ending point.
00:07:14.980 --> 00:07:18.140
Now, let me see if I
can prove that to you.
00:07:18.140 --> 00:07:19.870
So let's start with the assumption
00:07:19.870 --> 00:07:21.530
that f can be written this way
00:07:21.530 --> 00:07:25.040
as the gradient of that
lowercase f can be written
00:07:25.040 --> 00:07:28.150
as the gradient of some uppercase F.
00:07:28.150 --> 00:07:31.093
So in that case, in that case,
00:07:32.071 --> 00:07:37.071
our integral, let's see well,
let's define our path first.
00:07:37.470 --> 00:07:41.360
So our position vector
function, we always need one
00:07:41.360 --> 00:07:44.690
of those to do a line integral
or a vector line integral,
00:07:44.690 --> 00:07:49.667
r of t is going to be
equal to x of t times i
00:07:50.510 --> 00:07:55.510
plus y of t times J for
t going between a and b,
00:07:56.780 --> 00:07:58.580
we've seen this multiple times.
00:07:58.580 --> 00:08:00.200
This is the definition of
00:08:00.200 --> 00:08:01.720
this is just a very general definition
00:08:01.720 --> 00:08:04.960
of pretty much any path in two dimensions.
00:08:04.960 --> 00:08:09.960
And then we're gonna say f,
f is going to be f of x, y
00:08:12.230 --> 00:08:13.620
is going to be equal to this
00:08:13.620 --> 00:08:15.930
it's going to be the partial derivative
00:08:15.930 --> 00:08:19.810
of uppercase F with respect
to x so we're assuming
00:08:19.810 --> 00:08:22.120
that this exists, that this is true
00:08:22.120 --> 00:08:25.790
except with times i plus
the partial of uppercase F
00:08:25.790 --> 00:08:29.230
with respect to y times j.
00:08:29.230 --> 00:08:34.230
Now, given this what is f
lowercase f lowercase dot dr
00:08:42.200 --> 00:08:45.120
going to equal over this path right here
00:08:45.120 --> 00:08:48.700
this path is divined by this
position function right there.
00:08:48.700 --> 00:08:51.540
Well, it's going to be
equal to what we need to get
00:08:51.540 --> 00:08:52.890
we need to figure out what dr is
00:08:52.890 --> 00:08:54.300
and we've done that in multiple videos
00:08:54.300 --> 00:08:56.510
so I'll do that on the right over here.
00:08:56.510 --> 00:08:59.610
Dr, we've seen it multiple times I'll just
00:08:59.610 --> 00:09:00.850
actually, I'll solve it out again.
00:09:00.850 --> 00:09:04.460
DR, dt by definition was equal
00:09:04.460 --> 00:09:09.460
to dx, dt is equal to dx,
dt times i plus dy, d,
00:09:13.840 --> 00:09:15.850
I don't know why it got all fat like that.
00:09:15.850 --> 00:09:20.850
Dy, dt times j, that's what dr, dt is.
00:09:21.500 --> 00:09:24.930
So if we wanna figure out what
dr is, the differential dr,
00:09:24.930 --> 00:09:26.750
if we wanna play with
differentials in this way,
00:09:26.750 --> 00:09:29.350
multiply both sides times dt,
00:09:29.350 --> 00:09:30.970
and actually I'm gonna treat dt as,
00:09:30.970 --> 00:09:32.700
well, I'll multiply
it, I'll distribute it.
00:09:32.700 --> 00:09:37.700
It's dx, dt times dt, i
plus dy, dt times dt, j.
00:09:44.050 --> 00:09:45.460
So if we're taking the dot product
00:09:45.460 --> 00:09:49.233
of f of f with dr, what are we gonna get?
00:09:50.310 --> 00:09:51.760
What are we gonna get?
00:09:51.760 --> 00:09:53.750
We are going to get, and this is, let me,
00:09:53.750 --> 00:09:55.120
so we're gonna take,
00:09:55.120 --> 00:09:59.920
so this is going to be the
integral over the curve,
00:09:59.920 --> 00:10:03.220
over the curve from, all
right, the c right there.
00:10:03.220 --> 00:10:06.730
We can write it in terms
of the end points of t,
00:10:06.730 --> 00:10:10.350
once we feel good that we
have everything in terms of t,
00:10:10.350 --> 00:10:12.590
but it's gonna be equal to this dot that
00:10:12.590 --> 00:10:14.300
which is equal to the partial,
00:10:14.300 --> 00:10:16.410
I'll try to stay color consistent,
00:10:16.410 --> 00:10:19.240
the partial of uppercase F with respect
00:10:19.240 --> 00:10:23.187
to x times that times dx, dt.
00:10:25.080 --> 00:10:29.940
I'm gonna write this dt in a
different color, times dt plus,
00:10:32.330 --> 00:10:37.000
plus the partial of
uppercase F with respect
00:10:37.000 --> 00:10:42.000
to y times this, we're multiplying
the j components, right?
00:10:42.040 --> 00:10:44.970
We can take the dot product,
multiply the i components,
00:10:44.970 --> 00:10:48.390
and then add that to, what
you get from the product
00:10:48.390 --> 00:10:49.223
of the j component.
00:10:49.223 --> 00:10:51.360
So this j component is
partial of uppercase F
00:10:51.360 --> 00:10:52.550
with respect to y.
00:10:52.550 --> 00:10:56.620
And then we have times,
let me switch to a yellow,
00:10:56.620 --> 00:11:01.620
dy, dt times that dt right over there
00:11:01.670 --> 00:11:06.670
times that dt over there, and
then we can factor out the dt.
00:11:06.820 --> 00:11:08.930
We could factor out the dt
00:11:08.930 --> 00:11:09.950
or actually it's just so I don't have
00:11:09.950 --> 00:11:11.050
to even write it again,
00:11:11.050 --> 00:11:12.820
right now, I wrote it without,
well, let me write it again.
00:11:12.820 --> 00:11:16.180
So this is equal to the integral,
00:11:16.180 --> 00:11:18.030
and let's say we have it in terms of t.
00:11:18.030 --> 00:11:19.490
We've written everything in terms of t,
00:11:19.490 --> 00:11:22.250
so t goes from a to a.
00:11:22.250 --> 00:11:26.370
And so this is going to be
equal to, I'll write it in blue,
00:11:26.370 --> 00:11:31.370
the partial of uppercase F
with respect to x times dx, dt
00:11:33.100 --> 00:11:34.940
plus, I'm distributing this dt out,
00:11:34.940 --> 00:11:39.777
plus the partial of uppercase
F with respect to y, dy, dt,
00:11:42.240 --> 00:11:46.550
all of that times dt.
00:11:46.550 --> 00:11:49.210
This is equivalent to that.
00:11:49.210 --> 00:11:51.100
Now you might realize why
00:11:51.100 --> 00:11:53.730
I talked about the
multivariable chain rule.
00:11:53.730 --> 00:11:55.530
What is this right here?
00:11:55.530 --> 00:11:57.130
What is that right there?
00:11:57.130 --> 00:11:59.090
You can do some pattern matching.
00:11:59.090 --> 00:12:04.090
That is the same thing as
the derivative of uppercase F
00:12:04.420 --> 00:12:05.970
with respect to t.
00:12:05.970 --> 00:12:07.870
Look at this, let me, let
me copy and paste this
00:12:07.870 --> 00:12:09.170
just so you appreciate it.
00:12:10.160 --> 00:12:12.250
Let me copy and paste that.
00:12:12.250 --> 00:12:15.333
You copy it, and then let me paste it.
00:12:17.160 --> 00:12:20.910
So this is our definition or this is our,
00:12:20.910 --> 00:12:22.930
I won't say definition
one can actually prove it,
00:12:22.930 --> 00:12:24.350
you don't have to start from there,
00:12:24.350 --> 00:12:27.230
but this is our multivariable
chain rule right here, right?
00:12:27.230 --> 00:12:29.300
The derivative of any
function with respect to t
00:12:29.300 --> 00:12:30.710
is the partial of that
function with respect
00:12:30.710 --> 00:12:33.080
to x times dx, dt plus the
partial of that function
00:12:33.080 --> 00:12:34.920
with respect to y, dy, dt.
00:12:34.920 --> 00:12:38.910
I have the partial of uppercase
F with respect to x, dx, dt
00:12:38.910 --> 00:12:42.440
plus the partial uppercase
F with respect to y.
00:12:42.440 --> 00:12:45.130
And this are identical if you
just replace this lowercase f
00:12:45.130 --> 00:12:46.460
with an uppercase F.
00:12:46.460 --> 00:12:47.880
So this in blue right here,
00:12:47.880 --> 00:12:50.170
so this whole expression is equal to,
00:12:50.170 --> 00:12:54.950
the integral from a to b, t
is equal a to t is equal to b
00:12:54.950 --> 00:12:58.930
of, of, in blue here,
00:12:58.930 --> 00:13:02.660
the derivative, regular derivative of f
00:13:02.660 --> 00:13:07.220
with respect to t, dt.
00:13:07.220 --> 00:13:08.270
And how do you evaluate?
00:13:08.270 --> 00:13:10.060
Let me read the dt in green.
00:13:10.060 --> 00:13:12.000
How do you evaluate something like this?
00:13:12.000 --> 00:13:12.890
And I just wanna make a point.
00:13:12.890 --> 00:13:16.500
This is just this, from the
multivariable chain rule.
00:13:16.500 --> 00:13:19.630
And how do you evaluate a
definite integral like this?
00:13:19.630 --> 00:13:22.250
Will you take the
anti-derivative of the inside
00:13:22.250 --> 00:13:25.110
with respect to dt?
00:13:25.110 --> 00:13:26.810
So what is this going to be equal to?
00:13:26.810 --> 00:13:28.440
You take the anti-derivative
of the inside,
00:13:28.440 --> 00:13:30.740
the anti-derivative of
the inside, that's just df
00:13:30.740 --> 00:13:32.100
oh, sorry, that's just f.
00:13:32.100 --> 00:13:35.563
So this is equal to f of t.
00:13:36.540 --> 00:13:38.420
And let me be clear, let me be clear here.
00:13:38.420 --> 00:13:41.730
We wrote before that f is a function,
00:13:41.730 --> 00:13:46.060
so our uppercase F is
a function of x and y
00:13:47.196 --> 00:13:48.920
which could also be
written since each of these
00:13:48.920 --> 00:13:53.250
are functions of t of, it
could be written as f of x of t
00:13:53.250 --> 00:13:55.870
of y of t, I'm just rewriting
it in different ways.
00:13:55.870 --> 00:13:58.850
And this could be just written as f of t.
00:13:58.850 --> 00:14:00.460
This is the same thing as f of t.
00:14:00.460 --> 00:14:01.800
These are all equivalent,
00:14:01.800 --> 00:14:02.730
depending on whether you wanna include
00:14:02.730 --> 00:14:04.930
the x's and the y's only or the t's only
00:14:04.930 --> 00:14:08.130
or them both cause both of the x's and y's
00:14:08.130 --> 00:14:10.400
are functions of t.
00:14:10.400 --> 00:14:13.650
So this is the derivative
of f with respect to t.
00:14:13.650 --> 00:14:15.280
If this was just in terms of t,
00:14:15.280 --> 00:14:17.480
this is the derivative of
that with respect to t.
00:14:17.480 --> 00:14:20.460
We take it's anti-derivative,
we're left just with f,
00:14:20.460 --> 00:14:22.190
and we have to evaluate it
00:14:23.320 --> 00:14:26.550
from t is equal to a to t is equal to b.
00:14:26.550 --> 00:14:29.750
And so this is equal to,
and this is the homestretch,
00:14:29.750 --> 00:14:34.507
this is equal to f of b minus f of a.
00:14:35.840 --> 00:14:38.100
And if you wanna think
about it in these terms,
00:14:38.100 --> 00:14:39.280
this is the same thing.
00:14:39.280 --> 00:14:44.280
This is equal to f of x of b, y of b,
00:14:46.440 --> 00:14:47.440
let me re-check out all the parentheses,
00:14:47.440 --> 00:14:52.440
minus f of x of a, y of
a, these are equivalent.
00:14:53.730 --> 00:14:58.170
You give me any point on the
x, y plane, an x and a y,
00:14:58.170 --> 00:15:00.100
and it tells me where I am.
00:15:00.100 --> 00:15:04.350
This is my capital F, it gives
me a height just like that.
00:15:04.350 --> 00:15:05.830
But what this tells me this,
00:15:05.830 --> 00:15:10.040
this associates a value with
every point on the x, y plane.
00:15:10.040 --> 00:15:12.210
And what this whole exercise,
00:15:12.210 --> 00:15:15.310
remember this is the same thing as that.
00:15:15.310 --> 00:15:17.000
This is our whole thing that
we were trying to prove.
00:15:17.000 --> 00:15:21.053
That is equal to f dot dr.
00:15:21.930 --> 00:15:25.980
F dot dr, our vector field
for which is the gradient
00:15:25.980 --> 00:15:28.870
of the capital F, remember F,
00:15:28.870 --> 00:15:30.770
F was equal to the gradient of f.
00:15:30.770 --> 00:15:32.160
We assume that it's the gradient
00:15:32.160 --> 00:15:34.460
of some function, capital F.
00:15:34.460 --> 00:15:36.210
If that is the case,
00:15:36.210 --> 00:15:38.530
then we just did a little
bit of calculus or algebra
00:15:38.530 --> 00:15:39.680
or whatever you wanna call it.
00:15:39.680 --> 00:15:42.030
And we found that we can
evaluate this integral
00:15:43.014 --> 00:15:46.850
by evaluating capital
F at t is equal to b,
00:15:46.850 --> 00:15:50.600
and then subtracting from that
capital f at t is equal to a.
00:15:50.600 --> 00:15:52.210
But what that tells you
is that this integral,
00:15:52.210 --> 00:15:56.860
the value of this integral
is only dependent,
00:15:56.860 --> 00:16:01.710
is only dependent at our
starting point, t is equal to a.
00:16:01.710 --> 00:16:06.710
This is the point x of a, y
of a, and the ending point
00:16:07.960 --> 00:16:12.960
t of b, x of, or t is equal
to b which is x of b, y of b.
00:16:13.850 --> 00:16:16.060
That integral is only
dependent on these two values.
00:16:16.060 --> 00:16:17.310
How do I know that?
00:16:17.310 --> 00:16:18.830
Because to solve it,
00:16:18.830 --> 00:16:21.080
because I'm saying that this thing exists,
00:16:21.080 --> 00:16:24.230
I just had to evaluate that
thing at both those two points.
00:16:24.230 --> 00:16:26.940
I didn't care about the curve in between.
00:16:26.940 --> 00:16:31.940
So this shows that if, if
f is equal to the gradient,
00:16:34.310 --> 00:16:36.400
this is often called a potential function
00:16:36.400 --> 00:16:38.180
of capital F, although they're usually
00:16:38.180 --> 00:16:40.210
the negative of each other,
but it's the same idea.
00:16:40.210 --> 00:16:43.160
If the vector field f is the gradient
00:16:43.160 --> 00:16:47.113
of some scalar field, uppercase F, then,
00:16:48.110 --> 00:16:52.720
then we can say that f is conservative.
00:16:52.720 --> 00:16:56.740
F is conservative or that the integral,
00:16:56.740 --> 00:17:01.010
the line integral of f dot
dr is path independent.
00:17:01.010 --> 00:17:03.290
It doesn't matter what path we go on
00:17:03.290 --> 00:17:06.114
as long as our starting and
ending points are the same.
00:17:06.114 --> 00:17:07.450
Hopefully, you found that useful.
00:17:07.450 --> 00:17:08.720
I will do some examples with that.
00:17:08.720 --> 00:17:09.820
And actually in the next video,
00:17:09.820 --> 00:17:12.670
I'll prove another interesting
outcome based on this one.
|
Geometric distribution mean and standard deviation | https://www.youtube.com/watch?v=XKCeLA4UsXw | vtt | https://www.youtube.com/api/timedtext?v=XKCeLA4UsXw&ei=8VWUZd7kJsfVxN8PkoSTiA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D8783375B49EA94232ED54962573324FBBC86541.9C9A94926381FE4CDC62855457ACDE2D11E0016A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.350 --> 00:00:02.230
- [Instructor] So let's say
we're going to play a game
00:00:02.230 --> 00:00:04.200
where on each person's turn,
00:00:04.200 --> 00:00:08.290
they're going to keep rolling
this fair six sided die,
00:00:08.290 --> 00:00:11.430
until we get a one.
00:00:11.430 --> 00:00:14.630
And we just want to see how
many rolls does it take.
00:00:14.630 --> 00:00:17.560
So let's say we define
some random variable,
00:00:17.560 --> 00:00:18.610
let's call it X,
00:00:18.610 --> 00:00:23.610
and let's call it the number
of rolls until we get a one.
00:00:29.630 --> 00:00:34.630
So what's the probability
that X is equal to one.
00:00:35.440 --> 00:00:37.880
Pause this video and think about it.
00:00:37.880 --> 00:00:40.720
All right, the probability
that X is equal to one means
00:00:40.720 --> 00:00:43.530
that it only takes us
one roll to get a one.
00:00:43.530 --> 00:00:47.370
Well, that's going to be
a one sixth probability.
00:00:47.370 --> 00:00:52.370
Well, what's the probability
that X is equal to two?
00:00:52.800 --> 00:00:54.690
Well, that means that
we on the first roll,
00:00:54.690 --> 00:00:56.570
we get something other than a one.
00:00:56.570 --> 00:00:59.430
So that is going to be five sixths,
00:00:59.430 --> 00:01:02.190
and then on the second roll, we get a one.
00:01:02.190 --> 00:01:06.620
So that has a one sixth probability.
00:01:06.620 --> 00:01:07.660
And we could keep going.
00:01:07.660 --> 00:01:11.580
What's the probability
that X is equal to three?
00:01:11.580 --> 00:01:14.040
Pause the video and think about that.
00:01:14.040 --> 00:01:16.300
Well, that means we miss on the first two.
00:01:16.300 --> 00:01:18.180
So we have a five sixth
chance of getting something
00:01:18.180 --> 00:01:20.550
other than a one on the first two rolls.
00:01:20.550 --> 00:01:23.830
So we could say that's
five sixth times five six,
00:01:23.830 --> 00:01:25.820
so we could write five sixth squared.
00:01:25.820 --> 00:01:27.710
And then on the third roll
00:01:27.710 --> 00:01:30.360
we have the one in six
chance of getting the one.
00:01:30.360 --> 00:01:32.290
So times one sixth.
00:01:32.290 --> 00:01:34.170
And I think you see a pattern here,
00:01:34.170 --> 00:01:36.020
and you might recognize what type
00:01:36.020 --> 00:01:37.880
of random variable this is.
00:01:37.880 --> 00:01:41.050
This is a geometric variable.
00:01:41.050 --> 00:01:42.420
Now how do we know that?
00:01:42.420 --> 00:01:44.780
Well each trial or each roll
00:01:44.780 --> 00:01:46.980
is either a success or a failure.
00:01:46.980 --> 00:01:50.220
Every time we roll, we
either get a one or we don't.
00:01:50.220 --> 00:01:51.660
We have the same probability
00:01:51.660 --> 00:01:54.430
of success of rolling a one each trial.
00:01:54.430 --> 00:01:56.840
These are independent trials.
00:01:56.840 --> 00:01:59.250
And that there's no set number of trials.
00:01:59.250 --> 00:02:01.070
It could take us an arbitrary number
00:02:01.070 --> 00:02:02.820
of trials to get the first success.
00:02:02.820 --> 00:02:04.870
So that's what tells us that we're dealing
00:02:04.870 --> 00:02:07.210
with the geometric random variable.
00:02:07.210 --> 00:02:11.645
Now one question is, is
what is going to be the mean
00:02:11.645 --> 00:02:14.660
of this geometric random variable?
00:02:14.660 --> 00:02:16.240
Well, we prove it in
another video where we talk
00:02:16.240 --> 00:02:18.960
about the expected value of
a geometric random variable.
00:02:18.960 --> 00:02:20.660
We're really talking about the mean
00:02:20.660 --> 00:02:22.720
of a geometric random variable.
00:02:22.720 --> 00:02:24.170
And it is a little bit intuitive.
00:02:24.170 --> 00:02:26.040
If you were to just
guess, what is the mean
00:02:26.040 --> 00:02:27.930
of a geometric random
variable where the chance
00:02:27.930 --> 00:02:30.000
of success on each roll is one sixth.
00:02:30.000 --> 00:02:31.530
You might say, well, maybe on average
00:02:31.530 --> 00:02:34.560
it takes you about six tries,
and you would be correct.
00:02:34.560 --> 00:02:36.630
The mean of a geometric random variable
00:02:36.630 --> 00:02:41.340
is one over the probability
of success on each trial.
00:02:41.340 --> 00:02:44.639
So in this situation the mean is going
00:02:44.639 --> 00:02:48.980
to be one over this probability
of success in each trial
00:02:48.980 --> 00:02:50.639
is one over six.
00:02:50.639 --> 00:02:52.660
So it's equal to six.
00:02:52.660 --> 00:02:54.930
So one way to think
about it is on average,
00:02:54.930 --> 00:02:58.460
you would have six trials
until you get a one.
00:02:58.460 --> 00:03:02.510
Now another question is
what's a measure of the spread
00:03:02.510 --> 00:03:04.040
of a geometric random variable?
00:03:04.040 --> 00:03:06.000
And we don't prove this in another video,
00:03:06.000 --> 00:03:07.430
maybe I'll do it eventually.
00:03:07.430 --> 00:03:09.778
That the standard deviation
00:03:09.778 --> 00:03:13.890
of a geometric random
variable is the mean times
00:03:13.890 --> 00:03:17.490
the square root of one minus
P, or you could just write this
00:03:17.490 --> 00:03:22.330
as a square root of one minus P over P.
00:03:22.330 --> 00:03:24.700
Now in this situation, what would this be?
00:03:24.700 --> 00:03:28.027
Well, the standard deviation
of this random variable,
00:03:28.027 --> 00:03:30.070
it's a geometric random variable.
00:03:30.070 --> 00:03:35.070
It's going to be the square
root of one minus one sixth,
00:03:35.610 --> 00:03:38.440
all of that over one sixth.
00:03:38.440 --> 00:03:41.260
So this is going to be
equal to the square root
00:03:41.260 --> 00:03:44.760
of five sixth over one sixth,
00:03:44.760 --> 00:03:49.550
which is equal to six times
the square root of five sixth.
00:03:49.550 --> 00:03:51.960
And this is going to
be approximately equal
00:03:51.960 --> 00:03:56.250
to five divided by six is equal to that.
00:03:56.250 --> 00:03:57.910
We'll take the square root of that.
00:03:57.910 --> 00:04:02.540
And then multiply that times
six, gets us to about 5.5.
00:04:03.950 --> 00:04:07.690
So approximately equal to 5.5.
00:04:07.690 --> 00:04:10.050
And what's interesting about
a geometric random variable,
00:04:10.050 --> 00:04:12.890
obviously the lowest value
here in this case is one,
00:04:12.890 --> 00:04:15.320
two, three, can go higher,
higher, but you can go arbitrary.
00:04:15.320 --> 00:04:17.140
You could get really unlucky
and it might take you
00:04:17.140 --> 00:04:19.550
a thousand rolls in order to get that one.
00:04:19.550 --> 00:04:20.760
It could take you a million rolls,
00:04:20.760 --> 00:04:23.580
very low probability, but it
could take you a million rolls
00:04:23.580 --> 00:04:24.860
in order to get that one.
00:04:24.860 --> 00:04:27.150
And so another thing to realize
00:04:27.150 --> 00:04:30.230
about a geometric random
variables distribution,
00:04:30.230 --> 00:04:35.100
it tends to look something like this
00:04:35.100 --> 00:04:38.670
where the mean might be over here.
00:04:38.670 --> 00:04:40.410
And so you have a very long tail
00:04:40.410 --> 00:04:41.660
to the right of your mean,
00:04:41.660 --> 00:04:44.124
and this is classic right skew.
00:04:44.124 --> 00:04:47.662
And so all geometric random
variables distributions
00:04:47.662 --> 00:04:49.250
are right skewed.
00:04:49.250 --> 00:04:51.030
They have a long tail of values,
00:04:51.030 --> 00:04:52.950
an infinitely long tail
of values they can take
00:04:52.950 --> 00:04:54.390
to the right.
00:04:54.390 --> 00:04:55.310
Now one last question,
00:04:55.310 --> 00:04:56.890
instead of dealing with a six sided die,
00:04:56.890 --> 00:04:58.880
what would be the situation
if we were dealing
00:04:58.880 --> 00:05:01.440
with a 12 sided die?
00:05:01.440 --> 00:05:04.080
What would then be the mean
of our random variable?
00:05:04.080 --> 00:05:06.300
And what would be the standard deviation
00:05:06.300 --> 00:05:07.140
of our random variable?
00:05:07.140 --> 00:05:09.700
Pause this video and think about that.
00:05:09.700 --> 00:05:12.760
Well, the mean would be one over one 12th,
00:05:12.760 --> 00:05:15.190
because you have a probability
of one 12th every time
00:05:15.190 --> 00:05:16.023
of getting it one.
00:05:16.023 --> 00:05:17.250
We're assuming we're playing the same game
00:05:17.250 --> 00:05:18.770
now with the 12 sided die.
00:05:18.770 --> 00:05:21.360
So one over one 12th would be 12.
00:05:21.360 --> 00:05:26.360
So on average it would take 12
rolls to get that first one.
00:05:26.520 --> 00:05:28.170
And then our standard deviation
00:05:28.170 --> 00:05:32.060
is going to be essentially
this times the square root
00:05:32.060 --> 00:05:34.130
of one minus one 12th.
00:05:34.130 --> 00:05:34.963
Or let me write it this way.
00:05:34.963 --> 00:05:39.271
It's one minus one 12th, over one over 12,
00:05:39.271 --> 00:05:42.500
which is the same thing as
12 times the square root
00:05:42.500 --> 00:05:44.182
of 11 12ths.
00:05:44.182 --> 00:05:48.300
11 divided by 12 is equal to,
00:05:48.300 --> 00:05:52.670
take the square root and
then multiply that times 12.
00:05:52.670 --> 00:05:55.612
And you get about 11.5.
00:05:55.612 --> 00:05:58.700
11.5.
00:05:58.700 --> 00:06:00.520
And so you can see with a 12 sided die,
00:06:00.520 --> 00:06:02.137
it has the same pattern,
00:06:02.137 --> 00:06:05.140
where you have your mean
of your random variable,
00:06:05.140 --> 00:06:06.862
and then you have a standard deviation
00:06:06.862 --> 00:06:11.180
that goes a reasonable bit
on either side of the mean,
00:06:11.180 --> 00:06:14.170
it's almost equal to the mean in actually
00:06:14.170 --> 00:06:15.260
in both situations.
00:06:15.260 --> 00:06:17.090
It's a little bit lower than the mean.
00:06:17.090 --> 00:06:18.840
But then there's many, many, many values
00:06:18.840 --> 00:06:21.020
that go far to the right of your mean.
00:06:21.020 --> 00:06:23.090
And so you have this classical right skew
00:06:23.090 --> 00:06:25.083
for a geometric random variable.
|
Worked example: Calculating the maximum wavelength capable of ionization | https://www.youtube.com/watch?v=BR7Svm1s8fs | vtt | https://www.youtube.com/api/timedtext?v=BR7Svm1s8fs&ei=8VWUZf_hKvHnxN8Pj6iOQA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EACA70AF70F1D0E48D07D9A24B5A3AB8B28E535A.9AF9B2434256BA5E49992B6D6FF944CF1E10AA68&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.910 --> 00:00:03.630
- [Instructor] We're told that
the first ionization energy
00:00:03.630 --> 00:00:08.630
of silver is 7.31 times 10
to the fifth joules per mole.
00:00:08.870 --> 00:00:11.690
What is the longest wavelength of light
00:00:11.690 --> 00:00:15.070
that is capable of
ionizing an atom of silver
00:00:15.070 --> 00:00:17.040
in the gas phase?
00:00:17.040 --> 00:00:19.360
All right, now before
I even ask you to pause
00:00:19.360 --> 00:00:20.980
and try to do this on your own,
00:00:20.980 --> 00:00:23.390
let's just remind ourselves
or try to understand
00:00:23.390 --> 00:00:26.430
what first ionization energy even is.
00:00:26.430 --> 00:00:29.760
This is the energy required
to get the highest energy
00:00:29.760 --> 00:00:33.800
or outermost electron
to escape from the atom.
00:00:33.800 --> 00:00:36.310
So it's not just going to
go to a higher energy level.
00:00:36.310 --> 00:00:38.010
It's just going to completely escape.
00:00:38.010 --> 00:00:40.640
You could view it as the
infinite energy level.
00:00:40.640 --> 00:00:41.710
And the reason why we're talking
00:00:41.710 --> 00:00:44.310
about the longest wavelength
of light is, remember,
00:00:44.310 --> 00:00:47.870
the longer the wavelength,
the lower the frequency,
00:00:47.870 --> 00:00:50.160
and the lower the energy.
00:00:50.160 --> 00:00:53.160
So this is saying really
what's the minimum frequency
00:00:53.160 --> 00:00:55.150
or the minimum energy that's associated
00:00:55.150 --> 00:00:57.090
with the longest wavelength of light
00:00:57.090 --> 00:01:01.070
for an atom of silver?
00:01:01.070 --> 00:01:03.280
So a couple things to pay attention to.
00:01:03.280 --> 00:01:05.450
They're giving us the
first ionization energy
00:01:05.450 --> 00:01:07.890
in terms of moles, not per atom.
00:01:07.890 --> 00:01:10.600
And then we just have
to remind ourselves all
00:01:10.600 --> 00:01:13.240
of our different ways of
connecting wavelength,
00:01:13.240 --> 00:01:15.260
frequency, and energy.
00:01:15.260 --> 00:01:18.090
Now, given all of this, I
encourage you to pause this video
00:01:18.090 --> 00:01:19.680
and see if you can figure this out.
00:01:19.680 --> 00:01:21.650
What is the longest wavelength of light
00:01:21.650 --> 00:01:25.430
that is capable of
ionizing an atom of silver
00:01:25.430 --> 00:01:27.430
in the gas phase?
00:01:27.430 --> 00:01:29.190
All right, now let's work
through this together.
00:01:29.190 --> 00:01:30.990
So the first thing to do is try
00:01:30.990 --> 00:01:34.750
to figure out the first
ionization energy per atom.
00:01:34.750 --> 00:01:36.440
And so maybe I'll write it like this.
00:01:36.440 --> 00:01:38.720
So the energy per atom,
00:01:38.720 --> 00:01:42.420
the first ionization
energy per atom is going
00:01:42.420 --> 00:01:44.860
to be equal to the ionization energy,
00:01:44.860 --> 00:01:49.860
7.31 times 10 to the fifth joules per mole
00:01:50.910 --> 00:01:53.610
times what if we wanna
figure out per atom?
00:01:53.610 --> 00:01:54.900
This is per mole.
00:01:54.900 --> 00:01:58.070
Well, how many moles are there per atom?
00:01:58.070 --> 00:02:01.750
Well, we know that they're
this number of atoms per mole,
00:02:01.750 --> 00:02:03.620
so if we wanna know moles per atom,
00:02:03.620 --> 00:02:06.530
it's going to be one mole
00:02:07.900 --> 00:02:12.710
for every 6.022 times 10
00:02:12.710 --> 00:02:14.610
to the 23rd atoms.
00:02:14.610 --> 00:02:15.670
I could write atoms here,
00:02:15.670 --> 00:02:17.850
and then that would
give us joules per atom,
00:02:17.850 --> 00:02:19.640
but we're just gonna get the
answer in terms of joules
00:02:19.640 --> 00:02:21.690
'cause the moles are going to cancel out.
00:02:21.690 --> 00:02:25.160
And so this is going to
give us approximately...
00:02:25.160 --> 00:02:27.963
Let's see, we have three
significant figures here.
00:02:32.310 --> 00:02:37.310
7.31 times 10 to the fifth
00:02:37.460 --> 00:02:42.460
divided by 6.022 times 10
00:02:42.820 --> 00:02:46.920
to the 23rd power is equal to,
00:02:46.920 --> 00:02:48.850
and we have three significant figure here,
00:02:48.850 --> 00:02:52.390
so 1.21, approximately equal to 1.21
00:02:52.390 --> 00:02:54.723
times 10 to the -18.
00:02:55.570 --> 00:02:59.543
1.21 times 10 to the -18,
00:03:00.920 --> 00:03:02.820
and the units here are joules.
00:03:02.820 --> 00:03:05.030
This is joules per atom.
00:03:05.030 --> 00:03:07.910
So now how do we figure out wavelength?
00:03:07.910 --> 00:03:09.710
Well, as I alluded to,
00:03:09.710 --> 00:03:13.150
we might wanna use these equations here.
00:03:13.150 --> 00:03:15.360
We know that the speed of light is equal
00:03:15.360 --> 00:03:17.830
to the wavelength of that light
00:03:17.830 --> 00:03:19.480
times the frequency of the light.
00:03:19.480 --> 00:03:21.590
This is the lowercase Greek letter nu.
00:03:21.590 --> 00:03:23.840
This is not a V right over here.
00:03:23.840 --> 00:03:26.430
So if we wanna solve for wavelength,
00:03:26.430 --> 00:03:28.500
we just divide both sides by frequency.
00:03:28.500 --> 00:03:30.060
And so you get the wavelength is equal
00:03:30.060 --> 00:03:33.140
to the speed of light
divided by frequency.
00:03:33.140 --> 00:03:35.680
But how do you figure out
frequency from energy?
00:03:35.680 --> 00:03:38.220
Well, that's what this
top equation gives us.
00:03:38.220 --> 00:03:41.600
Energy is equal to Planck's
constant times frequency.
00:03:41.600 --> 00:03:43.230
So if you wanna solve for frequency,
00:03:43.230 --> 00:03:45.310
divide both sides by Planck's constant.
00:03:45.310 --> 00:03:49.180
So that top equation can
be rewritten as frequency,
00:03:49.180 --> 00:03:50.060
I'll write it here,
00:03:50.060 --> 00:03:54.610
frequency is equal to energy
divided by Planck's constant.
00:03:54.610 --> 00:03:58.810
And so we could take this
and substitute it over here,
00:03:58.810 --> 00:04:01.660
and we would get that
our wavelength is equal
00:04:01.660 --> 00:04:06.090
to the speed of light divided by energy
00:04:06.090 --> 00:04:08.360
divided by Planck's constant,
00:04:08.360 --> 00:04:10.950
or we can just rewrite this as being equal
00:04:10.950 --> 00:04:14.050
to the speed of light
times Planck's constant
00:04:15.350 --> 00:04:17.180
divided by,
00:04:17.180 --> 00:04:21.050
try to keep the colors
consistent, divided by energy.
00:04:21.050 --> 00:04:23.710
Well, we know what the speed of light is.
00:04:23.710 --> 00:04:27.590
It is 2.998,
00:04:27.590 --> 00:04:29.780
or it's approximately 2.998,
00:04:29.780 --> 00:04:33.730
times 10 to the eighth meters per second.
00:04:33.730 --> 00:04:36.940
We're gonna multiply that
time Planck's constant,
00:04:36.940 --> 00:04:41.290
which is 6.626 times 10
00:04:41.290 --> 00:04:45.740
to the -34th joule seconds.
00:04:45.740 --> 00:04:47.840
And then we're going to divide that
00:04:47.840 --> 00:04:51.770
by the first ionization energy per atom,
00:04:51.770 --> 00:04:53.400
which we figured out right over here.
00:04:53.400 --> 00:04:57.510
So we're gonna divide that,
this E right over here.
00:04:57.510 --> 00:04:59.730
This is going to be, we figured it out,
00:04:59.730 --> 00:05:04.730
1.21 times 10 to the -18 joules.
00:05:05.220 --> 00:05:07.380
Now let's make sure
all the units work out.
00:05:07.380 --> 00:05:10.600
So this seconds is going to
cancel out with this seconds.
00:05:10.600 --> 00:05:12.880
This joules is gonna cancel
out with this joules.
00:05:12.880 --> 00:05:14.060
And we're just gonna be left with meters,
00:05:14.060 --> 00:05:15.030
which makes sense.
00:05:15.030 --> 00:05:17.650
The wavelength can be measured in meters.
00:05:17.650 --> 00:05:19.940
And so let's just get our calculator out
00:05:19.940 --> 00:05:23.610
and calculate out what
this is going to be.
00:05:23.610 --> 00:05:26.420
2.998 times 10 to the eighth
00:05:29.224 --> 00:05:30.823
times 6.626
00:05:33.150 --> 00:05:37.820
times 10 to the -34.
00:05:37.820 --> 00:05:39.580
And then I'm gonna divide that
00:05:39.580 --> 00:05:41.570
by 1.21 times 10
00:05:45.030 --> 00:05:45.947
to the -18.
00:05:47.120 --> 00:05:49.370
I think we deserve a
little bit of a drum roll.
00:05:49.370 --> 00:05:51.910
That gets us that.
00:05:51.910 --> 00:05:52.860
And let's see.
00:05:52.860 --> 00:05:56.490
If we have three significant
figures is our smallest amount
00:05:56.490 --> 00:05:57.660
in this calculation,
00:05:57.660 --> 00:06:00.590
so we're gonna go to these
three right over here.
00:06:00.590 --> 00:06:03.350
And so this is going to be 1.64 times 10
00:06:03.350 --> 00:06:06.790
to the negative one, two, three, four,
00:06:06.790 --> 00:06:09.640
five, six, seven.
00:06:09.640 --> 00:06:12.150
So this is going to be approximately equal
00:06:12.150 --> 00:06:15.540
to 1.64 times 10
00:06:15.540 --> 00:06:17.960
to the -7 meters.
00:06:17.960 --> 00:06:18.793
And we're done.
|
Column chromatography | https://www.youtube.com/watch?v=UHF1HXdkrZQ | vtt | https://www.youtube.com/api/timedtext?v=UHF1HXdkrZQ&ei=8VWUZcKaKt_DmLAPgtmAmAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=4AA29E6DDD9EB68675BA81C93C43132D1C92AE05.54AC0923DF2E40AD043760BD79D8586AD10C1DC9&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.750 --> 00:00:01.900
- In our previous video
00:00:01.900 --> 00:00:05.200
we talked about Thin Layer Chromatography
00:00:05.200 --> 00:00:07.090
and it was this technique used
00:00:07.090 --> 00:00:08.299
to figure out how many things
00:00:08.299 --> 00:00:10.210
you have in a sample
00:00:10.210 --> 00:00:12.950
or maybe say the relative properties
00:00:12.950 --> 00:00:14.650
say the relative polarity
00:00:14.650 --> 00:00:16.360
of the things that you have in the sample
00:00:16.360 --> 00:00:17.500
and so what you do is
00:00:17.500 --> 00:00:19.481
you put a sample
00:00:19.481 --> 00:00:21.960
on typically a silica gel,
00:00:21.960 --> 00:00:23.960
which is the stationary phase
00:00:23.960 --> 00:00:28.290
and then you put a mobile phase down here,
00:00:28.290 --> 00:00:31.080
which in this case might be less polar
00:00:31.080 --> 00:00:32.540
and then it's going to move
00:00:32.540 --> 00:00:35.870
its way up the silica gel
00:00:35.870 --> 00:00:38.260
and as it does, you can imagine,
00:00:38.260 --> 00:00:40.600
it's going to interact
with your original sample
00:00:40.600 --> 00:00:42.450
and so parts of the original sample
00:00:42.450 --> 00:00:46.230
are going to move up
with your mobile phase
00:00:46.230 --> 00:00:47.460
and different parts
00:00:47.460 --> 00:00:48.510
are going to be attracted
00:00:48.510 --> 00:00:49.840
to that mobile phase
00:00:49.840 --> 00:00:52.280
and not attracted to the silica gel
00:00:52.280 --> 00:00:54.320
to different degrees, you can imagine.
00:00:54.320 --> 00:00:56.240
If there's a part of your original sample
00:00:56.240 --> 00:00:59.050
that is more polar
00:00:59.050 --> 00:01:00.550
then it's going to be harder to move
00:01:00.550 --> 00:01:01.670
cause it's going to be attracted
00:01:01.670 --> 00:01:02.920
to the stationary phase
00:01:02.920 --> 00:01:05.090
and less attracted to the mobile phase
00:01:05.090 --> 00:01:06.670
and so it's going to move less.
00:01:06.670 --> 00:01:07.503
So this might be
00:01:07.503 --> 00:01:09.490
the more polar part of your sample
00:01:10.400 --> 00:01:12.470
as it moves from its original location
00:01:12.470 --> 00:01:14.022
and the part that's less polar,
00:01:14.022 --> 00:01:15.270
well it's not going to be
00:01:15.270 --> 00:01:17.690
as attracted to the stationary phase
00:01:17.690 --> 00:01:21.100
and so it's going to be more dissolvable
00:01:21.100 --> 00:01:23.490
in the less polar mobile phase
00:01:23.490 --> 00:01:25.700
and so it will go further.
00:01:25.700 --> 00:01:28.230
So this will be the less polar part
00:01:28.230 --> 00:01:30.650
of your original sample
00:01:30.650 --> 00:01:32.022
and so you can see that separation
00:01:32.022 --> 00:01:33.890
and you could come up with other insights
00:01:33.890 --> 00:01:34.723
that we talk about that
00:01:34.723 --> 00:01:36.320
in that other video.
00:01:36.320 --> 00:01:37.153
In this video,
00:01:37.153 --> 00:01:38.100
I'm gonna introduce you to
00:01:38.100 --> 00:01:41.190
a very very very similar idea
00:01:41.190 --> 00:01:42.310
it's just things are moving
00:01:42.310 --> 00:01:43.530
in a different direction
00:01:43.530 --> 00:01:47.530
and that is the notion
of Column Chromatography.
00:01:47.530 --> 00:01:49.820
What you do in Column Chromatography,
00:01:49.820 --> 00:01:51.500
just like Thin Layer Chromatography
00:01:51.500 --> 00:01:53.650
is let's say you have some type of vile,
00:01:53.650 --> 00:01:54.690
some type of a column,
00:01:54.690 --> 00:01:55.680
I guess I could say
00:01:57.855 --> 00:01:58.688
you'll typically see it
00:01:58.688 --> 00:02:00.030
with a little tap drawn down here
00:02:00.030 --> 00:02:00.950
because you might wanna see
00:02:00.950 --> 00:02:02.910
what comes out through the bottom
00:02:02.910 --> 00:02:04.000
but what you do is you fill it
00:02:04.000 --> 00:02:05.040
with the stationary phase
00:02:05.040 --> 00:02:07.890
which once again is oftentimes silica gel.
00:02:07.890 --> 00:02:10.540
So this is stationary phase
00:02:10.540 --> 00:02:13.300
stationary phase
00:02:13.300 --> 00:02:16.140
and if it's silica gel in this case,
00:02:16.140 --> 00:02:18.280
silica gel
00:02:18.280 --> 00:02:19.420
it doesn't have to be silica gel
00:02:19.420 --> 00:02:20.520
but that's pretty common.
00:02:20.520 --> 00:02:22.630
This is going to be very polar
00:02:22.630 --> 00:02:26.150
so let me write this, very polar
00:02:26.150 --> 00:02:28.470
and then you put some of your sample
00:02:28.470 --> 00:02:29.890
at the top here.
00:02:29.890 --> 00:02:31.800
So that's your original sample
00:02:31.800 --> 00:02:32.910
you put it at the top
00:02:32.910 --> 00:02:35.380
and then you have some mobile phase,
00:02:35.380 --> 00:02:39.330
the solvent that you're going to put
00:02:39.330 --> 00:02:40.680
on top of that.
00:02:40.680 --> 00:02:42.210
So you're gonna do something like that
00:02:42.210 --> 00:02:44.740
and what do you think is going to happen?
00:02:44.740 --> 00:02:45.930
Well, your mobile phase
00:02:45.930 --> 00:02:48.530
is going to start moving its way down
00:02:48.530 --> 00:02:49.940
through your stationary phase
00:02:49.940 --> 00:02:52.460
and it's going to
interact with your sample.
00:02:52.460 --> 00:02:53.440
Now what's going to happen
00:02:53.440 --> 00:02:56.330
to the more polar
components of your sample?
00:02:56.330 --> 00:02:59.450
Well, the more polar
components of your sample
00:02:59.450 --> 00:03:00.930
are going to be more attracted
00:03:00.930 --> 00:03:02.140
to the stationary phase,
00:03:02.140 --> 00:03:04.670
less attracted to the mobile phase
00:03:04.670 --> 00:03:06.100
so they're gonna move less.
00:03:06.100 --> 00:03:07.989
So the more polar parts of your sample
00:03:07.989 --> 00:03:10.273
might only go, maybe that far
00:03:10.273 --> 00:03:12.544
while the less polar parts of your sample,
00:03:12.544 --> 00:03:13.377
they'll move,
00:03:13.377 --> 00:03:14.472
there'll be less attracted
00:03:14.472 --> 00:03:16.810
to your stationary phase
00:03:16.810 --> 00:03:19.780
and they'll move with
your mobile phase more
00:03:19.780 --> 00:03:20.988
and so you might have
00:03:20.988 --> 00:03:23.806
they might move down,
00:03:23.806 --> 00:03:25.222
down over there
00:03:25.222 --> 00:03:27.510
and so the big takeaway,
00:03:27.510 --> 00:03:28.720
the difference between the two
00:03:28.720 --> 00:03:30.560
is just the direction you're moving in.
00:03:30.560 --> 00:03:31.930
In Thin Layer Chromatography
00:03:31.930 --> 00:03:34.023
your more polar thing is the lower dot
00:03:34.023 --> 00:03:36.070
while in Column Chromatography,
00:03:36.070 --> 00:03:37.430
your more polar thing
00:03:37.430 --> 00:03:40.010
is the upper layer right over here,
00:03:40.010 --> 00:03:41.240
this purple area right over here
00:03:41.240 --> 00:03:43.390
and of course, all of that depends on
00:03:45.264 --> 00:03:47.230
the polarity of your stationary phase
00:03:47.230 --> 00:03:49.570
and the relative polarity
of your mobile phase
00:03:49.570 --> 00:03:52.160
but what I just showed you
is a typical situation.
00:03:52.160 --> 00:03:53.990
So keep in mind whether you're looking
00:03:53.990 --> 00:03:55.480
at Thin Layer Chromatography
00:03:55.480 --> 00:03:57.040
or Column Chromatography
00:03:57.040 --> 00:03:59.553
which to pay attention to the direction.
|
7 Tips for Motivating Middle School and High School Kids During Distance Learning | https://www.youtube.com/watch?v=JLh0_ZvPVJo | vtt | https://www.youtube.com/api/timedtext?v=JLh0_ZvPVJo&ei=8VWUZe3aL5Kvp-oP_66TEA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C14F11376D5340B3ED42589CBF82668FB08871CD.31258196BAB3A04C2BF1A4BCA3CC3FD6D909CD21&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:05.060 --> 00:00:07.310
Hi everyone, thank you
for joining us today
00:00:07.310 --> 00:00:10.540
on our webinar on Seven Tips
for Motivating Middle School
00:00:10.540 --> 00:00:13.090
and High School Kids
During Distance Learning.
00:00:13.090 --> 00:00:15.610
My name is Dan Tu and I'll
be kicking us off today,
00:00:15.610 --> 00:00:17.990
as well as moderating our Q and A portion
00:00:17.990 --> 00:00:19.410
of today's segment.
00:00:19.410 --> 00:00:21.180
Before we get started, there's
a couple of announcements
00:00:21.180 --> 00:00:22.280
I'd like to make.
00:00:22.280 --> 00:00:24.420
First of all, this
webinar is being recorded
00:00:24.420 --> 00:00:27.730
and you will automatically
be emailed a copy of it
00:00:27.730 --> 00:00:29.480
as well, we'll be posting this online
00:00:29.480 --> 00:00:31.760
and available for your
review at your convenience.
00:00:31.760 --> 00:00:33.640
So don't worry if you miss anything
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or if you wanna go back
and watch something.
00:00:35.760 --> 00:00:37.510
Secondly, we're really excited to announce
00:00:37.510 --> 00:00:40.420
for the first time that we're
making this webinar available
00:00:40.420 --> 00:00:42.230
in Spanish captioning.
00:00:42.230 --> 00:00:46.620
So if you want, you can
go to this Bitly URL
00:00:46.620 --> 00:00:50.080
that's also being entered
in our chat box right now.
00:00:50.080 --> 00:00:51.510
So you can click to that.
00:00:51.510 --> 00:00:52.343
And the way you'll see it
00:00:52.343 --> 00:00:54.120
is just don't close out of this webinar,
00:00:54.120 --> 00:00:56.230
you'll still be watching this webinar.
00:00:56.230 --> 00:00:58.580
And that link will take
you to a captioning site
00:00:58.580 --> 00:01:00.840
where you'll see the
translations as we speak,
00:01:00.840 --> 00:01:03.940
or as close to possible as we speak.
00:01:03.940 --> 00:01:06.660
And we'd also like to
thank several organizations
00:01:06.660 --> 00:01:09.280
who've really helped us
with philanthropic support
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which has enabled us to
bring new programming
00:01:11.120 --> 00:01:12.400
like today's session.
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So we wanna give a special
thanks to AT and T,
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Bank of America, Google.org,
Fastly and Novartis.
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With that, I'd like to introduce you all
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to Kristen DiCerbo, who'll
be walking through the tips
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and answering your live questions.
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Kristen's our amazing
Chief Learning Officer.
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She's also an expert in learning science,
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and she's gonna be sharing
all of her expertise
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with you today.
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So with that, take it away Kristen.
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- Great, thanks Dan.
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And welcome too all of you.
00:01:44.100 --> 00:01:45.970
Thanks so much for joining.
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I know that raising
teenagers is difficult.
00:01:52.800 --> 00:01:56.150
So one of the big jobs of a teenager
00:01:56.150 --> 00:02:00.640
is to differentiate
themselves from their parents
00:02:00.640 --> 00:02:05.640
and to think about who they
are outside of their family.
00:02:05.680 --> 00:02:08.640
And that means that
sometimes it's really hard
00:02:08.640 --> 00:02:10.260
to know what's going on with them
00:02:10.260 --> 00:02:12.140
and they're trying on new identities
00:02:12.140 --> 00:02:14.030
and they're trying new things.
00:02:14.030 --> 00:02:17.750
So I'm not gonna tell you that
I have all the answers today.
00:02:17.750 --> 00:02:21.530
Sorry, but hopefully I can
provide some strategies
00:02:21.530 --> 00:02:23.280
that maybe you haven't thought of before,
00:02:23.280 --> 00:02:28.280
other things to try, things
you might give a chance to.
00:02:28.680 --> 00:02:30.500
There's nothing that's
gonna work for everyone.
00:02:30.500 --> 00:02:33.050
There's nothing that's
gonna work for every kid,
00:02:33.050 --> 00:02:35.420
but there's some things we
can all think about trying,
00:02:35.420 --> 00:02:40.130
sharing to make things a little
bit easier for ourselves.
00:02:40.130 --> 00:02:42.900
So with that disclaimer, I'll start off.
00:02:42.900 --> 00:02:47.540
I'm gonna go through the tips
that are based on research
00:02:47.540 --> 00:02:50.350
and what we know, and then let it go.
00:02:50.350 --> 00:02:52.130
And Dan will ask some of the questions
00:02:52.130 --> 00:02:54.790
that you guys are putting
into the questions piece
00:02:54.790 --> 00:02:59.020
on the webinar, and we'll
have some time for Q and A.
00:02:59.020 --> 00:03:02.630
So with that, when you
take all of the research
00:03:02.630 --> 00:03:05.590
about motivation and think about, okay,
00:03:05.590 --> 00:03:07.560
what is the big thing?
00:03:07.560 --> 00:03:09.190
What are the big takeaways?
00:03:09.190 --> 00:03:11.570
It turns out that it's pretty simple.
00:03:11.570 --> 00:03:14.280
We're all motivated to do things.
00:03:14.280 --> 00:03:17.800
When one, we expect to
be successful at them
00:03:17.800 --> 00:03:20.650
and two, we value the activity.
00:03:20.650 --> 00:03:22.640
So this probably makes sense.
00:03:22.640 --> 00:03:25.010
Who wants to do things when
they think they're gonna fail
00:03:25.010 --> 00:03:27.860
at them or not be successful?
00:03:27.860 --> 00:03:30.240
And second we wanna do things that matter,
00:03:30.240 --> 00:03:32.040
that are important to us.
00:03:32.040 --> 00:03:34.670
Now, one of the tricks with teenagers,
00:03:34.670 --> 00:03:37.940
is that the things they value are changing
00:03:37.940 --> 00:03:40.090
and sometimes they're not communicating
00:03:40.090 --> 00:03:42.340
the things that they value anymore.
00:03:42.340 --> 00:03:44.750
And so that can make it difficult
00:03:44.750 --> 00:03:49.020
to think about how do
you help them increase
00:03:49.020 --> 00:03:52.230
their perceived value of an activity,
00:03:52.230 --> 00:03:53.570
because it's not always clear.
00:03:53.570 --> 00:03:54.740
So I'm gonna talk a little bit more
00:03:54.740 --> 00:03:59.420
about ways to use that
lever of value and also ways
00:03:59.420 --> 00:04:01.750
that we can help our students
00:04:01.750 --> 00:04:03.870
feel like they're gonna be successful.
00:04:03.870 --> 00:04:06.540
So if we think about all
of the rest of the tips
00:04:06.540 --> 00:04:09.640
that I'm gonna give, they're
pretty much based on doing one
00:04:09.640 --> 00:04:11.740
or both of these things.
00:04:11.740 --> 00:04:13.540
So if you keep that in your mind,
00:04:13.540 --> 00:04:15.810
even if these particular
tips aren't working,
00:04:15.810 --> 00:04:17.220
you might think of other ways
00:04:17.220 --> 00:04:19.600
that you can help students be successful
00:04:19.600 --> 00:04:22.550
or help them really see
value in the activities
00:04:22.550 --> 00:04:24.600
that they're being asked to do in school.
00:04:25.580 --> 00:04:30.420
So one of the biggest things
that hits on both value
00:04:30.420 --> 00:04:34.260
and the success is setting goals.
00:04:34.260 --> 00:04:35.870
And the reason it's related to success
00:04:35.870 --> 00:04:39.540
is because nothing makes you
feel like you can be successful
00:04:39.540 --> 00:04:42.390
as having had some success in the past.
00:04:42.390 --> 00:04:45.200
So if you set some short-term goals
00:04:45.200 --> 00:04:48.230
and students are able to achieve those
00:04:48.230 --> 00:04:49.730
they start to gain momentum.
00:04:49.730 --> 00:04:52.460
They start to see themselves as learners.
00:04:52.460 --> 00:04:54.600
And that can be really important
00:04:54.600 --> 00:04:56.440
just in changing the mindset.
00:04:56.440 --> 00:05:01.230
So think about for teenagers,
for kind of middle school
00:05:01.230 --> 00:05:03.950
and high school students,
you don't wanna set a goal
00:05:03.950 --> 00:05:06.160
that's gonna take longer than a week.
00:05:06.160 --> 00:05:10.340
Because even at this age, more
than a week is a long time
00:05:10.340 --> 00:05:12.550
to kind of be able to move through.
00:05:12.550 --> 00:05:15.280
So if you do wanna set like
your goal for the month
00:05:15.280 --> 00:05:18.270
or for the semester, you're
gonna wanna break that up
00:05:18.270 --> 00:05:20.470
into pieces so that it's something
00:05:20.470 --> 00:05:24.480
that there is a tangible
achievement pretty quickly.
00:05:24.480 --> 00:05:26.170
So you start to get that feeling
00:05:26.170 --> 00:05:28.770
of success and build that momentum.
00:05:28.770 --> 00:05:32.350
And the other piece you
wanna do is find ways to know
00:05:32.350 --> 00:05:34.400
if you're on track to meet that goal.
00:05:34.400 --> 00:05:36.020
So if you have a weekly goal,
00:05:36.020 --> 00:05:39.270
say, we're gonna try
to read three chapters
00:05:39.270 --> 00:05:41.370
in this book by the end of the week,
00:05:41.370 --> 00:05:44.100
think about what does that
break down to per day?
00:05:44.100 --> 00:05:46.610
Think about that's a
way to monitor progress
00:05:46.610 --> 00:05:50.090
so that then they know, are they on track?
00:05:50.090 --> 00:05:53.020
Oh, I didn't quite read
that many pages yesterday
00:05:53.020 --> 00:05:55.650
so I'm gonna read this many today.
00:05:55.650 --> 00:05:57.380
Or I'm gonna read a few extra today
00:05:57.380 --> 00:05:59.460
so I don't have to read as many tomorrow.
00:05:59.460 --> 00:06:02.090
Those kinds of conversations are important
00:06:02.090 --> 00:06:06.130
to help students build that
muscle of being able to think
00:06:06.130 --> 00:06:07.660
about their own progress
00:06:07.660 --> 00:06:09.820
and whether they're on track or not.
00:06:09.820 --> 00:06:12.850
So we wanna keep, when we're
thinking about setting goals,
00:06:12.850 --> 00:06:16.110
we don't wanna set too
many, keep them a few,
00:06:16.110 --> 00:06:17.690
not more than three.
00:06:17.690 --> 00:06:22.060
So think about short
goals, brief number of them
00:06:22.060 --> 00:06:23.790
and goals that you can really measure.
00:06:23.790 --> 00:06:26.270
So, you know when you've met them.
00:06:26.270 --> 00:06:29.810
Which leads us to the next
piece, celebrate success.
00:06:29.810 --> 00:06:33.970
So when students do meet their
goal, you wanna make sure
00:06:33.970 --> 00:06:37.287
that that's a big message
that they're getting.
00:06:37.287 --> 00:06:39.730
"Hey, you were successful."
00:06:39.730 --> 00:06:41.400
So that can be a variety of things.
00:06:41.400 --> 00:06:43.820
It can be your tone of voice
when you're talking about it.
00:06:43.820 --> 00:06:47.410
It can be high fives and hugs.
00:06:47.410 --> 00:06:50.980
It can be choosing what's for dinner.
00:06:50.980 --> 00:06:53.010
We're gonna talk more
about tangible rewards
00:06:53.010 --> 00:06:54.290
a little bit later.
00:06:54.290 --> 00:06:57.310
But you're thinking
about ways to celebrate
00:06:57.310 --> 00:06:59.480
when students do meet their goals
00:06:59.480 --> 00:07:02.190
and also take that as a time to reflect.
00:07:02.190 --> 00:07:05.210
So it's important when students are
00:07:05.210 --> 00:07:08.010
and when they're not
successful to think about
00:07:08.010 --> 00:07:10.030
what were the things that
helped them meet that goal?
00:07:10.030 --> 00:07:12.510
What did they do that
helps them be successful?
00:07:12.510 --> 00:07:14.410
Or what were the obstacles
that got in the way
00:07:14.410 --> 00:07:16.410
so that they weren't successful?
00:07:16.410 --> 00:07:18.480
And how can they think about
00:07:18.480 --> 00:07:20.750
what they might do differently next time
00:07:20.750 --> 00:07:22.900
or what they're gonna repeat next time
00:07:22.900 --> 00:07:24.640
to be able to have success?
00:07:24.640 --> 00:07:27.270
So that little bit of reflection
can be really important
00:07:27.270 --> 00:07:30.140
for students to be able to get to that.
00:07:30.140 --> 00:07:32.980
And both with setting
goals and reflecting,
00:07:32.980 --> 00:07:34.430
you wanna bring the students in.
00:07:34.430 --> 00:07:37.850
You don't wanna be as a parent
setting the goal for them.
00:07:37.850 --> 00:07:40.730
You want to be working
with them to set goals.
00:07:40.730 --> 00:07:43.120
And also when we're talking
about school and learning,
00:07:43.120 --> 00:07:45.450
a good idea to connect with their teacher
00:07:45.450 --> 00:07:48.200
to look at what their goals
that are already set out
00:07:48.200 --> 00:07:50.790
by their teachers are so you can make sure
00:07:50.790 --> 00:07:54.493
that that's all in lock step
with where students need to be.
00:07:55.360 --> 00:07:57.800
So the other piece of reflection
00:07:57.800 --> 00:08:00.163
is thinking about what happens,
00:08:01.030 --> 00:08:03.320
what happened when they
maybe ran into trouble
00:08:03.320 --> 00:08:05.110
or got stuck a little bit.
00:08:05.110 --> 00:08:07.450
And that relates to the third tip
00:08:07.450 --> 00:08:09.810
is helping to manage roadblocks.
00:08:09.810 --> 00:08:12.920
So, sometimes particularly
with distance learning,
00:08:12.920 --> 00:08:16.300
students will get to a place
where they just don't know
00:08:16.300 --> 00:08:17.640
what to do next.
00:08:17.640 --> 00:08:22.110
So, they're stuck and they
don't know what to do.
00:08:22.110 --> 00:08:25.110
And then they get frustrated
and it starts to get them
00:08:25.110 --> 00:08:27.660
to this kind of emotional spiral with it.
00:08:27.660 --> 00:08:29.680
You wanna think about managing roadblocks
00:08:29.680 --> 00:08:31.740
before they get to that point.
00:08:31.740 --> 00:08:34.370
So when you were talking
about what are your goals
00:08:34.370 --> 00:08:37.140
for the week, that's
the time to talk about,
00:08:37.140 --> 00:08:39.170
so what are you gonna
do when you get stuck?
00:08:39.170 --> 00:08:41.453
And they might even have
a little list of things
00:08:41.453 --> 00:08:42.704
that they can refer to.
00:08:42.704 --> 00:08:44.210
What to do when I get stuck.
00:08:44.210 --> 00:08:45.650
How do they get help from you
00:08:45.650 --> 00:08:49.600
if you are available when
they're working on their work?
00:08:49.600 --> 00:08:51.660
I know lots of us are
also working from home
00:08:51.660 --> 00:08:52.550
at the same time.
00:08:52.550 --> 00:08:54.780
So what are the indicators that you have
00:08:54.780 --> 00:08:56.550
when it's okay to ask you for help?
00:08:56.550 --> 00:08:59.240
And hey, when you're on
a call and it's not okay
00:08:59.240 --> 00:09:00.073
to ask for help.
00:09:00.073 --> 00:09:03.070
Like being really specific
about how to get help from you.
00:09:03.070 --> 00:09:05.600
How can they get help from their teacher?
00:09:05.600 --> 00:09:07.980
How can they find help online?
00:09:07.980 --> 00:09:10.260
How can they get help from their peers?
00:09:10.260 --> 00:09:12.480
So all of those things
we should think about
00:09:12.480 --> 00:09:15.350
what are the strategies that
they have when they get stuck.
00:09:15.350 --> 00:09:17.270
Maybe one of the
strategies is to walk away
00:09:17.270 --> 00:09:18.840
for a little bit and come back.
00:09:18.840 --> 00:09:20.130
That's a good strategy
00:09:20.130 --> 00:09:22.140
especially when you
start to feel frustrated.
00:09:22.140 --> 00:09:26.500
So think about how to
manage those roadblocks
00:09:26.500 --> 00:09:28.180
before they get in the situation
00:09:28.180 --> 00:09:30.313
of needing to know what to do.
00:09:31.330 --> 00:09:33.660
From there, you wanna think
00:09:33.660 --> 00:09:37.660
about emphasizing that
effort leads to success.
00:09:37.660 --> 00:09:39.650
So remember we talked about this idea
00:09:39.650 --> 00:09:41.720
of feeling like you'll be successful.
00:09:41.720 --> 00:09:44.570
But by early teens,
00:09:44.570 --> 00:09:46.640
lots of kids already have some perceptions
00:09:46.640 --> 00:09:48.660
of things they're just not good at.
00:09:48.660 --> 00:09:52.120
And we wanna make sure and
try to break those ideas.
00:09:52.120 --> 00:09:55.800
That even when we are
not maybe naturally good
00:09:55.800 --> 00:09:59.590
at something, if we keep
practicing at it we'll get better.
00:09:59.590 --> 00:10:03.210
And we actually have
on the Academy website,
00:10:03.210 --> 00:10:05.720
a course called growth mindset
00:10:05.720 --> 00:10:08.890
and in that there were
some pretty good videos
00:10:08.890 --> 00:10:11.157
that talk about not just saying,
00:10:11.157 --> 00:10:13.030
"Hey, you know, keep trying."
00:10:13.030 --> 00:10:16.950
But the way our brains work,
there are cells in our brains,
00:10:16.950 --> 00:10:18.530
we call them neurons.
00:10:18.530 --> 00:10:21.110
And when we learn something new,
00:10:21.110 --> 00:10:24.290
those neurons form new
connections with each other.
00:10:24.290 --> 00:10:26.790
And so what practice does
00:10:26.790 --> 00:10:30.040
and what even practice
when we're not succeeding,
00:10:30.040 --> 00:10:32.400
even practice that we're getting wrong
00:10:32.400 --> 00:10:34.610
helps to build those linkages.
00:10:34.610 --> 00:10:37.720
And it's almost like when
you're lifting weights
00:10:37.720 --> 00:10:41.020
and you can make this analogy
that your brain is a muscle.
00:10:41.020 --> 00:10:42.510
And when you're lifting weight,
00:10:42.510 --> 00:10:43.980
sometimes it's a little too heavy
00:10:43.980 --> 00:10:46.130
and you can't quite lift that weight
00:10:46.130 --> 00:10:49.527
but you go down a little
bit and you practice it that
00:10:49.527 --> 00:10:51.130
and it builds up your muscles.
00:10:51.130 --> 00:10:55.090
The same thing you practice at that level,
00:10:55.090 --> 00:10:57.260
that's a little bit hard for you
00:10:57.260 --> 00:10:59.730
and your brain is going
to make more connections.
00:10:59.730 --> 00:11:01.750
If you just practice same
with lifting weights.
00:11:01.750 --> 00:11:03.090
If you're just lifting
the two pound weights
00:11:03.090 --> 00:11:05.540
and it's not really hard for you,
00:11:05.540 --> 00:11:07.970
well, you're probably
not building your muscles
00:11:07.970 --> 00:11:09.590
the same way if you're
just practicing stuff
00:11:09.590 --> 00:11:11.380
you already know that super easy,
00:11:11.380 --> 00:11:13.750
you're not making those
connections in your brain.
00:11:13.750 --> 00:11:15.530
So we find that in the research
00:11:15.530 --> 00:11:17.140
that when kids start to understand
00:11:17.140 --> 00:11:20.470
a little bit about actually
there's biology basis
00:11:20.470 --> 00:11:22.880
for trying things and working on things
00:11:22.880 --> 00:11:24.453
that are kind of hard for you,
00:11:25.650 --> 00:11:27.957
that actually motivates them to think
00:11:27.957 --> 00:11:29.490
"Oh, I can be successful.
00:11:29.490 --> 00:11:32.640
I can improve at this
thing that I'm doing."
00:11:32.640 --> 00:11:35.140
So recommend checking
out some of those videos
00:11:35.140 --> 00:11:38.260
but also thinking about how
to help your students see
00:11:38.260 --> 00:11:40.170
that things aren't always easy.
00:11:40.170 --> 00:11:42.380
And that learning actually is hard work
00:11:42.380 --> 00:11:44.400
and that's okay, because
if they put in the work,
00:11:44.400 --> 00:11:46.420
they're gonna get better at it.
00:11:46.420 --> 00:11:50.230
So that's the fourth piece.
00:11:50.230 --> 00:11:53.117
The fifth one is to encourage curiosity.
00:11:53.117 --> 00:11:57.420
And this can be tough in
particular with teens and preteens.
00:11:57.420 --> 00:12:00.110
And thinking about all of a
sudden, they're not interested
00:12:00.110 --> 00:12:02.680
in the same things they
used to be interested in.
00:12:02.680 --> 00:12:06.265
And so it can take some
work to try to figure out
00:12:06.265 --> 00:12:08.940
what kinds of things are
they interested in now?
00:12:08.940 --> 00:12:11.960
How do we help keep them thinking about,
00:12:11.960 --> 00:12:13.703
I wonder how the world works.
00:12:16.340 --> 00:12:19.860
So one thing you can do is
model that kind of thinking,
00:12:19.860 --> 00:12:23.000
ask those questions out
loud, ask those things
00:12:23.000 --> 00:12:24.980
like when you're riding your bike,
00:12:24.980 --> 00:12:28.900
why does pedaling the
pedal move the big wheel?
00:12:28.900 --> 00:12:32.980
All of these kinds of
things, how is this tree-
00:12:32.980 --> 00:12:34.660
It doesn't seem to be getting any food.
00:12:34.660 --> 00:12:36.950
How is it continuing to grow?
00:12:36.950 --> 00:12:38.270
And what does that look like?
00:12:38.270 --> 00:12:40.940
So if you're asking those
questions and modeling,
00:12:40.940 --> 00:12:44.930
being curious about the world,
students will pick up on that
00:12:44.930 --> 00:12:47.410
to those, "Oh, that is interesting."
00:12:47.410 --> 00:12:50.550
And they'll start to find things
and it won't be everything.
00:12:50.550 --> 00:12:52.810
And sometimes they'll roll their eyes
00:12:52.810 --> 00:12:56.590
but as you keep trying and
keep putting things out there,
00:12:56.590 --> 00:12:59.137
different things and
they'll start to kind of,
00:12:59.137 --> 00:13:00.690
"Oh, maybe that is interesting."
00:13:00.690 --> 00:13:02.730
Or start to have a
conversation about that,
00:13:02.730 --> 00:13:04.270
or start to build on that.
00:13:04.270 --> 00:13:07.850
So keep encouraging that sense
of interest and curiosity
00:13:07.850 --> 00:13:08.860
in the world.
00:13:08.860 --> 00:13:12.470
Because what this does, is
it increases that value piece
00:13:12.470 --> 00:13:13.970
that I was talking about.
00:13:13.970 --> 00:13:17.700
So if learning in school can
help you understand the world
00:13:17.700 --> 00:13:20.870
and help you understand
things you're curious about,
00:13:20.870 --> 00:13:22.910
then that's gonna increase that value
00:13:22.910 --> 00:13:25.783
and make you more motivated
to do the activities
00:13:25.783 --> 00:13:27.993
that you're doing related to school.
00:13:29.900 --> 00:13:34.160
So next piece is related to that,
00:13:34.160 --> 00:13:36.520
which is help to establish relevance.
00:13:36.520 --> 00:13:40.363
So if you talk to teachers,
they will almost always say,
00:13:42.060 --> 00:13:43.817
they hate the question when kids say,
00:13:43.817 --> 00:13:47.260
"When will I ever need to learn this?"
00:13:47.260 --> 00:13:50.780
But it turns out that when we
again think of that value side
00:13:50.780 --> 00:13:55.380
of the equation, that
thinking about how something
00:13:55.380 --> 00:13:59.630
is related to your interests, your goals,
00:13:59.630 --> 00:14:02.000
what you might wanna be when you grow up,
00:14:02.000 --> 00:14:03.670
related to learning something else
00:14:03.670 --> 00:14:05.670
that you're interested in learning,
00:14:05.670 --> 00:14:08.780
all of those things increase
the value of the activity
00:14:08.780 --> 00:14:11.720
and make students more likely
to want to engage in it.
00:14:11.720 --> 00:14:13.950
So those are important pieces
00:14:13.950 --> 00:14:17.480
to think about how do we
establish that relevance?
00:14:17.480 --> 00:14:21.760
So this comes back to knowing
what your kids' interests are
00:14:21.760 --> 00:14:23.850
which can involve some detective work.
00:14:23.850 --> 00:14:25.620
It can involve you observing them.
00:14:25.620 --> 00:14:28.870
It can involve talking to
them, all those conversations.
00:14:28.870 --> 00:14:30.320
Sometimes they're not gonna wanna talk
00:14:30.320 --> 00:14:32.450
but that's okay. Keep going.
00:14:32.450 --> 00:14:35.060
Persistence on your part is important too
00:14:35.060 --> 00:14:36.910
and they will recognize that.
00:14:36.910 --> 00:14:41.470
So thinking about how to
establish what is relevant
00:14:41.470 --> 00:14:45.200
to your students, to your
kids, you'll have to figure out
00:14:45.200 --> 00:14:46.530
what are their interests?
00:14:46.530 --> 00:14:48.210
What are their things
that are important to them
00:14:48.210 --> 00:14:50.300
to be able to help make those links?
00:14:50.300 --> 00:14:52.040
But you have a better chance of doing that
00:14:52.040 --> 00:14:53.530
than their teacher does.
00:14:53.530 --> 00:14:57.580
So the more you can do
that the better impact
00:14:57.580 --> 00:14:59.580
you're likely to have on their learning.
00:15:01.240 --> 00:15:05.640
So next, then finally, we
talk a lot about rewards.
00:15:05.640 --> 00:15:08.170
And we get a lot of
questions from parents,
00:15:08.170 --> 00:15:10.640
like, "Is this bribing my kid?
00:15:10.640 --> 00:15:13.290
I don't wanna bribe them to do their work.
00:15:13.290 --> 00:15:14.400
They should want to do it."
00:15:14.400 --> 00:15:15.670
Those kinds of things.
00:15:15.670 --> 00:15:18.140
So a couple of pieces of guidance.
00:15:18.140 --> 00:15:21.420
One is we all use rewards.
00:15:21.420 --> 00:15:23.890
I know I use rewards for myself sometimes.
00:15:23.890 --> 00:15:27.950
And I think about that when
I have to do a lot of writing
00:15:27.950 --> 00:15:29.730
and it's kind of going slowly,
00:15:29.730 --> 00:15:33.360
I'll say, "If I just finished this page,
00:15:33.360 --> 00:15:35.340
I can give myself a Hershey's kiss."
00:15:35.340 --> 00:15:37.710
I guess the little piece of
chocolate, not a big reward
00:15:37.710 --> 00:15:40.500
but a little something
that's a reward for doing it.
00:15:40.500 --> 00:15:42.720
We're not all intrinsically motivated
00:15:42.720 --> 00:15:44.510
to do everything all the time.
00:15:44.510 --> 00:15:46.490
Sometimes we need a little bit of boost.
00:15:46.490 --> 00:15:48.870
And so rewards are used
00:15:48.870 --> 00:15:53.870
and our best shoes, when they're
something that we can take
00:15:54.180 --> 00:15:57.560
and get students going on a path.
00:15:57.560 --> 00:16:01.020
So if it's something they don't
have any interest in doing,
00:16:01.020 --> 00:16:04.070
a reward can be that little
boost that gets them started.
00:16:04.070 --> 00:16:06.720
And once they get started,
they can start to again,
00:16:06.720 --> 00:16:08.330
experience some success.
00:16:08.330 --> 00:16:11.060
They can start to find
out interesting things.
00:16:11.060 --> 00:16:13.020
They can start to see
themselves as learners.
00:16:13.020 --> 00:16:15.460
But they need that little
boost to get going.
00:16:15.460 --> 00:16:18.600
So rewards can definitely help do that.
00:16:18.600 --> 00:16:21.440
They also don't have
to be tangible things.
00:16:21.440 --> 00:16:25.210
They can be like spending time with you.
00:16:25.210 --> 00:16:27.590
They can be spending
time with their friends.
00:16:27.590 --> 00:16:32.280
They can be an extra
half hour on the computer
00:16:32.280 --> 00:16:34.360
playing the video game
they're interested in.
00:16:34.360 --> 00:16:36.130
It can be picking the movie.
00:16:36.130 --> 00:16:39.080
It can be, picking what's for dinner.
00:16:39.080 --> 00:16:41.000
All kinds of things can be rewarding.
00:16:41.000 --> 00:16:44.120
They don't have to be a tangible something
00:16:44.120 --> 00:16:47.650
that is money related to
cost and buying things.
00:16:47.650 --> 00:16:51.540
So think about using
rewards to get things going,
00:16:51.540 --> 00:16:56.510
keep them small, you can
brainstorm with your kid
00:16:56.510 --> 00:17:00.530
about what things are rewarding to them.
00:17:00.530 --> 00:17:05.500
And that can be good to come
up with a continuum of rewards.
00:17:05.500 --> 00:17:09.280
If your student says, "Yeah,
a trip to Disney world."
00:17:09.280 --> 00:17:10.680
That can be on one end,
00:17:10.680 --> 00:17:12.610
it can go on the way bottom of the list
00:17:12.610 --> 00:17:14.050
but I'm not gonna encourage using
00:17:14.050 --> 00:17:16.070
those kinds of big rewards.
00:17:16.070 --> 00:17:18.880
It really are not effective
because they require,
00:17:18.880 --> 00:17:23.080
the "Hey, if you get A's
all year, you can get this."
00:17:23.080 --> 00:17:27.190
It's just too long of a timeline
and too big of a stakes.
00:17:27.190 --> 00:17:30.760
So you wanna do small things
so if they don't get it
00:17:30.760 --> 00:17:34.260
then that's okay, because
they'll have another chance
00:17:34.260 --> 00:17:36.800
which is the final thing
about using rewards.
00:17:36.800 --> 00:17:39.260
It shouldn't be something
they either earn,
00:17:39.260 --> 00:17:41.480
or they have no chance
of ever earning again.
00:17:41.480 --> 00:17:44.250
It should be okay if you
didn't earn it this time,
00:17:44.250 --> 00:17:45.620
we can set a new goal
00:17:45.620 --> 00:17:48.050
and you can try to earn
it again the next time.
00:17:48.050 --> 00:17:52.590
So you wanna think about
things that are small
00:17:52.590 --> 00:17:55.240
and able to, if they don't
make it the first time
00:17:55.240 --> 00:17:58.510
are able to try again
to earn those things.
00:17:58.510 --> 00:18:01.960
So those are some of
the big tips and ideas
00:18:01.960 --> 00:18:05.330
for thinking about generally again,
00:18:05.330 --> 00:18:08.300
thinking about this balance
of how can we help kids
00:18:08.300 --> 00:18:10.030
think they'll be successful
00:18:10.030 --> 00:18:11.970
and how can we help them
value the activities
00:18:11.970 --> 00:18:13.630
we're asking them to do.
00:18:13.630 --> 00:18:15.430
So I will stop and pause there.
00:18:15.430 --> 00:18:20.430
And Dan ask you to give us
some of the questions we have.
00:18:20.800 --> 00:18:22.170
- Great, so thanks Kristen.
00:18:22.170 --> 00:18:24.410
Before we get into the Q and A portion,
00:18:24.410 --> 00:18:26.580
a couple of reminders for folks.
00:18:26.580 --> 00:18:29.870
If you want a handout version
of this and go to webinar,
00:18:29.870 --> 00:18:32.270
there's a handout section
with a link to this PDF
00:18:32.270 --> 00:18:33.930
with these seven tips.
00:18:33.930 --> 00:18:35.630
And then also we are already getting
00:18:35.630 --> 00:18:37.700
a lot of great questions but
if you have any questions,
00:18:37.700 --> 00:18:39.620
please put them in the question box.
00:18:39.620 --> 00:18:42.230
There's a team of moderators,
kind of behind the scenes
00:18:42.230 --> 00:18:45.180
putting in all the questions
and surfacing them up.
00:18:45.180 --> 00:18:49.100
So go ahead and start
entering them right now.
00:18:49.100 --> 00:18:51.880
So Kristen, we already had a
couple of questions come in.
00:18:51.880 --> 00:18:54.630
One from email from a couple of days ago.
00:18:54.630 --> 00:18:57.280
Question is from the Person S.
00:18:57.280 --> 00:19:00.100
How do we get our older
kids not to play games
00:19:00.100 --> 00:19:01.540
on their school issued devices
00:19:01.540 --> 00:19:04.240
without policing them constantly?
00:19:04.240 --> 00:19:07.600
It's a huge distraction and
very difficult to control.
00:19:07.600 --> 00:19:09.872
We already have contacted
the school several times
00:19:09.872 --> 00:19:12.410
about blocking some of these sites.
00:19:12.410 --> 00:19:13.520
It's still an issue.
00:19:13.520 --> 00:19:14.970
I mean I would assume for younger kids,
00:19:14.970 --> 00:19:17.210
it's probably Minecraft,
for the middle kid
00:19:17.210 --> 00:19:18.300
is probably Fortnight.
00:19:18.300 --> 00:19:20.290
And then now it's the among us game.
00:19:20.290 --> 00:19:23.280
So there's this all of
this constant distractions
00:19:23.280 --> 00:19:24.980
that are available for the kiddos.
00:19:25.960 --> 00:19:29.080
- Oh my gosh, I just saw
the Congress people playing
00:19:29.080 --> 00:19:30.730
among us the other day.
00:19:30.730 --> 00:19:32.213
Wow, that was crazy.
00:19:33.560 --> 00:19:37.660
So there's a couple of
things here absolutely.
00:19:37.660 --> 00:19:41.520
One of the challenges
of learning from home
00:19:41.520 --> 00:19:44.870
is that there are so
many more distractions
00:19:44.870 --> 00:19:49.300
and that it can be really
difficult to think about
00:19:49.300 --> 00:19:51.990
okay, how do we help kids focus?
00:19:51.990 --> 00:19:56.990
So there's a couple of ways
to kind of attack this issue.
00:19:57.360 --> 00:20:02.080
One is, if I'm gonna keep
hitting on this goals piece.
00:20:02.080 --> 00:20:05.230
If they have goals that are set
00:20:05.230 --> 00:20:07.970
so that this is what they need to achieve,
00:20:07.970 --> 00:20:12.110
then we wanna work with them
to make sure they're on track
00:20:12.110 --> 00:20:13.840
to do that.
00:20:13.840 --> 00:20:18.840
Then they'll think about,
okay, if I'm doing this,
00:20:18.900 --> 00:20:20.600
does that get me off track
00:20:20.600 --> 00:20:22.350
to meet the thing that I need to do?
00:20:22.350 --> 00:20:25.010
I need to read 30 pages today.
00:20:25.010 --> 00:20:29.430
All right, can I read 15
and then play a little bit
00:20:29.430 --> 00:20:30.870
and then read 15 more?
00:20:30.870 --> 00:20:32.610
Like have these kinds of conversations
00:20:32.610 --> 00:20:35.980
with them about how they might
still be able to play some
00:20:35.980 --> 00:20:39.000
if the plan is allowed at
all on the device side.
00:20:39.000 --> 00:20:40.910
There's a couple of different
ways this might be going,
00:20:40.910 --> 00:20:41.900
this question could be going.
00:20:41.900 --> 00:20:44.650
like, if it's a games are
not allowed on the devices,
00:20:44.650 --> 00:20:46.040
you probably need to think
00:20:46.040 --> 00:20:49.260
about those technological
solution that block them.
00:20:49.260 --> 00:20:51.050
But if gaming's allowed
00:20:51.050 --> 00:20:53.020
but they need to be doing her schoolwork,
00:20:53.020 --> 00:20:55.800
think about how you can
potentially set up schedules
00:20:55.800 --> 00:20:57.780
that let them have some game time.
00:20:57.780 --> 00:21:00.890
Like have a little bit
of game time have breaks?
00:21:00.890 --> 00:21:01.810
Breaks are good.
00:21:01.810 --> 00:21:03.580
We all need breaks.
00:21:03.580 --> 00:21:04.700
And then they need to come back
00:21:04.700 --> 00:21:07.780
from the break and think
about continuing their school.
00:21:07.780 --> 00:21:10.170
And they're working with those are.
00:21:10.170 --> 00:21:14.063
Those can be good ways to think
about teaching moderation,
00:21:15.473 --> 00:21:17.580
think about teaching a little bit of that,
00:21:17.580 --> 00:21:19.270
kind of control of what they're doing.
00:21:19.270 --> 00:21:22.090
Set the timer for however
you know, 15 minutes
00:21:22.090 --> 00:21:24.410
that they can play and then come back
00:21:24.410 --> 00:21:28.120
to doing what they're doing
and think about what that is.
00:21:28.120 --> 00:21:30.540
They've also told you,
this is a really rewarding
00:21:30.540 --> 00:21:32.100
and interesting thing for me.
00:21:32.100 --> 00:21:34.840
So if you can think about
how to use that as a reward
00:21:34.840 --> 00:21:38.170
and turn it into a reward,
that that's something
00:21:38.170 --> 00:21:39.870
that they're probably gonna work for
00:21:39.870 --> 00:21:42.423
because that's where it is
and how to get it there.
00:21:44.910 --> 00:21:48.010
Probably any other kind
of punitive measures
00:21:48.010 --> 00:21:50.580
and all of that are not
gonna be that successful.
00:21:50.580 --> 00:21:55.090
It's more like turning up the
dial on some of the schoolwork
00:21:55.090 --> 00:21:58.590
and letting them have pieces of the game
00:21:58.590 --> 00:22:00.250
at different times when it's appropriate
00:22:00.250 --> 00:22:03.040
and help them figure out
how to make a schedule
00:22:03.040 --> 00:22:05.003
that fits into to help those work.
00:22:07.084 --> 00:22:09.050
So they can play a little bit.
00:22:09.050 --> 00:22:09.883
- That's super helpful.
00:22:09.883 --> 00:22:11.770
I love the suggestion of turning it
00:22:11.770 --> 00:22:14.780
into part of the incentives piece.
00:22:14.780 --> 00:22:18.240
Kristen, we have a
question from Nun who asks,
00:22:18.240 --> 00:22:19.073
it's related to the goal.
00:22:19.073 --> 00:22:21.270
So once after you've kind
of figured out the goal,
00:22:21.270 --> 00:22:22.700
the question is, how
do you convince the kid
00:22:22.700 --> 00:22:26.300
that achieving the goal
will lead to success?
00:22:26.300 --> 00:22:29.193
A lot of the times the
kids don't believe you.
00:22:30.930 --> 00:22:32.870
- So one thing is to set up
00:22:32.870 --> 00:22:35.770
meeting the goal itself is success.
00:22:35.770 --> 00:22:40.770
Like, if again, you're gonna try to do
00:22:42.870 --> 00:22:47.870
35 practice problems on
factoring polynomials.
00:22:50.660 --> 00:22:52.580
Like meeting that goal itself,
00:22:52.580 --> 00:22:56.550
like doing 35 practice problems
and meeting polynomials,
00:22:56.550 --> 00:22:58.330
that was a success in itself.
00:22:58.330 --> 00:22:59.290
That's great.
00:22:59.290 --> 00:23:04.290
So you wanna make that
itself an end point for them.
00:23:04.670 --> 00:23:08.440
Like, that's really good
that they've done that.
00:23:08.440 --> 00:23:12.367
So it's that piece that
then makes them feel like,
00:23:12.367 --> 00:23:17.367
"Hey, so next week the math
challenge is gonna be adding
00:23:18.150 --> 00:23:19.970
and subtracting polynomials."
00:23:19.970 --> 00:23:24.400
But now you already were
successful at factoring them
00:23:24.400 --> 00:23:26.840
so it's really likely that
you're gonna be successful
00:23:26.840 --> 00:23:28.730
with adding and subtracting them
00:23:28.730 --> 00:23:31.360
because you already were successful once.
00:23:31.360 --> 00:23:33.710
This other thing that
was pretty hard to learn
00:23:33.710 --> 00:23:34.950
and you did it.
00:23:34.950 --> 00:23:38.550
So the key is to use kind
of their past successes
00:23:38.550 --> 00:23:42.670
and their successes once they
in themselves are a success.
00:23:42.670 --> 00:23:44.930
And then using those to build on those
00:23:44.930 --> 00:23:47.863
of why they're likely to be
successful in future things.
00:23:49.170 --> 00:23:50.750
- That's great. That's great.
00:23:50.750 --> 00:23:53.100
Kristen, we have a question from Arlene
00:23:53.100 --> 00:23:54.810
and the parent asks a question
00:23:54.810 --> 00:23:57.870
that I think a lot of us have experienced.
00:23:57.870 --> 00:23:59.187
One, I'm a parent of a high school
00:23:59.187 --> 00:24:00.950
and a middle school counselor.
00:24:00.950 --> 00:24:03.100
A lot of our students are
struggling with depression
00:24:03.100 --> 00:24:06.360
and anxiety from being in
the house since last March.
00:24:06.360 --> 00:24:09.060
They're not motivated and
upset because they're failing.
00:24:09.060 --> 00:24:11.160
How can we motivate them
when they're mostly upset
00:24:11.160 --> 00:24:13.610
from being in the house
for six plus months?
00:24:13.610 --> 00:24:15.050
I think it's just really
important to recognize
00:24:15.050 --> 00:24:16.620
that that's pretty normal.
00:24:16.620 --> 00:24:18.350
I mean, I know that I've experienced
00:24:18.350 --> 00:24:21.273
a little bit of that too,
during these last eight months.
00:24:22.130 --> 00:24:24.980
- Absolutely, so the
first thing I'm gonna say
00:24:24.980 --> 00:24:27.183
is that mental health is more important
00:24:27.183 --> 00:24:29.470
than school progress.
00:24:29.470 --> 00:24:34.470
So the first thing I
would say is, think about,
00:24:35.240 --> 00:24:39.720
as you said, Dan, some amount
of just being mildly depressed
00:24:39.720 --> 00:24:41.540
and a little bit anxious is pretty normal
00:24:41.540 --> 00:24:43.670
in these kinds of times.
00:24:43.670 --> 00:24:47.530
If you're finding that it
seems to be beyond a little bit
00:24:47.530 --> 00:24:50.800
if it's really interfering
with their interactions
00:24:50.800 --> 00:24:53.440
with your family, if
it's really interfering
00:24:53.440 --> 00:24:56.410
with their just daily lives,
like they are not getting
00:24:56.410 --> 00:25:01.410
out of bed, those kinds of signs,
00:25:02.170 --> 00:25:05.453
I would absolutely
recommend professional help.
00:25:06.620 --> 00:25:10.090
Talk to your pediatrician
is a good starting point.
00:25:10.090 --> 00:25:12.690
Make sure to think
about what are the signs
00:25:12.690 --> 00:25:15.850
of someone who's needing,
00:25:15.850 --> 00:25:17.740
for whom this is a
little bit more than us.
00:25:17.740 --> 00:25:18.573
This is tough.
00:25:20.160 --> 00:25:22.120
So that's the first thing I would say
00:25:22.120 --> 00:25:24.180
is know when to get help.
00:25:24.180 --> 00:25:27.010
There's lots of good ways to check it.
00:25:27.010 --> 00:25:30.110
But what psychologists usually look for
00:25:30.110 --> 00:25:32.450
is when it starts to
interfere with your daily life
00:25:32.450 --> 00:25:34.480
as kind of a good rule of thumb
00:25:34.480 --> 00:25:37.200
for when it makes sense to get help.
00:25:37.200 --> 00:25:39.490
But if it is like less than that
00:25:39.490 --> 00:25:42.900
and it's, hey, I just am sad today.
00:25:42.900 --> 00:25:45.110
I'm just feeling anxious today.
00:25:45.110 --> 00:25:45.943
All of those things.
00:25:45.943 --> 00:25:49.510
So first, as the parent is empathize.
00:25:49.510 --> 00:25:52.030
Just like Dan just did,
"Hey, you know what?
00:25:52.030 --> 00:25:55.250
I get it, this situation is no fun."
00:25:55.250 --> 00:25:56.920
Like all of us are struggling
00:25:56.920 --> 00:26:00.260
and it is totally okay to struggle.
00:26:00.260 --> 00:26:03.690
I also encourage the way this was written
00:26:03.690 --> 00:26:05.190
was being in the house.
00:26:05.190 --> 00:26:06.930
It does help if you're in a place,
00:26:06.930 --> 00:26:10.360
even if it's not with other people
00:26:10.360 --> 00:26:14.220
to at least get some outside air
00:26:14.220 --> 00:26:19.140
to go out and move and get some fresh air
00:26:19.140 --> 00:26:22.280
if that's possible, where
you live and in your weather
00:26:22.280 --> 00:26:24.083
and all of those kinds of things.
00:26:25.520 --> 00:26:28.460
The next piece is that
exercise piece like moving,
00:26:28.460 --> 00:26:31.730
it can be important and
can help kids get up.
00:26:31.730 --> 00:26:34.700
So even if you're thinking
about the school day
00:26:34.700 --> 00:26:37.070
they should have breaks
in their school day
00:26:37.070 --> 00:26:39.830
where they are getting up
and moving and walking.
00:26:39.830 --> 00:26:43.920
And I'm saying, this is
do as I say, not as I do,
00:26:43.920 --> 00:26:44.940
I'm the worst.
00:26:44.940 --> 00:26:48.330
I've been sitting in my chair
here for like eight hours.
00:26:48.330 --> 00:26:51.950
But thinking about giving
up and moving is okay.
00:26:51.950 --> 00:26:54.920
And if making sure some
of that's built in.
00:26:54.920 --> 00:26:57.290
And the final thing that
teens really struggle with,
00:26:57.290 --> 00:26:59.480
I think is the peer interaction
00:26:59.480 --> 00:27:03.300
and the reduced peer interaction
they've had in these times.
00:27:03.300 --> 00:27:07.320
So if there are ways that
you can help facilitate
00:27:07.320 --> 00:27:11.400
whether that's online, video interactions,
00:27:11.400 --> 00:27:16.020
whether that's, if you
have a small safe group,
00:27:16.020 --> 00:27:18.520
I know some people are doing,
hey there's two other families
00:27:18.520 --> 00:27:22.310
that we all have kind of the same view
00:27:22.310 --> 00:27:25.720
on what's acceptable in terms of safety.
00:27:25.720 --> 00:27:27.440
And we all get together.
00:27:27.440 --> 00:27:30.130
Finding some ways that kids can connect
00:27:30.130 --> 00:27:33.680
with other kids can be
helpful too in these times
00:27:33.680 --> 00:27:34.513
that we've found.
00:27:34.513 --> 00:27:37.370
So lots of different potential things
00:27:37.370 --> 00:27:42.370
but empathize, definitely,
talk to your kids about it,
00:27:43.200 --> 00:27:44.500
try to keep those doors open
00:27:44.500 --> 00:27:47.143
so that they can talk to
you when they have concerns.
00:27:48.030 --> 00:27:50.130
- That's great advice, thanks Kristen.
00:27:50.130 --> 00:27:53.640
We have a question from
Barbara, who's asking advice
00:27:53.640 --> 00:27:57.200
for kids who strive for
perfection, who are super motivated
00:27:57.200 --> 00:27:59.760
but they are also, they
kind of are worried
00:27:59.760 --> 00:28:02.130
about doing things that are imperfect
00:28:02.130 --> 00:28:05.250
and that experience in
itself overwhelms them.
00:28:05.250 --> 00:28:08.640
So how do you help those students?
00:28:08.640 --> 00:28:10.650
I think some of the compartmentalizing
00:28:10.650 --> 00:28:12.360
and making things more chunkable
00:28:12.360 --> 00:28:13.660
that you've talked about earlier
00:28:13.660 --> 00:28:16.693
was super super relevant for
this type of case as well.
00:28:17.760 --> 00:28:18.790
- Yeah, definitely.
00:28:18.790 --> 00:28:23.790
Thinking about how to
think about what is done,
00:28:26.320 --> 00:28:31.320
what is acceptable on for
an assignment, what is okay.
00:28:31.420 --> 00:28:33.820
And the other piece is
to really try to focus
00:28:33.820 --> 00:28:37.240
on learning as opposed to grades.
00:28:37.240 --> 00:28:38.950
So one of the things that often happens
00:28:38.950 --> 00:28:41.470
with kids who kind of have
that perfectionist streak
00:28:41.470 --> 00:28:44.730
is they really start to
focus on getting a hundred
00:28:44.730 --> 00:28:48.360
or getting really that perfection piece.
00:28:48.360 --> 00:28:52.140
And what do you wanna try
to do is to turn that focus
00:28:52.140 --> 00:28:53.690
to what did you learn today?
00:28:53.690 --> 00:28:55.360
What are the new skills you have?
00:28:55.360 --> 00:28:58.010
What are the new ideas you understand?
00:28:58.010 --> 00:29:03.010
And the more you can ask
questions about those things
00:29:03.210 --> 00:29:06.350
and start to try to celebrate
learning something new
00:29:06.350 --> 00:29:08.890
or getting a new skill or
being able to do something
00:29:08.890 --> 00:29:11.350
you couldn't do before
and trying to get them
00:29:11.350 --> 00:29:15.460
to focus on that piece, as
opposed to what was your grade
00:29:15.460 --> 00:29:17.560
or score on this can be helpful
00:29:17.560 --> 00:29:21.353
in reducing some of that perfection piece.
00:29:22.900 --> 00:29:27.703
The other thing I would say
is to try to communicate
00:29:29.540 --> 00:29:31.080
that failure is okay.
00:29:31.080 --> 00:29:33.140
And failure is actually how we learn.
00:29:33.140 --> 00:29:37.450
That gets back to some of that
growth mindset communication
00:29:37.450 --> 00:29:41.440
that it's okay to not
be successful sometimes.
00:29:41.440 --> 00:29:45.380
That helps us learn
and trying to help kids
00:29:45.380 --> 00:29:46.213
be okay with that.
00:29:46.213 --> 00:29:48.700
And interestingly for
all the talk about games,
00:29:48.700 --> 00:29:51.565
games are actually pretty good at teaching
00:29:51.565 --> 00:29:54.317
that it's okay to fail and you end up,
00:29:54.317 --> 00:29:57.639
you can get your lives
back, you can start over.
00:29:57.639 --> 00:29:58.820
It's all okay.
00:29:58.820 --> 00:30:01.140
But kind of communicating about that idea
00:30:01.140 --> 00:30:02.640
can be important too for kids.
00:30:03.620 --> 00:30:06.100
- Nice, great, great Kristen.
00:30:06.100 --> 00:30:09.620
One question we have
from Dennis who's asking,
00:30:09.620 --> 00:30:12.640
remote learning's a big part
of this year's curriculum.
00:30:12.640 --> 00:30:15.410
This allows for different
routines in the day.
00:30:15.410 --> 00:30:16.610
Some days it's work from home.
00:30:16.610 --> 00:30:20.450
Some days the kids can
work, stay in their pajamas
00:30:20.450 --> 00:30:21.790
and take some classes.
00:30:21.790 --> 00:30:24.150
What advice would you
have or how much emphasis
00:30:24.150 --> 00:30:28.220
would you say in maintaining
a consistent routine
00:30:28.220 --> 00:30:30.313
versus altering the routine?
00:30:32.450 --> 00:30:33.400
- So good question.
00:30:34.490 --> 00:30:37.550
Kids generally do thrive on routine
00:30:37.550 --> 00:30:41.280
and knowing what to expect
and what's gonna come next.
00:30:41.280 --> 00:30:42.370
But that doesn't mean
00:30:42.370 --> 00:30:46.530
it has to be always the exact same thing.
00:30:46.530 --> 00:30:50.200
So what I would advise
in terms of maintaining
00:30:50.200 --> 00:30:54.070
is maintaining a schedule.
00:30:54.070 --> 00:30:57.400
So at nine o'clock this happens,
at 10 o'clock this happens.
00:30:57.400 --> 00:31:01.360
That it's written down is
usually helpful with visual cues.
00:31:01.360 --> 00:31:05.120
So they can take a look at
it and really reference,
00:31:05.120 --> 00:31:06.760
okay, here's, what's coming next.
00:31:06.760 --> 00:31:10.150
Here's what's coming up today
for the rest of the day.
00:31:10.150 --> 00:31:14.340
And so if that part is maintained,
00:31:14.340 --> 00:31:17.320
like they know what's coming,
then you can flex a little bit
00:31:17.320 --> 00:31:19.750
like other things, like
what are they wearing?
00:31:19.750 --> 00:31:22.377
It's okay, if they're gonna think about.
00:31:22.377 --> 00:31:24.740
And you can think even schools do this.
00:31:24.740 --> 00:31:25.630
If you remember back too
00:31:25.630 --> 00:31:27.470
when your kids were in elementary schools,
00:31:27.470 --> 00:31:31.633
they probably did, it's
crazy day, it's pajama day.
00:31:32.480 --> 00:31:35.640
All of those things are really good flexes
00:31:35.640 --> 00:31:39.580
to make in the routine so it
doesn't just become monotonous.
00:31:39.580 --> 00:31:42.030
And there's new things that they're doing.
00:31:42.030 --> 00:31:44.440
I will say you also talked
about classes lounging
00:31:44.440 --> 00:31:45.690
on the futon.
00:31:45.690 --> 00:31:48.199
I have mixed feelings about that.
00:31:48.199 --> 00:31:49.112
(both laughing)
00:31:49.112 --> 00:31:52.320
It's good if kids have a space to learn.
00:31:52.320 --> 00:31:54.330
That's kind of signals to them mentally,
00:31:54.330 --> 00:31:57.510
I'm on now, because as we were talking
00:31:57.510 --> 00:31:59.240
about all those other distractions,
00:31:59.240 --> 00:32:00.800
if you're kind of trying to do school
00:32:00.800 --> 00:32:03.270
in the same place that you
hang out and play video games
00:32:03.270 --> 00:32:06.880
at night in the same place
that you're watching movies,
00:32:06.880 --> 00:32:08.617
that's kind of not communicating,
00:32:08.617 --> 00:32:12.530
"Hey, now's the time I need
to kind of tell my brain
00:32:12.530 --> 00:32:14.400
it's time to focus on schoolwork."
00:32:14.400 --> 00:32:16.630
So the more you can in terms of the place,
00:32:16.630 --> 00:32:21.020
have some kind of a set place
that is communicating to them,
00:32:21.020 --> 00:32:24.040
this is where the schoolwork happens
00:32:24.040 --> 00:32:25.720
is probably a good idea.
00:32:25.720 --> 00:32:27.850
But one class lounging on the futon.
00:32:27.850 --> 00:32:31.770
One video isn't gonna hurt anyone.
00:32:31.770 --> 00:32:32.603
- I love that.
00:32:32.603 --> 00:32:33.700
I know for myself personally
00:32:33.700 --> 00:32:35.440
I've been in this room for eight months.
00:32:35.440 --> 00:32:37.610
And then I think once
a month I decide to go
00:32:37.610 --> 00:32:39.920
to the kitchen or the dining room
00:32:39.920 --> 00:32:42.970
and try to change things
up just a little bit.
00:32:42.970 --> 00:32:44.320
- Yes, yes absolutely.
00:32:44.320 --> 00:32:45.380
- Kristen, we have a follow-up
00:32:45.380 --> 00:32:47.710
about the rewards and incentives.
00:32:47.710 --> 00:32:51.740
So Kiki ask, "I've used
Fortnite as reward in the past
00:32:51.740 --> 00:32:56.740
but they find that my son
rushes through his work
00:32:56.760 --> 00:32:59.870
in order to quickly get
to playing this game.
00:32:59.870 --> 00:33:01.190
So how do you get them to understand
00:33:01.190 --> 00:33:03.100
that it's not just the quantity
00:33:03.100 --> 00:33:06.097
but actually the quality of
the work that is important?"
00:33:08.130 --> 00:33:11.743
- Well, it's a reward has to
be contingent on the quality.
00:33:13.110 --> 00:33:17.420
So the reward can't just be
doing the 10 RAF problems.
00:33:17.420 --> 00:33:20.260
It has to be doing the 10 math problems
00:33:20.260 --> 00:33:23.100
and maybe explaining to
you why they're right.
00:33:23.100 --> 00:33:26.280
If this starts depending
I know some math problems
00:33:26.280 --> 00:33:28.430
right now there's probably
some math problems
00:33:28.430 --> 00:33:29.630
I couldn't grade.
00:33:29.630 --> 00:33:32.560
I wouldn't know if they
were right or wrong.
00:33:32.560 --> 00:33:34.863
And some pre-calculus problems and things.
00:33:36.260 --> 00:33:38.970
And so if it's the case where
you actually aren't sure
00:33:38.970 --> 00:33:43.120
if they're right or wrong,
have your student explain them
00:33:43.120 --> 00:33:45.680
to you and walk you through the steps.
00:33:45.680 --> 00:33:48.890
And if he can do that, then he can play.
00:33:48.890 --> 00:33:50.410
So it's definitely a matter
00:33:50.410 --> 00:33:52.510
of trying to set that goal for quality.
00:33:52.510 --> 00:33:54.130
If it's something that you can look at
00:33:54.130 --> 00:33:56.680
and see if he's met a
quality standard great.
00:33:56.680 --> 00:33:59.770
If not, having them explain it
to you and see if they've met
00:33:59.770 --> 00:34:01.283
that kind of standard.
00:34:02.530 --> 00:34:05.580
- I think this is one challenge
that I remember as a kid.
00:34:05.580 --> 00:34:07.940
You have to finish your
homework before you get to play
00:34:07.940 --> 00:34:09.640
with your friends and
you would just go home
00:34:09.640 --> 00:34:12.080
and rush through your
homework just to go play
00:34:12.080 --> 00:34:13.590
with your friends.
00:34:13.590 --> 00:34:15.210
- Absolutely, absolutely.
00:34:15.210 --> 00:34:17.200
So there it has to.
00:34:17.200 --> 00:34:18.920
I know this puts burden on parents
00:34:18.920 --> 00:34:20.940
to say you've got to
check it a little bit,
00:34:20.940 --> 00:34:23.831
but if you're thinking about
rewards, you kind of do
00:34:23.831 --> 00:34:26.681
otherwise you're gonna get
those unintended consequences.
00:34:27.540 --> 00:34:29.790
- So Kristen, I think we
have time for maybe one
00:34:29.790 --> 00:34:31.220
or two more.
00:34:31.220 --> 00:34:33.660
We have a really good question from Ranga.
00:34:33.660 --> 00:34:37.040
These recommendations require
parents to constantly engage
00:34:37.040 --> 00:34:38.420
throughout the day.
00:34:38.420 --> 00:34:40.710
Otherwise the children go back to playing,
00:34:40.710 --> 00:34:41.883
whatever they like.
00:34:43.879 --> 00:34:45.970
How are you kind of constantly engage?
00:34:45.970 --> 00:34:47.310
I think this poses a question
00:34:47.310 --> 00:34:50.820
where I don't know if you do
have to be constantly engaging.
00:34:50.820 --> 00:34:53.030
I think the assumption here
00:34:53.030 --> 00:34:56.270
is that you have to be
kind of with your child
00:34:56.270 --> 00:34:57.103
the whole time.
00:34:57.103 --> 00:34:59.340
I think part of your
recommendations that allows you
00:34:59.340 --> 00:35:00.820
to free up some of that time.
00:35:00.820 --> 00:35:03.810
So can you speak to how
do you kind of balance
00:35:03.810 --> 00:35:06.020
the engagement and the
time that as a parent,
00:35:06.020 --> 00:35:07.793
you have to do your day job.
00:35:09.480 --> 00:35:11.050
- So first just let me recognize it.
00:35:11.050 --> 00:35:14.630
It's absolutely we're asking way too much
00:35:14.630 --> 00:35:15.580
with parents right now.
00:35:15.580 --> 00:35:18.250
We are asking them to do multiple jobs
00:35:18.250 --> 00:35:22.990
and not giving any break
on the amount of time
00:35:22.990 --> 00:35:23.943
needed to do them.
00:35:25.020 --> 00:35:27.710
But I do think that what you wanna do
00:35:27.710 --> 00:35:30.560
is think about how you
can structure the day
00:35:30.560 --> 00:35:33.730
so that they have set things
they're supposed to do
00:35:33.730 --> 00:35:35.260
at set times.
00:35:35.260 --> 00:35:37.210
And then you can do, check-ins
00:35:37.210 --> 00:35:39.023
to see if they got those done.
00:35:40.396 --> 00:35:43.120
And again, you wanna think
about positive reinforcement.
00:35:43.120 --> 00:35:47.690
So you may have to start
off with very small chunks
00:35:47.690 --> 00:35:51.960
but over time you can
gradually extend them.
00:35:51.960 --> 00:35:55.110
So if you're thinking
about, at the beginning,
00:35:55.110 --> 00:35:56.947
you may need to say okay,
here's what we're gonna do
00:35:56.947 --> 00:35:58.880
in the next hour.
00:35:58.880 --> 00:36:02.020
And if we get that done,
then you set the goal
00:36:02.020 --> 00:36:02.853
for the next hour.
00:36:02.853 --> 00:36:05.870
So that would require
like hourly check-ins.
00:36:05.870 --> 00:36:09.550
But over time as they
start to again, see, okay,
00:36:09.550 --> 00:36:12.530
what's our goal for the next two hours?
00:36:12.530 --> 00:36:15.913
And again, using rewards
is not a bad thing.
00:36:16.760 --> 00:36:20.900
Think about how you can
reward meeting those goals
00:36:20.900 --> 00:36:23.340
that you set for those short time periods,
00:36:23.340 --> 00:36:25.910
and then lengthen them over time
00:36:25.910 --> 00:36:28.610
so that you don't have to
check in so frequently.
00:36:28.610 --> 00:36:31.640
And they're still getting
that feeling of success
00:36:31.640 --> 00:36:32.803
and staying on task.
00:36:35.000 --> 00:36:36.970
- So I think we have time for one more.
00:36:36.970 --> 00:36:39.510
And we have a couple of
questions around the same theme,
00:36:39.510 --> 00:36:42.010
which is from Linda and Anika.
00:36:42.010 --> 00:36:45.470
They're both wondering
what ideas do you have
00:36:45.470 --> 00:36:49.020
for students who sees
zero value in school?
00:36:49.020 --> 00:36:53.690
Or if they they're just the
kids desire to fit in socially
00:36:53.690 --> 00:36:57.083
causes them to kind of
degress academically.
00:36:58.700 --> 00:37:01.700
- Yeah, they're probably a bit separate
00:37:01.700 --> 00:37:06.500
but so if your kid is really
motivated by social things
00:37:06.500 --> 00:37:08.840
you wanna think about
how to tie social things
00:37:08.840 --> 00:37:12.623
into learning, how to provide
social learning experiences.
00:37:13.690 --> 00:37:17.250
Are there small study
groups, even if the two kids
00:37:17.250 --> 00:37:22.190
are just on their computers
and have the video on,
00:37:22.190 --> 00:37:23.600
but aren't studying together.
00:37:23.600 --> 00:37:26.000
There's just like some
social interaction there.
00:37:27.240 --> 00:37:30.230
Can you think about having
them access to peers?
00:37:30.230 --> 00:37:32.430
Is this something that's
rewarding for them?
00:37:33.770 --> 00:37:36.570
So find ways to give them
that social experience,
00:37:36.570 --> 00:37:40.210
but tie it into also learning goals
00:37:40.210 --> 00:37:42.610
and being able to learn
together with their peers
00:37:42.610 --> 00:37:44.120
and what they're doing.
00:37:44.120 --> 00:37:45.690
So that's kind of the social piece.
00:37:45.690 --> 00:37:47.970
The other piece for kids
who just don't see the value
00:37:47.970 --> 00:37:52.720
of school is the toughest
thing about teenagers
00:37:52.720 --> 00:37:55.320
is probably for those who
it's tough to figure out
00:37:55.320 --> 00:37:56.830
what they are interested in.
00:37:56.830 --> 00:37:58.701
But that's my advice is to figure out
00:37:58.701 --> 00:38:00.240
what does interest them?
00:38:00.240 --> 00:38:03.810
What are the things that they value?
00:38:03.810 --> 00:38:06.000
What are the things that
are interesting to them?
00:38:06.000 --> 00:38:09.260
Is it working on old cars?
00:38:09.260 --> 00:38:11.283
Is it baking?
00:38:12.425 --> 00:38:15.090
What is something that they like to do?
00:38:15.090 --> 00:38:18.160
And then think about how you can tie in
00:38:18.160 --> 00:38:22.350
things they're learning in
school to that piece of things.
00:38:22.350 --> 00:38:26.270
I use baking a lot because
it's easy to set up.
00:38:26.270 --> 00:38:28.280
There's a lot of math in baking
00:38:28.280 --> 00:38:32.130
and you can kind of make
some of those ties in there.
00:38:32.130 --> 00:38:35.470
But the key is to think
about what are the things
00:38:35.470 --> 00:38:38.960
that are interesting and
trying to make those links,
00:38:38.960 --> 00:38:42.380
whether it's future careers,
whether it's learning something
00:38:42.380 --> 00:38:46.380
that helps them be better at
that thing that they're doing.
00:38:46.380 --> 00:38:49.970
Relating their physics lessons,
to things that are going on.
00:38:49.970 --> 00:38:52.433
Whatever that is that
they're interested in.
00:38:54.943 --> 00:38:56.710
And it can be tough to figure out.
00:38:56.710 --> 00:38:59.370
Sometimes teenagers can
seem pretty apathetic
00:38:59.370 --> 00:39:01.830
about a lot of stuff and
don't wanna show their parents
00:39:01.830 --> 00:39:04.330
when they're interested in things.
00:39:04.330 --> 00:39:09.330
But again, put on your detective
hat so you can figure out
00:39:10.600 --> 00:39:12.817
what it is that they are interested in
00:39:12.817 --> 00:39:15.953
and it starts with trying to
build some of those bridges.
00:39:17.400 --> 00:39:18.880
- That's wonderful.
00:39:18.880 --> 00:39:20.660
Unfortunately, that's all the time we have
00:39:20.660 --> 00:39:22.170
for questions today.
00:39:22.170 --> 00:39:24.690
And so Kristen, thank you
for sharing your expertise
00:39:24.690 --> 00:39:26.070
with our audience.
00:39:26.070 --> 00:39:28.500
And we wanna thank you all
you busy parents out there.
00:39:28.500 --> 00:39:30.410
We know it's an incredibly busy time
00:39:30.410 --> 00:39:31.640
and you're balancing a lot.
00:39:31.640 --> 00:39:34.660
So we wanna thank you for
joining our session today.
00:39:34.660 --> 00:39:36.700
A couple of reminders,
if you missed anything
00:39:36.700 --> 00:39:39.430
or you wanna review, by
registering for this webinar
00:39:39.430 --> 00:39:43.610
you'll automatically be
emailed this recording.
00:39:43.610 --> 00:39:46.420
If you wanna download the PDF as well
00:39:46.420 --> 00:39:48.090
that'll automatically be sent to you.
00:39:48.090 --> 00:39:49.590
And we will be also be posting this
00:39:49.590 --> 00:39:51.810
in YouTube afterwards as well.
00:39:51.810 --> 00:39:53.700
So you'll have multiple chances to go back
00:39:53.700 --> 00:39:56.960
and look at some of the
content if you missed anything.
00:39:56.960 --> 00:39:59.210
And then secondly, we have
a lot of resources available
00:39:59.210 --> 00:40:03.690
on our
keeplearning.khanacademy.orgmicrosite
00:40:03.690 --> 00:40:06.440
which it has all of our
distance learning materials
00:40:06.440 --> 00:40:07.950
in one place.
00:40:07.950 --> 00:40:10.350
And then before we sign
off, we wanna ask you
00:40:10.350 --> 00:40:12.250
to do two things for us.
00:40:12.250 --> 00:40:14.410
First, there's a poll that will pop up
00:40:14.410 --> 00:40:15.970
and we will be asking you
00:40:15.970 --> 00:40:17.750
how could we make future iterations
00:40:17.750 --> 00:40:20.340
of this session more useful for you?
00:40:20.340 --> 00:40:23.240
And then secondly, we
will ask you your advice
00:40:23.240 --> 00:40:25.000
on what kinds of sessions would you like
00:40:25.000 --> 00:40:27.170
to see us build on next?
00:40:27.170 --> 00:40:29.340
So please let us know.
00:40:29.340 --> 00:40:31.970
This was actually a result
of some of your feedback
00:40:31.970 --> 00:40:33.220
in the past as well.
00:40:33.220 --> 00:40:36.150
And we're totally here to
support you in any way we can.
00:40:36.150 --> 00:40:38.360
So from all of us at Khan
Academy, thank you again
00:40:38.360 --> 00:40:41.493
for joining us and have
a great, great evening.
|
Simpson's index of diversity | https://www.youtube.com/watch?v=bfxhh7l-LQw | vtt | https://www.youtube.com/api/timedtext?v=bfxhh7l-LQw&ei=91WUZdPTIM6jhcIPv_eK0Ac&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C72128390590E136A00F68AF82B7F3FFC995F21F.D1DD308014BFA59F3322B25D74FEF1AED7FCCD06&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.240 --> 00:00:01.570
- [Instructor] So in this table here
00:00:01.570 --> 00:00:03.010
we have two different communities,
00:00:03.010 --> 00:00:05.070
community one and community two,
00:00:05.070 --> 00:00:08.070
and each of them contain
three different species.
00:00:08.070 --> 00:00:10.910
And we see the populations of
those three different species.
00:00:10.910 --> 00:00:12.410
And we also see that the total number
00:00:12.410 --> 00:00:14.810
of individuals in each
community is the same.
00:00:14.810 --> 00:00:18.640
They both have a total
of 1,000 individuals.
00:00:18.640 --> 00:00:20.900
Now, my question to you, just intuitively
00:00:20.900 --> 00:00:22.900
based on the data in this table,
00:00:22.900 --> 00:00:27.810
which community would you
say is more diverse and why,
00:00:27.810 --> 00:00:30.393
community one or community two?
00:00:32.120 --> 00:00:34.650
All right, now let's
think about this together.
00:00:34.650 --> 00:00:35.760
So as we already talked about,
00:00:35.760 --> 00:00:38.510
they have the same number of individuals,
00:00:38.510 --> 00:00:41.040
and you might be thinking
that the number of species
00:00:41.040 --> 00:00:43.630
could be related to the
diversity, and you'd be right.
00:00:43.630 --> 00:00:46.620
The number of species does
contribute to the diversity,
00:00:46.620 --> 00:00:49.100
but we're dealing with a
situation where both communities
00:00:49.100 --> 00:00:50.650
have the same number of species.
00:00:50.650 --> 00:00:53.100
They each have three species.
00:00:53.100 --> 00:00:54.630
But when we look at the data,
00:00:54.630 --> 00:00:58.720
it's clear that community
two is mostly species A
00:00:58.720 --> 00:01:02.640
and you have very small groups
of species B and species C,
00:01:02.640 --> 00:01:05.850
while community one is more evenly spread.
00:01:05.850 --> 00:01:09.450
So just intuitively it
feels like community one
00:01:09.450 --> 00:01:13.140
is maybe more diverse,
00:01:13.140 --> 00:01:16.090
but this was just on my
intuition or our intuition,
00:01:16.090 --> 00:01:18.280
and the numbers are pretty clear here.
00:01:18.280 --> 00:01:20.580
It's evenly distributed
amongst the species here,
00:01:20.580 --> 00:01:24.400
and here it's very heavily
weighted on species A,
00:01:24.400 --> 00:01:26.760
but it might not always be this clear.
00:01:26.760 --> 00:01:30.100
So it'd be useful to have
some type of quantitative way
00:01:30.100 --> 00:01:33.200
to measure the diversity of a population.
00:01:33.200 --> 00:01:36.680
And lucky for us, there is a
quantitative way to do that
00:01:36.680 --> 00:01:39.820
called Simpson's, I'll write it down,
00:01:39.820 --> 00:01:44.763
Simpson's diversity index,
00:01:46.360 --> 00:01:48.150
and the way you calculate it,
00:01:48.150 --> 00:01:52.270
it's equal to one minus the sum of,
00:01:52.270 --> 00:01:55.585
for each species you take
the number of that species
00:01:55.585 --> 00:01:59.340
divided by the community size squared.
00:01:59.340 --> 00:02:02.890
So for each of the species,
you do this calculation,
00:02:02.890 --> 00:02:06.460
square it and then you add it
up for each of those species.
00:02:06.460 --> 00:02:09.100
So let's figure out
Simpson's diversity index
00:02:09.100 --> 00:02:11.180
for both communities
one and community two.
00:02:11.180 --> 00:02:12.620
And I encourage you you
could pause the video
00:02:12.620 --> 00:02:13.940
and try to work on it on your own
00:02:13.940 --> 00:02:15.895
before I work through it with you.
00:02:15.895 --> 00:02:19.430
So let's start with community one.
00:02:19.430 --> 00:02:24.010
So I'll say diversity
index for community one.
00:02:24.010 --> 00:02:25.670
I'll just put that in parentheses,
00:02:25.670 --> 00:02:28.740
is going to be equal to one minus,
00:02:28.740 --> 00:02:33.740
so we have 325 over, over 1,000 squared.
00:02:37.740 --> 00:02:39.920
Remember, we're gonna sum
on each of these species
00:02:39.920 --> 00:02:44.920
plus 305, 305 over 1,000 squared
00:02:47.240 --> 00:02:52.240
plus 370 over 1,000 squared.
00:02:54.120 --> 00:02:57.190
And I need to close my parentheses,
00:02:57.190 --> 00:02:59.420
and I can simplify this a bit.
00:02:59.420 --> 00:03:03.340
This is going to be equal to one minus,
00:03:03.340 --> 00:03:05.060
so all of these thousand squares,
00:03:05.060 --> 00:03:06.340
a thousand squared is a million.
00:03:06.340 --> 00:03:11.060
So it's gonna be everything
over 1 million, 1 million,
00:03:11.060 --> 00:03:15.080
and then we're going to have 325 squared,
00:03:15.080 --> 00:03:20.080
plus 305 squared, plus 370 squared.
00:03:22.190 --> 00:03:25.630
And that is going to give us 325 squared,
00:03:28.170 --> 00:03:33.170
plus 305 squared, plus 370
squared is equal to that.
00:03:37.160 --> 00:03:38.910
That's the numerator here,
and I'm willing to divide
00:03:38.910 --> 00:03:41.340
that by a million divided by,
00:03:41.340 --> 00:03:44.020
one, one, two, three, one, two, three.
00:03:44.020 --> 00:03:45.660
And that is a million.
00:03:45.660 --> 00:03:47.120
It equals this.
00:03:47.120 --> 00:03:49.350
And then I'm gonna subtract that from one.
00:03:49.350 --> 00:03:50.720
So let's put a negative sign here
00:03:50.720 --> 00:03:55.327
and say, plus one is equal to 0.664.
00:03:57.952 --> 00:04:01.280
So this is going to be
approximately equal to 0.6664.
00:04:03.180 --> 00:04:07.350
Now let's do the same
thing for community two.
00:04:07.350 --> 00:04:09.220
So if I write it over here,
00:04:09.220 --> 00:04:13.540
the diversity index for community
two is going to be equal
00:04:13.540 --> 00:04:17.720
to one minus, I put a
big parenthesis here,
00:04:17.720 --> 00:04:22.720
and we're going to have
925 over 1,000 squared,
00:04:24.540 --> 00:04:28.210
plus 40 over 1,000 squared,
00:04:30.260 --> 00:04:35.260
plus 35 over 1,000 squared.
00:04:35.500 --> 00:04:37.290
And if we simplify in a similar way,
00:04:37.290 --> 00:04:39.930
that's gonna be equal to one minus
00:04:39.930 --> 00:04:41.310
all these thousand squares.
00:04:41.310 --> 00:04:45.340
That's just a million, and
that's a common denominator.
00:04:45.340 --> 00:04:48.220
And so you're gonna have 925 squared,
00:04:48.220 --> 00:04:52.550
plus 40 squared, plus 35 squared.
00:04:52.550 --> 00:04:54.740
And then this is going to be approximately
00:04:54.740 --> 00:04:59.740
equal to 925 squared, plus 40 squared,
00:05:02.230 --> 00:05:07.230
plus 35 squared is equal to
this divided by a million.
00:05:09.870 --> 00:05:13.530
So divided by one, one,
two, three, one, two, three.
00:05:13.530 --> 00:05:15.620
Yep, six zeros is equal to that.
00:05:15.620 --> 00:05:20.440
And then you subtract
that from one and you get,
00:05:20.440 --> 00:05:23.143
which is approximately equal to 0.142.
00:05:25.580 --> 00:05:27.180
And so we see very clearly
00:05:27.180 --> 00:05:29.300
when we use Simpson's diversity index
00:05:29.300 --> 00:05:32.730
that consistent with our
intuition community two
00:05:32.730 --> 00:05:35.820
has a lower diversity
index than community one.
00:05:35.820 --> 00:05:37.350
And it's consistent with our intuition
00:05:37.350 --> 00:05:39.020
that it is less diverse.
00:05:39.020 --> 00:05:40.470
And I encourage you after this video
00:05:40.470 --> 00:05:42.770
think about why that
makes mathematical sense.
|
The van der Waals equation | https://www.youtube.com/watch?v=9_epJ4vUsNI | vtt | https://www.youtube.com/api/timedtext?v=9_epJ4vUsNI&ei=8VWUZdiTNY6Dp-oP1LW4gAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245345&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2C9755EBDE965C8C30E98C077A2D85BDC5FA7737.CF9D78630618C265EA28AD3D71D49EE7BEA51B9D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.150 --> 00:00:02.020
- [Instructor] We have
so far spent many videos
00:00:02.020 --> 00:00:04.270
talking about the ideal gas law,
00:00:04.270 --> 00:00:06.150
that pressure times volume is equal
00:00:06.150 --> 00:00:08.670
to the number of moles
times the ideal gas constant
00:00:08.670 --> 00:00:11.760
times temperature measured in kelvin.
00:00:11.760 --> 00:00:13.030
What we're going to do in this video
00:00:13.030 --> 00:00:16.300
is attempt to modify the ideal gas law
00:00:16.300 --> 00:00:18.170
to try to take into account
00:00:18.170 --> 00:00:19.940
when we're dealing with real gases,
00:00:19.940 --> 00:00:23.570
gases where the volume
of the actual particles
00:00:23.570 --> 00:00:25.670
are worth considering,
that we don't just say
00:00:25.670 --> 00:00:28.160
they're negligible compared to
the volume of the container.
00:00:28.160 --> 00:00:30.010
And intermolecular forces are something
00:00:30.010 --> 00:00:32.400
that we would like to
take into consideration.
00:00:32.400 --> 00:00:34.310
So let's think about how
we could modify this.
00:00:34.310 --> 00:00:35.510
And to help us a little bit,
00:00:35.510 --> 00:00:36.810
I'm just gonna solve for P.
00:00:36.810 --> 00:00:38.960
So I'm gonna divide both sides by volume,
00:00:38.960 --> 00:00:41.580
so we can say pressure is
equal to number of moles
00:00:41.580 --> 00:00:42.860
times ideal gas constant
00:00:42.860 --> 00:00:46.940
times temperature measured
in kelvin divided by volume.
00:00:46.940 --> 00:00:49.090
So first, how would we adjust this
00:00:49.090 --> 00:00:52.570
if we want to take into
account the actual volume
00:00:52.570 --> 00:00:55.690
in which the molecules can move around?
00:00:55.690 --> 00:00:56.970
Well, if we wanted to do that,
00:00:56.970 --> 00:00:59.870
we would replace this
volume right over here
00:00:59.870 --> 00:01:04.870
with this volume minus the
volume of the actual particles.
00:01:04.950 --> 00:01:07.930
So what's the volume of the
actual particles going to be?
00:01:07.930 --> 00:01:11.280
Well, it's going to be
the number of particles
00:01:11.280 --> 00:01:12.830
times some constant,
00:01:12.830 --> 00:01:15.390
based on how large each
of those particles are,
00:01:15.390 --> 00:01:16.500
maybe on average.
00:01:16.500 --> 00:01:18.723
And let's just call that b.
00:01:20.240 --> 00:01:25.000
So we could view this as a
modified ideal gas law equation,
00:01:25.000 --> 00:01:27.330
we're now all of a sudden,
we are taking into account
00:01:27.330 --> 00:01:30.330
the fact that these particles
have some real volume to them,
00:01:31.780 --> 00:01:32.710
but of course we also
know it's not just about
00:01:32.710 --> 00:01:35.200
the volume of the particles,
we also need to adjust
00:01:35.200 --> 00:01:37.830
for the intermolecular
forces between the particles.
00:01:37.830 --> 00:01:40.680
And we know that in many cases
those intermolecular forces
00:01:40.680 --> 00:01:42.020
are attractive forces,
00:01:42.020 --> 00:01:44.900
and so they would take
away from the pressure.
00:01:44.900 --> 00:01:46.970
And so we need some term
that accounts for that,
00:01:46.970 --> 00:01:49.640
a term that accounts for
taking away the pressure
00:01:49.640 --> 00:01:51.490
due to intermolecular forces.
00:01:51.490 --> 00:01:56.127
So term for intermolecular forces.
00:02:01.720 --> 00:02:03.427
Now I know what some
of y'all are thinking.
00:02:03.427 --> 00:02:05.070
"Do we always subtract?
00:02:05.070 --> 00:02:06.970
Might not there be some situations
00:02:06.970 --> 00:02:10.200
in which we actually have
repulsive forces between particles
00:02:10.200 --> 00:02:12.000
and it would actually
add to the pressure?"
00:02:12.000 --> 00:02:13.700
And there could be scenarios like that.
00:02:13.700 --> 00:02:16.850
You could imagine if they all
have a strong negative charge,
00:02:16.850 --> 00:02:19.130
they wanna get away from each
other as far as they can.
00:02:19.130 --> 00:02:22.030
And that could actually
add to the pressure,
00:02:22.030 --> 00:02:24.810
but in that situation, we
could subtract a negative
00:02:24.810 --> 00:02:27.140
and then that would be additive.
00:02:27.140 --> 00:02:30.010
Now, how could we take
this into consideration?
00:02:30.010 --> 00:02:32.660
So we know from Coulomb's
law that the force
00:02:32.660 --> 00:02:35.180
between two particles,
two charged particles
00:02:35.180 --> 00:02:36.210
is going to be proportional
00:02:36.210 --> 00:02:39.670
to the charge on one
particle times the charge
00:02:39.670 --> 00:02:43.350
on the other particle divided
by the distance squared.
00:02:43.350 --> 00:02:46.220
Now, obviously if we're
dealing with a lot of particles
00:02:46.220 --> 00:02:47.780
in a container, we're not
gonna be able to think
00:02:47.780 --> 00:02:51.040
about the forces for
between any two particles.
00:02:51.040 --> 00:02:52.470
But one way to think about it is
00:02:52.470 --> 00:02:55.420
in terms of how concentrated
are the particles generally.
00:02:55.420 --> 00:02:56.840
So when we're trying to think of a term
00:02:56.840 --> 00:02:59.350
that takes into account
the intermolecular forces
00:02:59.350 --> 00:03:00.840
or how much we're reducing the pressure
00:03:00.840 --> 00:03:03.110
because of those intermolecular forces,
00:03:03.110 --> 00:03:06.984
maybe that can be proportional
to not just the concentration
00:03:06.984 --> 00:03:10.030
of the particles, and that'd
be the number of particles
00:03:10.030 --> 00:03:13.764
divided by the volume,
but that times itself,
00:03:13.764 --> 00:03:15.840
because we're talking
about the interaction
00:03:15.840 --> 00:03:17.390
between two particles at a time,
00:03:17.390 --> 00:03:19.060
very similar to what we
see in Coulomb's law,
00:03:19.060 --> 00:03:19.893
because the end of the day
00:03:19.893 --> 00:03:21.760
these really are just Coulomb forces.
00:03:21.760 --> 00:03:23.990
So this thing right over
here is gonna be proportional
00:03:23.990 --> 00:03:26.560
to the concentration times itself.
00:03:26.560 --> 00:03:29.600
Or we could maybe call this some constant,
00:03:29.600 --> 00:03:34.600
for the proportionality,
times n over v squared,
00:03:34.950 --> 00:03:37.700
where a would depend on
the attractive forces
00:03:37.700 --> 00:03:39.240
between gas particles.
00:03:39.240 --> 00:03:40.810
And what we have just constructed,
00:03:40.810 --> 00:03:43.950
and let me rewrite it again,
this ideal gas equation,
00:03:43.950 --> 00:03:46.410
and actually let me put this orange term
00:03:46.410 --> 00:03:47.630
back on the left hand side.
00:03:47.630 --> 00:03:51.167
So if I write it this
way, that pressure plus a
00:03:53.530 --> 00:03:58.530
times n over v squared is equal to n R T
00:04:01.830 --> 00:04:04.730
over the volume of our container
00:04:04.730 --> 00:04:07.820
minus the number of molecules we have
00:04:07.820 --> 00:04:11.660
times some constant b, based
on how large on average
00:04:11.660 --> 00:04:14.190
those molecules or those particles are.
00:04:14.190 --> 00:04:18.480
This right over here is a
pretty good competence equation
00:04:18.480 --> 00:04:20.780
for when we're dealing
with more real gases,
00:04:20.780 --> 00:04:22.600
ones that have intermolecular forces,
00:04:22.600 --> 00:04:25.670
and one where the actual
particles have volume.
00:04:25.670 --> 00:04:28.140
And this actually does a pretty good job,
00:04:28.140 --> 00:04:29.420
and there's a name for it,
00:04:29.420 --> 00:04:33.080
it's called the Van der Waals equation.
00:04:33.080 --> 00:04:35.020
And there's many different
ways you might see it,
00:04:35.020 --> 00:04:36.440
you could see it written like this,
00:04:36.440 --> 00:04:38.260
or we could try to take this blue part
00:04:38.260 --> 00:04:39.550
and get it on the left hand side
00:04:39.550 --> 00:04:41.820
so it really looks like
what we saw at the top.
00:04:41.820 --> 00:04:44.320
Where there it would be
written as, and I'll write it,
00:04:44.320 --> 00:04:45.180
actually write it this way.
00:04:45.180 --> 00:04:50.180
Pressure plus some constant
times the density squared,
00:04:52.180 --> 00:04:54.070
let me close that parentheses,
00:04:54.070 --> 00:04:58.920
times the volume minus
the number of molecules
00:04:58.920 --> 00:05:03.480
times some constant is
going to be equal n R T,
00:05:03.480 --> 00:05:06.390
is going to be equal to n R T.
00:05:06.390 --> 00:05:08.350
And all of this looks really complicated,
00:05:08.350 --> 00:05:11.000
but the end of the day it
is just our ideal gas law
00:05:11.000 --> 00:05:13.730
modified for intermolecular forces
00:05:13.730 --> 00:05:16.513
and the actual volume of the particles.
|
Electronic transitions and energy | https://www.youtube.com/watch?v=ukYSvaRyE3c | vtt | https://www.youtube.com/api/timedtext?v=ukYSvaRyE3c&ei=8lWUZaalC5CJp-oP4PSskAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245346&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2B9DEAF6C7E2CF7A49B61FF2837D0F41E85A80DC.6FCCB363C9C9F85957D03BE7991BFA8E9E475251&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.930 --> 00:00:02.150
- [Lecturer] In this video,
00:00:02.150 --> 00:00:06.310
we're going to be talking
about exciting electrons.
00:00:06.310 --> 00:00:07.810
We can interpret that both ways
00:00:07.810 --> 00:00:09.560
that electrons can be exciting
00:00:09.560 --> 00:00:11.050
and that we're going to excite them
00:00:11.050 --> 00:00:12.990
into higher energy levels.
00:00:12.990 --> 00:00:14.470
Or we're going to think about what happens
00:00:14.470 --> 00:00:16.000
when they get unexcited,
00:00:16.000 --> 00:00:18.560
when they go back into
lower energy levels.
00:00:18.560 --> 00:00:20.040
And to help us understand this,
00:00:20.040 --> 00:00:21.800
I'll start with a simple atom.
00:00:21.800 --> 00:00:23.700
Hydrogen is the simplest I know,
00:00:23.700 --> 00:00:26.060
and we're gonna think about
the version of a hydrogen
00:00:26.060 --> 00:00:27.430
that we typically see the isotope
00:00:27.430 --> 00:00:30.190
that only has one proton in its nucleus.
00:00:30.190 --> 00:00:34.590
And it typically has one
or will have one electron
00:00:34.590 --> 00:00:36.380
if it's a neutral hydrogen atom
00:00:36.380 --> 00:00:38.600
and it would normally
be in its ground state,
00:00:38.600 --> 00:00:39.810
if it isn't excited yet.
00:00:39.810 --> 00:00:41.360
So it's going to be in that first shell
00:00:41.360 --> 00:00:42.970
but it can be excited to other shells.
00:00:42.970 --> 00:00:45.560
It could be excited to the second shell
00:00:45.560 --> 00:00:49.080
or the third shell
00:00:49.080 --> 00:00:50.450
or the fourth shell.
00:00:50.450 --> 00:00:51.990
And this is obviously hand drawn
00:00:51.990 --> 00:00:53.350
and not hand drawn that well,
00:00:53.350 --> 00:00:55.470
and this is really just to help us
00:00:55.470 --> 00:00:56.780
for visualization purposes.
00:00:56.780 --> 00:00:59.320
We know that electrons don't orbit nuclei
00:00:59.320 --> 00:01:01.200
the way planets orbit stars.
00:01:01.200 --> 00:01:04.300
They have both particle
and wave like properties,
00:01:04.300 --> 00:01:06.300
and they're more of a
probability density function
00:01:06.300 --> 00:01:07.680
of where you might find them.
00:01:07.680 --> 00:01:10.050
And these energy levels are associated
00:01:10.050 --> 00:01:13.990
with different probability
densities of various energies.
00:01:13.990 --> 00:01:16.420
But this is what an electron
will typically look like.
00:01:16.420 --> 00:01:19.210
If we're thinking about just
a neutral hydrogen atom,
00:01:19.210 --> 00:01:21.260
where the electrons in its ground state.
00:01:21.260 --> 00:01:23.424
Now let's say we're dealing
with a hydrogen atom
00:01:23.424 --> 00:01:25.860
where the electron has already
been excited a little bit.
00:01:25.860 --> 00:01:27.810
So instead of it being in the first shell,
00:01:27.810 --> 00:01:31.970
it's already in the second
shell right over here.
00:01:31.970 --> 00:01:34.820
And what we're going to
do is we're gonna hit it
00:01:34.820 --> 00:01:38.470
with a photon that excites it even more.
00:01:38.470 --> 00:01:39.590
And the photon.
00:01:39.590 --> 00:01:41.760
And we know that light has both particle
00:01:41.760 --> 00:01:42.990
and wave like properties.
00:01:42.990 --> 00:01:44.180
When we think of it as a particle,
00:01:44.180 --> 00:01:45.760
we think of it as a photon,
00:01:45.760 --> 00:01:47.860
but I will depict it like this.
00:01:47.860 --> 00:01:52.860
So this light has a
wavelength of 486 nanometers.
00:01:55.630 --> 00:01:59.520
And we know that that photon that hits it
00:01:59.520 --> 00:02:01.900
with a wavelength of 486 nanometers
00:02:01.900 --> 00:02:06.680
has sufficient energy to excite
this electron in this case,
00:02:06.680 --> 00:02:11.220
actually from N equals
two from the second shell
00:02:11.220 --> 00:02:12.590
to the fourth shell.
00:02:12.590 --> 00:02:17.590
So it'll go all the way over there.
00:02:17.900 --> 00:02:20.252
So it will absorb that photon.
00:02:20.252 --> 00:02:23.760
And then after some time
it can come back down
00:02:23.760 --> 00:02:26.030
and when it comes back down,
I could do it over here.
00:02:26.030 --> 00:02:30.530
So after some time it can,
that electron right over here,
00:02:30.530 --> 00:02:34.370
that excited electron, it can
go back from the fourth shell
00:02:34.370 --> 00:02:35.920
to the second shell.
00:02:35.920 --> 00:02:36.930
And when it does it,
00:02:36.930 --> 00:02:41.530
it will emit a photon
of that same wavelength.
00:02:41.530 --> 00:02:43.060
So why is that does that
00:02:43.060 --> 00:02:48.060
it will emit a photon of 486 nanometers.
00:02:50.070 --> 00:02:50.903
So just like that,
00:02:50.903 --> 00:02:52.820
we already are starting to understand
00:02:52.820 --> 00:02:54.610
that photons of the right energy
00:02:54.610 --> 00:02:59.380
can excite an electron by a
shell or more than one shell.
00:02:59.380 --> 00:03:00.500
When we talk about quantum mechanics,
00:03:00.500 --> 00:03:03.380
is this notion that photons
need a certain amount of energy
00:03:03.380 --> 00:03:05.350
in order to be able to excite the electron
00:03:05.350 --> 00:03:08.470
to the next energy level or
the energy level after that.
00:03:08.470 --> 00:03:10.360
Things in between don't work.
00:03:10.360 --> 00:03:13.220
And the same thing is true when
you're emitting the energy,
00:03:13.220 --> 00:03:16.460
the electrons is not gonna go
from the fourth energy level
00:03:16.460 --> 00:03:19.310
to someplace in between
the fourth and the third.
00:03:19.310 --> 00:03:20.380
It can't do that.
00:03:20.380 --> 00:03:22.480
It has these quantum states.
00:03:22.480 --> 00:03:24.200
It's going to be there in
the fourth or the third
00:03:24.200 --> 00:03:26.230
or the second or the first,
00:03:26.230 --> 00:03:28.910
there's no such thing as
a three and a half shell.
00:03:28.910 --> 00:03:31.660
And we can actually answer based on this,
00:03:31.660 --> 00:03:34.090
we can think about what
is the energy difference
00:03:34.090 --> 00:03:36.340
between these shells.
00:03:36.340 --> 00:03:38.710
And the energy difference
between the shells
00:03:38.710 --> 00:03:42.100
is essentially the energy
of the photon that we emit
00:03:42.100 --> 00:03:44.570
when we go from the fourth energy shell
00:03:44.570 --> 00:03:47.000
from the fourth shell to the second shell.
00:03:47.000 --> 00:03:48.990
To figure out the energy of that photon,
00:03:48.990 --> 00:03:51.820
we just have to think
about some useful formulas
00:03:51.820 --> 00:03:53.520
in quantum mechanics.
00:03:53.520 --> 00:03:56.200
The first and I'm gonna just
look at it right over here
00:03:56.200 --> 00:03:58.830
is that the energy is
equal to Planck's constant
00:03:58.830 --> 00:04:00.430
times the frequency.
00:04:00.430 --> 00:04:01.950
So this thing that looks like a V
00:04:01.950 --> 00:04:03.292
this is actually the Greek letter,
00:04:03.292 --> 00:04:06.050
the lowercase Greek letter Nu,
00:04:06.050 --> 00:04:08.480
and this is what we
typically use for frequency,
00:04:08.480 --> 00:04:10.340
especially when we're
talking about frequencies
00:04:10.340 --> 00:04:11.470
of things like light.
00:04:11.470 --> 00:04:14.900
And we also know how to go
between frequency and wavelength,
00:04:14.900 --> 00:04:16.470
because we see that the speed of light
00:04:16.470 --> 00:04:20.120
is equal to whatever the
wavelength of that light is
00:04:20.120 --> 00:04:22.530
times the frequency of that light.
00:04:22.530 --> 00:04:25.590
So how would we figure out
the energy of one photon,
00:04:25.590 --> 00:04:28.290
of 486 nanometer light?
00:04:28.290 --> 00:04:30.130
Well, we could think about it this way.
00:04:30.130 --> 00:04:32.670
We can first figure out its frequency
00:04:32.670 --> 00:04:35.680
using C is equal to Lambda times new.
00:04:35.680 --> 00:04:37.100
Let me write this down.
00:04:37.100 --> 00:04:39.390
So we know that see the speed of light
00:04:39.390 --> 00:04:41.810
is equal to the wavelength of the light
00:04:41.810 --> 00:04:46.040
times the frequency of that light.
00:04:46.040 --> 00:04:48.160
And so if we know the wavelength,
00:04:48.160 --> 00:04:50.380
we can figure out the frequency
00:04:50.380 --> 00:04:53.260
by dividing both sides by Lambda.
00:04:53.260 --> 00:04:54.810
So let's do that.
00:04:54.810 --> 00:04:56.800
So if we divide both sides by Lambda,
00:04:56.800 --> 00:05:00.030
we get that the frequency of the light
00:05:00.030 --> 00:05:02.060
is going to be equal to the speed of light
00:05:02.060 --> 00:05:04.290
divided by the wavelength of the light.
00:05:04.290 --> 00:05:06.550
Remember, they've given us the
wavelength of the light here,
00:05:06.550 --> 00:05:09.940
486 nanometers, or at least
I have given it to you.
00:05:09.940 --> 00:05:12.420
And then you could take
this and plug it back
00:05:12.420 --> 00:05:14.790
into Planck's equation up here,
00:05:14.790 --> 00:05:16.540
that energy is equal to Planck's constant
00:05:16.540 --> 00:05:19.390
times the frequency to
figure out the energy.
00:05:19.390 --> 00:05:20.770
So let me write that down.
00:05:20.770 --> 00:05:24.720
So the energy is going to be
equal to Planck's constant
00:05:24.720 --> 00:05:26.040
times the frequency,
00:05:26.040 --> 00:05:27.720
well we know the
frequency right over here.
00:05:27.720 --> 00:05:31.190
So it's going to be equal
to Planck's constant times,
00:05:31.190 --> 00:05:36.190
the speed of light divided by
the wavelength of our light,
00:05:36.810 --> 00:05:40.370
which we know is 486 nanometers,
00:05:40.370 --> 00:05:44.500
486 nanometers.
00:05:44.500 --> 00:05:47.170
So we could say, just
scroll down a little bit,
00:05:47.170 --> 00:05:49.930
that the energy is going to
be equal to Planck's constant
00:05:49.930 --> 00:05:54.930
times the speed of light divided by
00:05:55.480 --> 00:05:58.360
instead of writing the wave
length is 486 nanometers,
00:05:58.360 --> 00:06:03.360
I can write it as 486 times 10
to the negative ninth meters
00:06:06.530 --> 00:06:10.260
a nanometer is just one
billionth of a meter,
00:06:10.260 --> 00:06:12.060
and then we can just
get our calculator out
00:06:12.060 --> 00:06:14.010
and we know what Planck's constant is.
00:06:14.010 --> 00:06:14.950
They give it right over here.
00:06:14.950 --> 00:06:17.120
We know what the speed of
light is right over here.
00:06:17.120 --> 00:06:19.140
And we know that we have a maximum,
00:06:19.140 --> 00:06:21.350
over here they're giving
us four significant figures
00:06:21.350 --> 00:06:22.280
in each of these.
00:06:22.280 --> 00:06:24.270
And then we have three
significant figures here.
00:06:24.270 --> 00:06:25.210
So our answer's going to be
00:06:25.210 --> 00:06:27.134
in terms of three significant figures.
00:06:27.134 --> 00:06:32.134
I'm going to get Planck's
constant, which is 6.626
00:06:34.550 --> 00:06:38.170
times 10 to the negative
34th joule seconds.
00:06:38.170 --> 00:06:39.960
So let me write that down.
00:06:39.960 --> 00:06:44.960
So times 10 to the negative 34th,
00:06:45.370 --> 00:06:48.460
and I'm gonna multiply that
times the speed of light.
00:06:48.460 --> 00:06:50.713
So times 2.998
00:06:54.140 --> 00:06:59.130
times 10 to the eighth meters per second
00:06:59.130 --> 00:07:01.070
gets me this business.
00:07:01.070 --> 00:07:03.413
And then I'm gonna divide that by 486
00:07:07.200 --> 00:07:11.670
times 10 to the negative ninth gives me,
00:07:11.670 --> 00:07:14.530
I think we deserve a
little bit of a drum roll,
00:07:14.530 --> 00:07:16.170
gives me this.
00:07:16.170 --> 00:07:19.950
And if we were to look at
three significant figures,
00:07:19.950 --> 00:07:24.950
this would be 4.09 times
10 to the negative 19th.
00:07:26.190 --> 00:07:28.870
And Planck's constant here
has given in terms of jewels,
00:07:28.870 --> 00:07:33.870
4.09 times 10 to the negative 19 joules.
00:07:35.950 --> 00:07:37.710
So what that tells us
is that the difference
00:07:37.710 --> 00:07:40.820
in these energy levels is this many joules
00:07:40.820 --> 00:07:42.580
or the energy of that photon
00:07:42.580 --> 00:07:45.640
that has a wavelength of 486 nanometers.
00:07:45.640 --> 00:07:50.640
That energy is 4.09 times 10
to the negative 19 joules.
|
Spectrophotometry and the Beer–Lambert Law | https://www.youtube.com/watch?v=fJRJLUYZe9c | vtt | https://www.youtube.com/api/timedtext?v=fJRJLUYZe9c&ei=8lWUZdiCDquhp-oP97OSuAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245346&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0FBE6167DD45F2E0F8FBA5925544986AC46E5950.3C6B16A44C9D464F743F02ACCA463EDA9AC5924A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.700 --> 00:00:02.959
- [Instructor] What I want
to do in this video is
00:00:02.959 --> 00:00:05.020
to talk a little bit
about spectrophotometry.
00:00:05.020 --> 00:00:09.330
Spectrophotometry, photometry,
00:00:09.330 --> 00:00:12.120
which sounds fairly sophisticated,
00:00:12.120 --> 00:00:15.480
but it's really based on
a fairly simple principle.
00:00:15.480 --> 00:00:19.356
So if I have, let's say
we have two solutions
00:00:19.356 --> 00:00:21.620
that contain some type of solute.
00:00:21.620 --> 00:00:25.240
So that is solution one, and
then this is solution two.
00:00:25.240 --> 00:00:28.620
And let's just assume that our
beakers have the same width.
00:00:28.620 --> 00:00:30.390
Now let's say solution,
let me put it right here.
00:00:30.390 --> 00:00:33.540
Number one, and number two.
00:00:33.540 --> 00:00:34.840
Now let's say that solution one
00:00:34.840 --> 00:00:37.870
has less of the solute in it.
00:00:37.870 --> 00:00:39.900
So let me, let me make...
00:00:39.900 --> 00:00:42.270
So that's the water line right there.
00:00:42.270 --> 00:00:44.520
So this guy has less of it,
and let's say it's yellow,
00:00:44.520 --> 00:00:46.330
or to our eyes, it looks yellow.
00:00:46.330 --> 00:00:48.160
So this has less of it.
00:00:48.160 --> 00:00:50.410
So this hasm actuallym
let me do it this way.
00:00:50.410 --> 00:00:51.550
Let me shade it in like this.
00:00:51.550 --> 00:00:54.400
So it has less of it.
00:00:54.400 --> 00:00:57.720
And let's say solution number
two has more of the solute,
00:00:57.720 --> 00:00:59.160
so it's more.
00:00:59.160 --> 00:01:01.550
So I'll just kind of represent that
00:01:01.550 --> 00:01:03.820
as more closely packed lines.
00:01:03.820 --> 00:01:06.410
So the concentration of
the solute is higher here.
00:01:06.410 --> 00:01:09.080
So let me write higher concentration.
00:01:09.080 --> 00:01:11.063
Higher concentration.
00:01:12.150 --> 00:01:14.800
Concentration, and let's say,
00:01:14.800 --> 00:01:19.650
and this is a lower, lower concentration.
00:01:19.650 --> 00:01:21.480
Now let's think about what will happen
00:01:21.480 --> 00:01:25.920
if we shine some light
through each of these beakers,
00:01:25.920 --> 00:01:29.510
and let's just assume that we
are shining at a wavelength
00:01:29.510 --> 00:01:32.687
of light that is specific to the...
00:01:32.687 --> 00:01:35.120
That that is specifically
sensitive to the solute
00:01:35.120 --> 00:01:37.080
that we have dissolved in here.
00:01:37.080 --> 00:01:39.980
But I'll just leave that
pretty general right now.
00:01:39.980 --> 00:01:43.530
So let's say I have some
light here of some intensity.
00:01:43.530 --> 00:01:45.350
So let's just call that...
00:01:45.350 --> 00:01:48.610
Let's call that the incident intensity.
00:01:48.610 --> 00:01:51.930
I'll just say that it's
I0, so it's some intensity.
00:01:51.930 --> 00:01:54.730
What's going to happen as the light exits
00:01:54.730 --> 00:01:57.450
the other side of this beaker right here?
00:01:57.450 --> 00:02:00.470
Well, some of it is going to be absorbed
00:02:00.470 --> 00:02:03.148
by our little molecules inside the beaker,
00:02:03.148 --> 00:02:05.320
so you're going to have less light
00:02:05.320 --> 00:02:06.450
come out to the other side.
00:02:06.450 --> 00:02:07.533
I'll call this I1.
00:02:09.530 --> 00:02:13.700
Now, in this situation, if
we shined the same amount
00:02:13.700 --> 00:02:17.118
of light into this beaker, so
it's the same number that is,
00:02:17.118 --> 00:02:18.380
that is the same, the
same intensity of light,
00:02:18.380 --> 00:02:19.530
what's going to happen?
00:02:20.369 --> 00:02:22.540
Well, more is going to
be absorbed as the light
00:02:22.540 --> 00:02:23.830
travels through this beaker.
00:02:23.830 --> 00:02:27.180
It's just going to bump
into more molecules,
00:02:27.180 --> 00:02:29.180
'cause it's a higher concentration here.
00:02:29.180 --> 00:02:31.510
So the light that comes out when you have
00:02:31.510 --> 00:02:34.890
a higher concentration, I'll
call that the intensity,
00:02:34.890 --> 00:02:37.946
I'll call that I2, this is going to have
00:02:37.946 --> 00:02:41.720
a lower intensity of light
that's being transmitted
00:02:41.720 --> 00:02:42.710
than this one over here.
00:02:42.710 --> 00:02:47.020
In this case, I2 is going
to have a lower intensity,
00:02:47.020 --> 00:02:49.680
is going to be less than I1.
00:02:49.680 --> 00:02:54.520
If you have another beaker
that is maybe twice as wide,
00:02:54.520 --> 00:02:57.210
it's twice as wide, and
let's say it has the same
00:02:57.210 --> 00:02:59.670
concentration as number
two, we'll call this one
00:02:59.670 --> 00:03:03.000
number three, it has the same
concentration as number two.
00:03:03.000 --> 00:03:05.420
So I'll try to make it
look fairly similar,
00:03:05.420 --> 00:03:08.270
and you were to shine some light in here.
00:03:08.270 --> 00:03:10.670
Let's say you shine
the same light in here,
00:03:10.670 --> 00:03:13.840
and you have some light that
makes it through, that exits,
00:03:13.840 --> 00:03:16.600
and then this is actually
what your eyes would see.
00:03:16.600 --> 00:03:19.300
So this is I3 right there.
00:03:19.300 --> 00:03:20.700
What do you think's going to happen?
00:03:20.700 --> 00:03:23.240
Well, it's the same
concentration, but this light
00:03:23.240 --> 00:03:26.110
has to travel a further
distance of that concentration.
00:03:26.110 --> 00:03:29.130
So once again, it's going
to bump into more molecules
00:03:29.130 --> 00:03:32.130
and more of it will be absorbed,
00:03:32.130 --> 00:03:34.520
and so less light will be transmitted.
00:03:34.520 --> 00:03:36.023
So I2 is less than I1, and I3,
00:03:37.890 --> 00:03:40.040
I3 is actually going to be the least.
00:03:40.040 --> 00:03:42.890
And if you were looking at
these, this has the least light,
00:03:42.890 --> 00:03:44.580
this has a little bit more
light being transmitted,
00:03:44.580 --> 00:03:46.940
this has the most light being transmitted.
00:03:46.940 --> 00:03:47.960
So if you were to look at this,
00:03:47.960 --> 00:03:50.280
if you placed your eyeball right here,
00:03:50.280 --> 00:03:52.960
this one right here would
have the lightest color.
00:03:52.960 --> 00:03:55.140
You're getting the most
light into your eye.
00:03:55.140 --> 00:03:56.910
This would be a slightly darker color,
00:03:56.910 --> 00:03:58.750
and this would be the darkest color.
00:03:58.750 --> 00:04:00.030
That makes complete sense.
00:04:00.030 --> 00:04:02.520
If you dissolve something,
if you dissolve a little bit
00:04:02.520 --> 00:04:04.490
of something in water, it will
still be pretty transparent.
00:04:04.490 --> 00:04:06.740
If you dissolve a lot
of something in water,
00:04:06.740 --> 00:04:08.090
it'll be more opaque.
00:04:08.090 --> 00:04:09.990
And if the cup that you're dissolving in,
00:04:09.990 --> 00:04:12.370
or the beaker that you're
in, gets even longer,
00:04:12.370 --> 00:04:14.200
it'll get even more opaque.
00:04:14.200 --> 00:04:16.441
So hopefully, that gives you the intuition
00:04:16.441 --> 00:04:18.660
behind spectrophotometry.
00:04:18.660 --> 00:04:20.598
And so the next question is, well,
00:04:20.598 --> 00:04:21.977
what is it even good for?
00:04:21.977 --> 00:04:22.810
Why would I even care?
00:04:22.810 --> 00:04:24.720
Well, you could actually
use this information.
00:04:24.720 --> 00:04:27.150
You could see how much
light is transmitted
00:04:27.150 --> 00:04:29.740
versus how much you put
in to actually figure out
00:04:29.740 --> 00:04:31.210
the concentration of a solution.
00:04:31.210 --> 00:04:32.880
That's why we're even talking about it
00:04:32.880 --> 00:04:35.010
in a chemistry context.
00:04:35.010 --> 00:04:36.060
So before we do that,
00:04:37.587 --> 00:04:39.839
and I'll show you an example
of that in the next video,
00:04:39.839 --> 00:04:42.640
let me just define some,
really, some terms of ways
00:04:42.640 --> 00:04:44.560
of measuring how concentrated this is,
00:04:44.560 --> 00:04:47.330
or ways of measuring how
much light is transmitted
00:04:47.330 --> 00:04:49.121
versus how much was put in.
00:04:49.121 --> 00:04:53.403
So the first thing I will
define is transmittance.
00:04:56.730 --> 00:04:59.080
And so when the people
who defined it said, well,
00:04:59.080 --> 00:05:01.100
you know, what we care about
is how much is transmitted
00:05:01.100 --> 00:05:04.520
versus how much went in, so
let's just define transmittance
00:05:04.520 --> 00:05:05.770
as that ratio.
00:05:05.770 --> 00:05:08.420
So in this example, the
transmittance of number one
00:05:08.420 --> 00:05:11.306
would be the amount that got through
00:05:11.306 --> 00:05:14.570
over the amount that you put in.
00:05:14.570 --> 00:05:18.470
Over here, the transmittance
would be the amount
00:05:18.470 --> 00:05:21.430
that you got out over the
amount that you put in.
00:05:21.430 --> 00:05:25.290
And as we see, this one right
here will be a lower number.
00:05:25.290 --> 00:05:27.580
I2 is lower than I1,
00:05:27.580 --> 00:05:31.020
so this will have a lower
transmittance then number one.
00:05:31.020 --> 00:05:32.900
So let's call this transmittance two.
00:05:32.900 --> 00:05:34.420
This is transmittance one.
00:05:34.420 --> 00:05:39.260
And transmittance three is
the light that comes out,
00:05:39.260 --> 00:05:42.610
that gets through, over
the light that goes in,
00:05:42.610 --> 00:05:44.760
and this is the smallest
number, followed by that,
00:05:44.760 --> 00:05:45.630
followed by that.
00:05:45.630 --> 00:05:47.540
So this will have the least transmittance,
00:05:47.540 --> 00:05:50.540
it's the most opaque, followed
by that, followed by that.
00:05:50.540 --> 00:05:53.300
Now another definition,
which is really kind of
00:05:53.300 --> 00:05:55.240
a derivative of the transmittance,
00:05:55.240 --> 00:05:56.450
and not in the calculus sense,
00:05:56.450 --> 00:05:58.970
it's just derived from
transmittance, and we'll see,
00:05:58.970 --> 00:06:02.260
it has pretty neat properties,
is the notion of absorbance.
00:06:02.260 --> 00:06:03.800
And so here, we're trying to measure,
00:06:03.800 --> 00:06:05.090
how good is it at absorbing?
00:06:05.090 --> 00:06:06.920
This is measuring, how good
are you at transmitting?
00:06:06.920 --> 00:06:08.900
A higher number says
you're transmitting a lot,
00:06:08.900 --> 00:06:11.270
but absorbance is how
good you're absorbing,
00:06:11.270 --> 00:06:12.380
so it's kind of the opposite.
00:06:12.380 --> 00:06:13.380
If you're good at transmitting,
00:06:13.380 --> 00:06:14.720
that means you're bad at absorbing,
00:06:14.720 --> 00:06:16.130
You don't have a lot to absorb.
00:06:16.130 --> 00:06:17.540
If you're good at absorbing,
00:06:17.540 --> 00:06:19.430
that means you're not transmitting much.
00:06:19.430 --> 00:06:20.710
So absorbance.
00:06:21.820 --> 00:06:26.020
Absorbance, right here,
and absorbance is defined
00:06:26.020 --> 00:06:31.020
as the negative log of transmittance.
00:06:31.040 --> 00:06:34.010
And this logarithm is base 10,
00:06:34.010 --> 00:06:36.610
or you could view that if the
transmittance, we've already
00:06:36.610 --> 00:06:41.150
defined as the negative, the
negative log of the light
00:06:41.150 --> 00:06:46.080
that is transmitted over
the light that is input,
00:06:46.080 --> 00:06:47.750
but the easiest way is the negative log
00:06:47.750 --> 00:06:49.344
of the transmittance.
00:06:49.344 --> 00:06:50.350
And so, if transmittance
is a large number,
00:06:50.350 --> 00:06:52.900
absorbance is a small
number, which makes sense.
00:06:52.900 --> 00:06:54.700
Now, what's also cool about this.
00:06:54.700 --> 00:06:56.810
is there something called
the Beer-Lambert law,
00:06:56.810 --> 00:06:59.500
which you could verify, and this is...
00:06:59.500 --> 00:07:01.790
We'll actually use this in the next video,
00:07:01.790 --> 00:07:04.610
Beer-Lambert law.
00:07:04.610 --> 00:07:07.180
I actually don't know the
history of where it came from,
00:07:07.180 --> 00:07:09.160
and I'm sure it's based
on somebody named Beer,
00:07:09.160 --> 00:07:11.540
but I always imagined it's
based on someone transmitting
00:07:11.540 --> 00:07:14.707
light through beer, the Beer-Lambert law.
00:07:16.688 --> 00:07:20.380
And this tells us, this
tells us that the absorbance
00:07:20.380 --> 00:07:24.360
is proportional to the path length.
00:07:24.360 --> 00:07:27.030
So this would be, how far
does the light have to go
00:07:27.030 --> 00:07:28.230
through the solution?
00:07:28.230 --> 00:07:31.230
So it's proportional to the path length
00:07:31.230 --> 00:07:34.920
times the concentration,
times the concentration.
00:07:34.920 --> 00:07:38.550
Usually we use molarity
for the concentration.
00:07:38.550 --> 00:07:41.970
Or another way to say it
is that the absorbance
00:07:41.970 --> 00:07:43.910
is equal to some constant.
00:07:43.910 --> 00:07:46.600
It's usually a lowercase
Epsilon like that.
00:07:46.600 --> 00:07:50.400
Some constant, and this is
dependent on the solution,
00:07:50.400 --> 00:07:53.210
or the solute in question,
what we actually have in here
00:07:53.210 --> 00:07:56.113
and the temperature and the
pressure and all of that.
00:07:56.113 --> 00:08:00.330
It's equal to constant times
the length it has to travel,
00:08:00.330 --> 00:08:02.150
times the concentration.
00:08:02.150 --> 00:08:03.360
Let me make it clear right here.
00:08:03.360 --> 00:08:04.840
This thing right here,
00:08:04.840 --> 00:08:07.253
this thing right here is concentration.
00:08:08.480 --> 00:08:10.100
Concentration.
00:08:10.100 --> 00:08:12.830
The reason why this is super
useful, as you can imagine,
00:08:12.830 --> 00:08:15.863
so let's say we have an axis right here.
00:08:16.890 --> 00:08:20.620
That's axis, and over here,
I'm measuring concentration.
00:08:20.620 --> 00:08:22.820
This is our concentration axis,
00:08:22.820 --> 00:08:24.809
and we're measuring it as molarity.
00:08:24.809 --> 00:08:26.730
And let's say the molarity starts at zero.
00:08:26.730 --> 00:08:31.297
It goes, you know, I
don't know, .1, .2, .3,
00:08:32.390 --> 00:08:33.570
so on and so forth.
00:08:33.570 --> 00:08:36.400
And over here, you are
measuring absorbance.
00:08:36.400 --> 00:08:39.040
In the vertical axis
you measure absorbance.
00:08:39.040 --> 00:08:42.100
Now, let's say you have some solution,
00:08:42.100 --> 00:08:43.390
and you know the concentration,
00:08:43.390 --> 00:08:46.620
you know it is a .1 molar concentration.
00:08:46.620 --> 00:08:49.090
So let me write down M for molar.
00:08:49.090 --> 00:08:50.237
And you measure its absorbance
00:08:50.237 --> 00:08:51.770
and you just get some number here.
00:08:51.770 --> 00:08:54.840
So you measure its absorbance
and you get its absorbance,
00:08:54.840 --> 00:08:57.660
so this is a low concentration,
didn't absorb that much.
00:08:57.660 --> 00:08:59.660
You get, I don't know some number here,
00:08:59.660 --> 00:09:00.760
so let's say it's .25.
00:09:04.940 --> 00:09:08.490
And then let's say that
you then take another known
00:09:08.490 --> 00:09:11.460
concentration, let's say .2 molar,
00:09:11.460 --> 00:09:14.130
and you say that, oh
look, it has an absorbance
00:09:14.130 --> 00:09:18.060
right here at .5, and I should
put a zero in front of these.
00:09:18.060 --> 00:09:20.300
0.5 and 0.25.
00:09:20.300 --> 00:09:22.980
What this tells you, this
is a linear relationship.
00:09:22.980 --> 00:09:24.807
For any concentration,
00:09:24.807 --> 00:09:27.170
the absorbance is going to be on a line.
00:09:27.170 --> 00:09:29.560
And if you want a little
review of algebra,
00:09:29.560 --> 00:09:31.390
Epsilon times the length
will be the slope.
00:09:31.390 --> 00:09:33.660
But the important thing to realize
00:09:33.660 --> 00:09:35.780
is that you have a line here.
00:09:35.780 --> 00:09:37.860
You have a line here, and why?
00:09:37.860 --> 00:09:39.660
And the reason that's useful
is you could use a little bit
00:09:39.660 --> 00:09:41.330
of algebra, figure out
the equation of a line,
00:09:41.330 --> 00:09:43.770
or you could just look at it
graphically and say, okay,
00:09:43.770 --> 00:09:45.750
I had two known concentrations,
00:09:45.750 --> 00:09:47.930
and I was able to figure
out the absorbance.
00:09:47.930 --> 00:09:50.310
You can then go the other way around.
00:09:50.310 --> 00:09:53.770
You could then measure for
some unknown concentration.
00:09:53.770 --> 00:09:55.110
You could figure out its absorbance.
00:09:55.110 --> 00:09:56.727
So let's say there's some
unknown concentration,
00:09:56.727 --> 00:10:00.670
and you figure out its
absorbance is right over here.
00:10:00.670 --> 00:10:02.060
Let's say it's .4.
00:10:02.060 --> 00:10:04.200
Then you can just go on this
line right here, and you say,
00:10:04.200 --> 00:10:06.500
okay, well then that must be,
00:10:06.500 --> 00:10:08.840
that must be a
concentration of this, well,
00:10:08.840 --> 00:10:10.040
whatever number this is.
00:10:10.040 --> 00:10:11.860
And you could measure it,
00:10:11.860 --> 00:10:13.587
or you could actually
figure it out algebraically.
00:10:13.587 --> 00:10:16.920
And so this will be
pretty close to .2 molar,
00:10:16.920 --> 00:10:18.710
a little bit less than 0.2 molar.
00:10:18.710 --> 00:10:20.620
And we're gonna actually
do an example of that
00:10:20.620 --> 00:10:21.953
in the next video.
|
Worked example: Calculating concentration using the Beer–Lambert law | https://www.youtube.com/watch?v=pbbHg_9zFbI | vtt | https://www.youtube.com/api/timedtext?v=pbbHg_9zFbI&ei=91WUZaDuHafy0wWk8rugDg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=79628DFF912FE13943D7CFFC5F02EDE41D4E0F9A.3B2389B9E661F0B6393490E945DA889C45BA0F45&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.173 --> 00:00:01.290
- [Instructor] So I have a question here
00:00:01.290 --> 00:00:03.740
from the Kotz, Treichel,
and Townsend Chemistry
00:00:03.740 --> 00:00:05.320
and Chemical Reactivity book,
00:00:05.320 --> 00:00:07.220
and I got their permission to do this.
00:00:07.220 --> 00:00:11.130
And it says a solution
of potassium permanganate
00:00:11.130 --> 00:00:15.143
has an absorbance of 0.539
00:00:16.840 --> 00:00:20.420
when measured at 540 nanometers
00:00:20.420 --> 00:00:23.291
in a one centimeter cell.
00:00:23.291 --> 00:00:28.291
What is the concentration of
the potassium permanganate?
00:00:28.900 --> 00:00:33.060
Prior to determining the
absorbance for the unknown solution
00:00:33.060 --> 00:00:35.720
the following calibration
data were collected
00:00:35.720 --> 00:00:38.660
for the spectrophotometer.
00:00:38.660 --> 00:00:40.830
So the way that we would tackle this
00:00:40.830 --> 00:00:43.900
is we know that there
is a linear relationship
00:00:43.900 --> 00:00:47.110
between absorbance and concentration.
00:00:47.110 --> 00:00:48.690
We could describe it something like this,
00:00:48.690 --> 00:00:50.930
that absorbance is going to be equal
00:00:50.930 --> 00:00:55.930
to sum slope times are concentration.
00:00:56.470 --> 00:00:58.440
And you could say sum y-intercept,
00:00:58.440 --> 00:01:00.040
if we're a purist about it,
00:01:00.040 --> 00:01:01.870
then the y intercept should be zero
00:01:01.870 --> 00:01:03.690
because at a zero concentration,
00:01:03.690 --> 00:01:06.090
you should have a zero absorbance.
00:01:06.090 --> 00:01:08.330
But the way that chemists
would typically do it,
00:01:08.330 --> 00:01:12.120
is that they would put
these points into a computer
00:01:12.120 --> 00:01:14.590
and then a computer do
a linear aggression.
00:01:14.590 --> 00:01:15.990
You could also do that by hand
00:01:15.990 --> 00:01:18.990
but that's a little bit out
of the scope of this video.
00:01:18.990 --> 00:01:21.050
And I did that, I went to Desmos
00:01:21.050 --> 00:01:24.560
and I typed in the numbers that they gave.
00:01:24.560 --> 00:01:26.960
And this is what I got,
00:01:26.960 --> 00:01:28.410
so I just typed in these numbers
00:01:28.410 --> 00:01:31.290
and then it fit a linear
regression line to it
00:01:31.290 --> 00:01:34.240
and it got these parameters,
m is equal to this
00:01:34.240 --> 00:01:36.240
and b is equal to this.
00:01:36.240 --> 00:01:37.970
Now we could say significant figures
00:01:37.970 --> 00:01:39.870
it seems like the small
significant figures here
00:01:39.870 --> 00:01:41.360
we have have our three,
00:01:41.360 --> 00:01:43.390
but we could just view the m and the b
00:01:43.390 --> 00:01:45.750
as intermediate numbers
in our calculations.
00:01:45.750 --> 00:01:48.570
What I'm going to do is
I'm gonna use m and b,
00:01:48.570 --> 00:01:50.380
and then my final I'll answer
00:01:50.380 --> 00:01:53.170
I'm going to round to
three significant figures.
00:01:53.170 --> 00:01:54.180
So what this tells us,
00:01:54.180 --> 00:01:57.333
is that absorbance is going to be 5.65333
00:02:01.070 --> 00:02:04.153
times our concentration minus 0.0086.
00:02:08.870 --> 00:02:11.710
And now they've given us what A is.
00:02:11.710 --> 00:02:14.530
Let me get rid of all of this stuff here.
00:02:14.530 --> 00:02:18.570
They told us that our absorbance is 0.539,
00:02:18.570 --> 00:02:23.570
so we know that 0.539 is equal
to 5.65333C minus 0.0086.
00:02:32.680 --> 00:02:34.300
And then if you wanna solve for C,
00:02:34.300 --> 00:02:36.360
let's see, we could add
this to both sides first.
00:02:36.360 --> 00:02:41.360
So you get 0.539 plus
0.0086 is equal to 5.65333C,
00:02:48.500 --> 00:02:50.360
and then divide both sides by this,
00:02:50.360 --> 00:02:52.200
and you would get C is equal to,
00:02:52.200 --> 00:02:54.920
is going to be approximately
equal to, be a little careful
00:02:54.920 --> 00:02:58.060
all of these would really be approximate.
00:02:58.060 --> 00:03:03.060
C is gonna be equal to 0.539
plus 0.0086 divided by 5.65333.
00:03:12.370 --> 00:03:15.540
And of course we want to round
to three significant figures.
00:03:15.540 --> 00:03:20.540
All right, 0.539 plus
0.0086 is equal to that,
00:03:23.870 --> 00:03:27.940
divided by 5.65333 is equal to this,
00:03:31.170 --> 00:03:33.660
so if we go three significant figures
00:03:33.660 --> 00:03:35.750
this is going to be 0.0969.
00:03:40.050 --> 00:03:41.780
So I would write the concentration
00:03:41.780 --> 00:03:44.213
is approximately 0.0969 Molar.
|
Introduction to spectroscopy | https://www.youtube.com/watch?v=LYseY0y2tgg | vtt | https://www.youtube.com/api/timedtext?v=LYseY0y2tgg&ei=91WUZdK_HpGYmLAPpK2FqA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=CBE74AFF98C879B259C413A8E744FE3F37346A78.2FEA2C375E1677FD7C8D667A907BD04E97C42C96&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.350 --> 00:00:03.250
- In this video, we're gonna
talk about spectroscopy,
00:00:03.250 --> 00:00:05.120
which is all about the interactions
00:00:05.120 --> 00:00:06.900
between light and matter.
00:00:06.900 --> 00:00:08.740
And when we're talking about light,
00:00:08.740 --> 00:00:10.750
we're not just talking
about visible light,
00:00:10.750 --> 00:00:14.910
We're talking about electromagnetic
radiation in general.
00:00:14.910 --> 00:00:17.210
And so what I'm going to do
to give us an intuition here
00:00:17.210 --> 00:00:20.480
is use the PhET simulator by
the University of Colorado.
00:00:20.480 --> 00:00:22.700
I encourage you to go to this URL
00:00:22.700 --> 00:00:24.610
and try it out for yourself.
00:00:24.610 --> 00:00:27.170
But you can see what the simulator does is
00:00:27.170 --> 00:00:31.120
it allows us to essentially
see how different wavelengths
00:00:31.120 --> 00:00:36.090
of electromagnetic radiation
can interact with matter,
00:00:36.090 --> 00:00:38.100
in this case various molecules.
00:00:38.100 --> 00:00:39.270
And just to get our bearings,
00:00:39.270 --> 00:00:41.760
we can click on this
light spectrum diagram,
00:00:41.760 --> 00:00:44.160
and we can see that on this diagram
00:00:44.160 --> 00:00:46.620
what people would normally
consider radio waves.
00:00:46.620 --> 00:00:49.030
These are some of the lowest frequencies
00:00:49.030 --> 00:00:51.680
and longest wavelengths of light.
00:00:51.680 --> 00:00:53.290
And then when you get
to higher frequencies,
00:00:53.290 --> 00:00:55.440
you get to microwave, and
the higher the frequency,
00:00:55.440 --> 00:00:57.640
there's also the higher
the energy per photon.
00:00:57.640 --> 00:00:59.660
And then you get higher
frequencies in that
00:00:59.660 --> 00:01:01.600
and higher energy, that's infrared,
00:01:01.600 --> 00:01:03.430
and then higher frequency and energy,
00:01:03.430 --> 00:01:04.290
that's visible light.
00:01:04.290 --> 00:01:06.080
That's what our eyes can sense.
00:01:06.080 --> 00:01:08.870
And then you get even higher
frequency, and more energy.
00:01:08.870 --> 00:01:12.610
You get to ultraviolet. Then
X-ray and then gamma rays.
00:01:12.610 --> 00:01:14.440
And this isn't a linear scale.
00:01:14.440 --> 00:01:16.610
You can see that this is
a logarithmic scale here.
00:01:16.610 --> 00:01:18.770
This is in powers of 10.
00:01:18.770 --> 00:01:22.190
So we see some pretty dramatic
increases in frequency
00:01:22.190 --> 00:01:25.130
and energy as we go from
the left to the right.
00:01:25.130 --> 00:01:28.250
But in this video, we're
gonna focus in particular,
00:01:28.250 --> 00:01:33.250
on microwave, infrared, visible
and ultraviolet wavelengths
00:01:33.660 --> 00:01:37.170
of electromagnetic light,
or electromagnetic waves,
00:01:37.170 --> 00:01:40.563
and think about how they
interact with molecules.
00:01:42.180 --> 00:01:44.690
So if we start with microwave radiation,
00:01:44.690 --> 00:01:46.370
and here we have a water molecule,
00:01:46.370 --> 00:01:47.940
I've picked that right over there
00:01:47.940 --> 00:01:50.520
and I can get my simulation going.
00:01:50.520 --> 00:01:54.760
You can see what it's doing
is, when it gets absorbed,
00:01:54.760 --> 00:01:58.700
it causes a rotational
transition in the water molecule.
00:01:58.700 --> 00:02:02.010
It makes the water molecule
rotate in a different way
00:02:02.010 --> 00:02:03.250
than it was before.
00:02:03.250 --> 00:02:06.230
And then the water molecule
can also emit the radiation
00:02:06.230 --> 00:02:08.100
and then rotate differently.
00:02:08.100 --> 00:02:10.050
And so you can see it
doesn't always do that.
00:02:10.050 --> 00:02:12.300
There's a little bit of
a probability involved,
00:02:12.300 --> 00:02:14.820
but this is actually the
basis of how microwaves work,
00:02:14.820 --> 00:02:16.090
your microwave oven,
00:02:16.090 --> 00:02:18.710
is it causes the water molecules
00:02:18.710 --> 00:02:21.570
to get agitated in a rotational way,
00:02:21.570 --> 00:02:24.770
which increases the heat in that system.
00:02:24.770 --> 00:02:27.390
Now we could also look at infrared light,
00:02:27.390 --> 00:02:29.000
which is once again, we have to remember,
00:02:29.000 --> 00:02:30.940
gets us into higher frequencies,
00:02:30.940 --> 00:02:33.113
and see what that does to molecules.
00:02:34.350 --> 00:02:36.060
So based on this simulation,
00:02:36.060 --> 00:02:40.080
it looks like the infrared
light is when it gets absorbed,
00:02:40.080 --> 00:02:43.240
it causes this water
molecule to start to vibrate.
00:02:43.240 --> 00:02:46.210
So microwave radiation caused it to rotate
00:02:46.210 --> 00:02:48.700
or to have a change in
state of its rotation,
00:02:48.700 --> 00:02:51.210
while infrared makes it vibrate.
00:02:51.210 --> 00:02:53.770
And we could see that with
other molecules as well.
00:02:53.770 --> 00:02:55.393
Let's try carbon monoxide.
00:02:56.370 --> 00:02:58.510
Once again, it's not rotating it,
00:02:58.510 --> 00:03:01.510
it's causing it to vibrate.
00:03:01.510 --> 00:03:03.560
Now what about visible light?
00:03:03.560 --> 00:03:05.860
Well, visible light will
have different interactions
00:03:05.860 --> 00:03:08.120
with different types of molecules,
00:03:08.120 --> 00:03:11.133
but let's try it out
with nitrogen dioxide.
00:03:12.340 --> 00:03:15.700
So there's certain situations
where nitrogen dioxide
00:03:15.700 --> 00:03:18.570
will absorb, that's
when you saw it glowing
00:03:18.570 --> 00:03:19.670
and what you see when it's glowing,
00:03:19.670 --> 00:03:21.880
what it's really doing
is it's putting electrons
00:03:21.880 --> 00:03:25.400
into a higher energy state,
or into a higher orbital
00:03:25.400 --> 00:03:27.240
and then when it stops glowing,
00:03:27.240 --> 00:03:29.480
it means that those
electrons are going back
00:03:29.480 --> 00:03:30.850
to a lower energy state.
00:03:30.850 --> 00:03:33.560
They are re-emitting radiation.
00:03:33.560 --> 00:03:34.393
So there, you can see it.
00:03:34.393 --> 00:03:38.330
You can see that just now,
it's remitting visible light,
00:03:38.330 --> 00:03:40.010
in this case a different direction.
00:03:40.010 --> 00:03:43.370
And when it did that, the
electron that was excited,
00:03:43.370 --> 00:03:46.290
went to a lower energy state.
00:03:46.290 --> 00:03:50.350
Now what about, let's think
about ultraviolet light,
00:03:50.350 --> 00:03:53.180
which has even higher
energy than visible light.
00:03:53.180 --> 00:03:54.030
What can that do?
00:03:55.860 --> 00:03:58.970
Well, here, we can see that
it takes, in certain cases,
00:03:58.970 --> 00:04:01.620
electrons, and it's able
to excite them so much
00:04:01.620 --> 00:04:04.050
that it's able to break that bond itself.
00:04:04.050 --> 00:04:06.140
And so let me keep resetting it.
00:04:06.140 --> 00:04:07.730
So you can actually break bonds.
00:04:07.730 --> 00:04:09.460
Let's see what it can do to some ozone?
00:04:09.460 --> 00:04:11.610
Same thing, it excites it so much
00:04:11.610 --> 00:04:13.710
that it can actually break the bond.
00:04:13.710 --> 00:04:17.020
It's exciting electrons so
much. I can keep resetting it.
00:04:17.020 --> 00:04:19.540
So the big picture here, the big takeaway.
00:04:19.540 --> 00:04:21.370
You could have microwave radiation,
00:04:21.370 --> 00:04:24.640
which tends to change the
rotational motion of a molecule.
00:04:24.640 --> 00:04:27.730
We saw that with the water molecules.
00:04:27.730 --> 00:04:29.800
You have infrared radiation,
00:04:29.800 --> 00:04:32.440
which is higher energy
and higher frequency,
00:04:32.440 --> 00:04:36.420
which tends to lead to a
change in vibrational motion.
00:04:36.420 --> 00:04:40.210
And then you have visible light,
which can excite electrons,
00:04:40.210 --> 00:04:41.700
take them to a higher energy state,
00:04:41.700 --> 00:04:44.530
and then be readmitted
when the electron goes back
00:04:44.530 --> 00:04:45.700
to its base state.
00:04:45.700 --> 00:04:47.780
And then you can have ultraviolet light,
00:04:47.780 --> 00:04:49.930
that's so powerful, it
can excite electrons
00:04:49.930 --> 00:04:53.153
so that in some cases it can
even break covalent bonds.
|
Real gases: Deviations from ideal behavior | https://www.youtube.com/watch?v=UABFOI1sb7A | vtt | https://www.youtube.com/api/timedtext?v=UABFOI1sb7A&ei=91WUZdmfIsG1mLAPtOSYsAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B2C1CF9598BE19655309D0652DD03B94914C6988.0C3ECA8C95279543629F77F9D0F45812130ED9DA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.760 --> 00:00:02.070
- [Instructor] We've
already spent some time
00:00:02.070 --> 00:00:05.710
looking at the ideal gas
law, and also thinking about
00:00:05.710 --> 00:00:08.420
scenarios where things might diverge
00:00:08.420 --> 00:00:11.130
from what at least the
ideal gas law might predict.
00:00:11.130 --> 00:00:12.610
And what we're going to do in this video
00:00:12.610 --> 00:00:14.670
is dig a little bit deeper into scenarios
00:00:14.670 --> 00:00:16.390
where we might diverge a little bit
00:00:16.390 --> 00:00:19.510
from the ideal gas law, or
maybe I guess, a lot of it
00:00:19.510 --> 00:00:21.540
in certain situations.
00:00:21.540 --> 00:00:23.620
So I have three scenarios here.
00:00:23.620 --> 00:00:25.960
This first scenario right over here,
00:00:25.960 --> 00:00:29.700
I have a high temperature,
high temperature,
00:00:29.700 --> 00:00:33.420
and I have a large volume.
00:00:33.420 --> 00:00:35.460
And both of these are really important
00:00:35.460 --> 00:00:37.810
because when we think
about when we get close
00:00:37.810 --> 00:00:41.670
to being ideal, that
situation's where the volume
00:00:41.670 --> 00:00:45.340
of the particles themselves
are negligible to the volume
00:00:45.340 --> 00:00:46.410
of the container.
00:00:46.410 --> 00:00:48.980
And at least here, looks
like that might be the case
00:00:48.980 --> 00:00:51.220
'cause we're dealing
with a very large volume.
00:00:51.220 --> 00:00:52.980
Even this isn't drawn to scale.
00:00:52.980 --> 00:00:54.480
I just drew the particles this size
00:00:54.480 --> 00:00:55.990
just so that you could see them.
00:00:55.990 --> 00:00:59.260
And high temperature,
that helps us realize
00:00:59.260 --> 00:01:02.760
that well maybe the
intermolecular interactions
00:01:02.760 --> 00:01:04.630
or attractions between the particles
00:01:04.630 --> 00:01:06.810
aren't going to be that significant.
00:01:06.810 --> 00:01:10.390
And so in a high temperature,
large volume scenario,
00:01:10.390 --> 00:01:14.290
this might be pretty close to ideal.
00:01:14.290 --> 00:01:15.830
Now it's not gonna be perfectly ideal
00:01:15.830 --> 00:01:18.440
because real gases have some volume,
00:01:18.440 --> 00:01:21.960
and they do have some
intermolecular interactions.
00:01:21.960 --> 00:01:24.290
But now let's change
things up a little bit.
00:01:24.290 --> 00:01:26.520
Let's now move to the same volume.
00:01:26.520 --> 00:01:28.703
So we're still dealing
with a large volume.
00:01:29.550 --> 00:01:31.870
But let's lower the temperature.
00:01:31.870 --> 00:01:34.050
So low temperature.
00:01:34.050 --> 00:01:36.190
And we can see because
temperature is proportional
00:01:36.190 --> 00:01:38.480
to average kinetic
energy of the particles,
00:01:38.480 --> 00:01:41.310
that here, these arrows on
average are a little bit smaller.
00:01:41.310 --> 00:01:42.930
And let's say we lower the temperature
00:01:42.930 --> 00:01:45.110
close to the condensation point.
00:01:45.110 --> 00:01:47.830
Remember, the condensation point of a gas,
00:01:47.830 --> 00:01:51.620
that's a situation where
the molecules are attracting
00:01:51.620 --> 00:01:53.810
each other, and even starting
to clump up together.
00:01:53.810 --> 00:01:55.930
They're starting to, if
we're thinking about say,
00:01:55.930 --> 00:01:59.360
water vapors, they're starting
to get into little droplets
00:01:59.360 --> 00:02:02.200
of liquid water, because
they're getting so attracted
00:02:02.200 --> 00:02:03.330
to each other.
00:02:03.330 --> 00:02:04.450
So in this situation,
00:02:04.450 --> 00:02:07.140
where we have just
lowered the temperature,
00:02:07.140 --> 00:02:10.520
the ideal gas law would already
predict that if you keep
00:02:10.520 --> 00:02:12.950
everything else constant, that
the pressure would go down.
00:02:12.950 --> 00:02:14.370
If we solve for pressure,
00:02:14.370 --> 00:02:18.620
we would have P is equal to nRT over V.
00:02:18.620 --> 00:02:20.570
So if you just lowered temperature,
00:02:20.570 --> 00:02:22.590
the ideal gas law would already predict
00:02:22.590 --> 00:02:24.680
that your pressure would be lower.
00:02:24.680 --> 00:02:27.520
But in this situation with a real gas,
00:02:27.520 --> 00:02:29.430
because we're close to
that condensation point,
00:02:29.430 --> 00:02:32.650
these gases, these particles
are more and more attracted
00:02:32.650 --> 00:02:33.483
to each other.
00:02:33.483 --> 00:02:35.790
So they're less likely
to bump into the sides
00:02:35.790 --> 00:02:36.960
of the container, or if they do,
00:02:36.960 --> 00:02:38.960
they're going to do it with less vigor.
00:02:38.960 --> 00:02:41.290
So in this situation for a real gas,
00:02:41.290 --> 00:02:44.290
because of the intermolecular attraction
00:02:44.290 --> 00:02:46.570
between the particles,
you would actually have
00:02:46.570 --> 00:02:50.440
a lower pressure than even the
ideal gas law would predict.
00:02:50.440 --> 00:02:52.040
Ideal gas law would already predict
00:02:52.040 --> 00:02:54.430
that if you lower the temperature,
pressure would go down.
00:02:54.430 --> 00:02:57.190
But you would see that a
real gas in this scenario,
00:02:57.190 --> 00:03:02.190
P, even lower, even lower for a real gas.
00:03:02.390 --> 00:03:04.110
Now let's go to another scenario.
00:03:04.110 --> 00:03:08.440
Let's go to a scenario where
we keep the high temperature
00:03:08.440 --> 00:03:10.910
that we had in the original scenario,
00:03:10.910 --> 00:03:15.910
but now we have a small
volume, small volume.
00:03:16.100 --> 00:03:19.210
Maybe this top of the
container is a piston,
00:03:19.210 --> 00:03:21.990
and we push it down like this.
00:03:21.990 --> 00:03:25.120
Well the ideal gas law, if
we just solve for P again,
00:03:25.120 --> 00:03:27.850
P is equal to nRT over V.
00:03:27.850 --> 00:03:29.040
It would already predict
00:03:29.040 --> 00:03:31.640
that if you decrease the denominator here,
00:03:31.640 --> 00:03:34.390
that's going to increase the
value of the entire expression.
00:03:34.390 --> 00:03:37.120
So it would already
predict that you would have
00:03:37.120 --> 00:03:40.460
a higher pressure, that
the particles will bounce
00:03:40.460 --> 00:03:42.870
into the sides of the
container more frequently,
00:03:42.870 --> 00:03:45.180
and with more vigor.
00:03:45.180 --> 00:03:47.660
But if we have a really small
volume of the container,
00:03:47.660 --> 00:03:49.630
we no longer can assume that the volume
00:03:49.630 --> 00:03:52.280
of the particles themselves
are going to be negligible
00:03:52.280 --> 00:03:54.120
compared to the volume of the container.
00:03:54.120 --> 00:03:57.310
And so the effective
volume, to move around in
00:03:57.310 --> 00:04:00.460
is even lower than we're
seeing in this equation.
00:04:00.460 --> 00:04:03.010
So these particles have even
less space to bounce around in
00:04:03.010 --> 00:04:05.240
because they take up some of the space.
00:04:05.240 --> 00:04:07.270
So they're going to bounce
off the sides of the container
00:04:07.270 --> 00:04:10.330
more frequently and even more vigor.
00:04:10.330 --> 00:04:15.330
So here, pressure even
higher for a real gas
00:04:15.630 --> 00:04:17.887
than what is predicted
by the ideal gas law.
|
7 Tips for Motivating Elementary School Kids During Distance Learning | https://www.youtube.com/watch?v=TqedL7WAT6M | vtt | https://www.youtube.com/api/timedtext?v=TqedL7WAT6M&ei=91WUZbK7GoSlvdIP_9CY8A4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E58646ACA5DB339EFDA7D45E9BEC93A83AAB1794.2D4B2325D015B59DD98ADAA497EFC429E56C4BEA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:09.670 --> 00:00:10.503
- Hi, everyone.
00:00:10.503 --> 00:00:12.790
Thank you for joining today on our webinar
00:00:12.790 --> 00:00:16.200
on 7 Tips for Motivating
Elementary School Kids
00:00:16.200 --> 00:00:17.700
During Distance Learning.
00:00:17.700 --> 00:00:19.070
Now, the tips we'll be sharing today
00:00:19.070 --> 00:00:20.210
are tailored to this moment,
00:00:20.210 --> 00:00:23.810
but they're really applicable
more broadly as needed.
00:00:23.810 --> 00:00:24.750
I'm Dan Tu,
00:00:24.750 --> 00:00:26.180
and I'll be kicking us off today
00:00:26.180 --> 00:00:28.940
as well as moderating the Q&A segment.
00:00:28.940 --> 00:00:30.380
But before we get started,
00:00:30.380 --> 00:00:33.530
we want to say a special thank
you to several organizations
00:00:33.530 --> 00:00:36.150
who have really helped us
with philanthropic support,
00:00:36.150 --> 00:00:39.300
enabling us to bring you
programming like today's session.
00:00:39.300 --> 00:00:41.870
So we want to say a special
thanks to Bank of America,
00:00:41.870 --> 00:00:44.290
Google.org, AT&T,
00:00:44.290 --> 00:00:46.500
Fastly, and Novartis.
00:00:46.500 --> 00:00:48.920
So I'd like to introduce
you all to Kristen DiCerbo,
00:00:48.920 --> 00:00:50.647
who will be walking
through the seven tips,
00:00:50.647 --> 00:00:53.195
and sharing her expert advice with you all
00:00:53.195 --> 00:00:55.580
while we answer your live questions.
00:00:55.580 --> 00:00:58.210
Kristen's our Chief Learning
Officer here at Khan Academy,
00:00:58.210 --> 00:00:59.930
and an expert in learning science.
00:00:59.930 --> 00:01:02.150
So if you have any
questions on today's topic,
00:01:02.150 --> 00:01:04.050
feel free to enter them into the chat.
00:01:04.050 --> 00:01:07.010
We have a team collecting
them for the Q&A portion,
00:01:07.010 --> 00:01:09.980
and all of this is going
to be recorded and posted.
00:01:09.980 --> 00:01:10.980
Since you've registered,
00:01:10.980 --> 00:01:12.990
this will automatically be emailed to you.
00:01:12.990 --> 00:01:15.860
So don't worry if you miss
anything or need to go back.
00:01:15.860 --> 00:01:17.833
So with that, Kristin, take it away.
00:01:19.080 --> 00:01:20.110
- Great, thanks.
00:01:20.110 --> 00:01:22.720
And thanks all of you for joining today.
00:01:22.720 --> 00:01:26.050
I'm going to spend about 15 minutes or so
00:01:26.050 --> 00:01:29.430
going through some of the
ideas and the research
00:01:29.430 --> 00:01:30.670
behind the tips,
00:01:30.670 --> 00:01:32.590
and then we'll open it up for questions,
00:01:32.590 --> 00:01:36.040
which I'm sure you all
have lots of in this time.
00:01:36.040 --> 00:01:38.060
So to start off with,
00:01:38.060 --> 00:01:40.140
as Dan said, I'm the
Chief Learning Officer,
00:01:40.140 --> 00:01:42.560
and one of my roles is to bring research
00:01:42.560 --> 00:01:46.360
about learning motivation
to our understanding
00:01:46.360 --> 00:01:47.690
of how to help students learn.
00:01:47.690 --> 00:01:51.040
So all of that that you'll
see here is based on
00:01:51.040 --> 00:01:53.960
what we understand about
motivation from research
00:01:53.960 --> 00:01:56.410
about how to keep kids motivated.
00:01:56.410 --> 00:01:59.743
And one of the first things to understand
00:01:59.743 --> 00:02:03.210
is that we can really boil
down a lot of the research
00:02:03.210 --> 00:02:06.372
on motivation to a pretty simple formula.
00:02:06.372 --> 00:02:09.970
We like to do things when first,
00:02:09.970 --> 00:02:12.410
we think we're gonna
be successful at them,
00:02:12.410 --> 00:02:16.640
and second, when we
think there's some value
00:02:16.640 --> 00:02:18.340
to doing that activity,
00:02:18.340 --> 00:02:20.070
which probably makes sense for you
00:02:20.070 --> 00:02:21.670
just as much as it does for your kids.
00:02:21.670 --> 00:02:23.287
Who wants to do something when you think,
00:02:23.287 --> 00:02:25.890
"Oh, I'm probably gonna fail at this"?
00:02:25.890 --> 00:02:27.290
You're not likely to do it.
00:02:27.290 --> 00:02:29.760
And second, you think
you want to do things
00:02:29.760 --> 00:02:31.070
that are important to you.
00:02:31.070 --> 00:02:34.970
And so, as we think about
how to motivate our kids,
00:02:34.970 --> 00:02:37.350
we can think about how
can I help them feel
00:02:37.350 --> 00:02:39.130
like they're likely to be successful
00:02:39.130 --> 00:02:41.210
and how can I help them
see some of the value
00:02:41.210 --> 00:02:42.350
in this activity?
00:02:42.350 --> 00:02:45.680
And so this kind of simple
formula drives a lot of the tips
00:02:45.680 --> 00:02:47.910
that I'm gonna be talking about.
00:02:47.910 --> 00:02:51.030
And one of the biggest
ways to help kids feel
00:02:51.030 --> 00:02:54.020
like they can be successful
at doing something
00:02:54.020 --> 00:02:57.090
is to help them experience some success.
00:02:57.090 --> 00:03:00.870
And one really good way to
do that is to set goals,
00:03:00.870 --> 00:03:03.530
because goals, by definition,
00:03:03.530 --> 00:03:06.390
help us see that we're making progress.
00:03:06.390 --> 00:03:09.290
And so, as you think about
this with elementary-aged kids,
00:03:09.290 --> 00:03:11.600
you want to set really short-term goals.
00:03:11.600 --> 00:03:14.130
So if you're talking
kindergartners or first graders,
00:03:14.130 --> 00:03:16.207
it could be something as simple as,
00:03:16.207 --> 00:03:17.923
"Hey, this afternoon,
00:03:17.923 --> 00:03:21.400
we're going to read this book together,"
00:03:21.400 --> 00:03:24.323
or "We're going to write three sentences."
00:03:24.323 --> 00:03:26.330
What are those things
that you want to work on
00:03:26.330 --> 00:03:28.180
just very short-term?
00:03:28.180 --> 00:03:29.497
And then at the end you can say,
00:03:29.497 --> 00:03:31.560
"Yes, look, we said we were going to try
00:03:31.560 --> 00:03:33.270
to write three sentences.
00:03:33.270 --> 00:03:35.490
We wrote four sentences."
00:03:35.490 --> 00:03:37.640
There's an experience of success.
00:03:37.640 --> 00:03:39.820
As kids get a little older,
you can stretch it out.
00:03:39.820 --> 00:03:41.060
You can think about in the morning
00:03:41.060 --> 00:03:42.700
setting goals for the day.
00:03:42.700 --> 00:03:45.630
You can think about
maybe setting a longer,
00:03:45.630 --> 00:03:49.900
maybe a week goal that then you
break down into daily goals.
00:03:49.900 --> 00:03:51.880
And the other piece that
when you're setting goals
00:03:51.880 --> 00:03:54.220
is to help kids think about
how they're gonna know
00:03:54.220 --> 00:03:55.520
if they're on track.
00:03:55.520 --> 00:03:58.560
So then one of the important pieces here
00:03:58.560 --> 00:04:01.290
in both goal setting and monitoring
00:04:01.290 --> 00:04:02.470
and making sure they're on track is
00:04:02.470 --> 00:04:03.680
to bring the kids into it.
00:04:03.680 --> 00:04:06.823
So instead of you saying,
"Our goal is this,"
00:04:06.823 --> 00:04:08.407
have the conversation and say,
00:04:08.407 --> 00:04:11.330
"So we want to set a goal
about writing sentences.
00:04:11.330 --> 00:04:14.100
How many sentences do you
think you can write today?"
00:04:14.100 --> 00:04:18.550
So think about helping
them set realistic goals,
00:04:18.550 --> 00:04:20.670
and that's then gonna help them be able
00:04:20.670 --> 00:04:23.040
to also not just see success,
00:04:23.040 --> 00:04:25.040
but also they're going to
value the activity more
00:04:25.040 --> 00:04:28.930
because they owned some
of the goal setting
00:04:28.930 --> 00:04:30.350
that went along with it.
00:04:30.350 --> 00:04:34.290
And so you get actually the
double plus there of thinking
00:04:34.290 --> 00:04:37.660
about both success and
value of the activity.
00:04:37.660 --> 00:04:38.850
So very strong.
00:04:38.850 --> 00:04:41.250
And that's why I encourage
a lot of goal setting
00:04:41.250 --> 00:04:43.010
and thinking about how to do that.
00:04:43.010 --> 00:04:44.230
But then when you meet them,
00:04:44.230 --> 00:04:46.730
definitely celebrate that success.
00:04:46.730 --> 00:04:51.530
So this can be everything from
high fives to thinking about,
00:04:51.530 --> 00:04:54.440
you know, small, different
things that kids like to do
00:04:54.440 --> 00:04:56.810
that they might find successful.
00:04:56.810 --> 00:04:59.110
We do everything online from, you know,
00:04:59.110 --> 00:05:03.060
a little online confetti to
all kinds of things that just,
00:05:03.060 --> 00:05:06.033
you know, recognize that
there's an achievement there.
00:05:06.970 --> 00:05:09.237
Also, this can be a good time to reflect.
00:05:09.237 --> 00:05:11.900
"Hey, what was it that
helped you be successful
00:05:11.900 --> 00:05:12.840
in meeting that goal?"
00:05:12.840 --> 00:05:15.670
And "Hey, was there a time
when you were trying to do this
00:05:15.670 --> 00:05:18.270
and it was hard and how
did you get over that?
00:05:18.270 --> 00:05:20.990
How did you get through the
place where you were stuck?"
00:05:20.990 --> 00:05:24.010
And that kind of reflection
helps them then think about,
00:05:24.010 --> 00:05:26.950
hey, next time they get
stuck, what might be the,
00:05:26.950 --> 00:05:28.140
what might be some strategies
00:05:28.140 --> 00:05:30.420
that they could do and work on.
00:05:30.420 --> 00:05:34.083
So definitely tip two is
celebrate those successes.
00:05:35.410 --> 00:05:37.730
Then thinking about those roadblocks,
00:05:37.730 --> 00:05:42.730
think about how you can help
your children have strategies
00:05:42.880 --> 00:05:47.030
for when they're going
to get into that place
00:05:47.030 --> 00:05:48.080
where they don't know what to do.
00:05:48.080 --> 00:05:49.730
And that's going to happen
when you're learning,
00:05:49.730 --> 00:05:51.880
because learning is hard.
00:05:51.880 --> 00:05:54.110
And when you're actually
engaged in learning,
00:05:54.110 --> 00:05:57.840
your learning edge, right when
you're learning new things,
00:05:57.840 --> 00:05:59.900
we know that often you
need a little bit of help
00:05:59.900 --> 00:06:00.760
to get over that.
00:06:00.760 --> 00:06:03.420
But what you want to do is
for your kids to have a plan
00:06:03.420 --> 00:06:06.950
for what to do so they don't
get frustrated in that moment.
00:06:06.950 --> 00:06:09.820
And before they get frustrated,
you want to make the plan.
00:06:09.820 --> 00:06:13.300
So this can be everything
from asking you for help.
00:06:13.300 --> 00:06:16.655
If you're also, say, working
from home at the same time
00:06:16.655 --> 00:06:18.930
your kids are in school, you
might want to think about,
00:06:18.930 --> 00:06:20.870
okay, how do you signal to your kids
00:06:20.870 --> 00:06:22.850
when it's okay to come
to you and ask for help
00:06:22.850 --> 00:06:23.970
and when they should wait,
00:06:23.970 --> 00:06:25.560
and what does that look like?
00:06:25.560 --> 00:06:28.140
Are there ways they can
ask their friends for help?
00:06:28.140 --> 00:06:30.780
How do they reach out to their teacher
00:06:30.780 --> 00:06:33.070
in this kind of place?
00:06:33.070 --> 00:06:35.350
So come up with a list of things
00:06:35.350 --> 00:06:37.840
that you might be able to work through
00:06:37.840 --> 00:06:39.527
to help your kids think about,
00:06:39.527 --> 00:06:40.660
"Hey, if I'm stuck,
00:06:40.660 --> 00:06:42.790
what are things I can do to get unstuck?"
00:06:42.790 --> 00:06:45.790
So you get before they get
to the place of frustration,
00:06:45.790 --> 00:06:47.393
they have strategies to use.
00:06:48.610 --> 00:06:51.010
After that, think about emphasizing
00:06:51.010 --> 00:06:53.130
that effort leads to success.
00:06:53.130 --> 00:06:55.810
And there's been a lot of writing recently
00:06:55.810 --> 00:07:00.420
about growth mindset and this
idea that if you work hard,
00:07:00.420 --> 00:07:02.770
your brain is like a muscle.
00:07:02.770 --> 00:07:04.560
And the more you work at it,
00:07:04.560 --> 00:07:07.900
the more it's ready to learn new things.
00:07:07.900 --> 00:07:11.280
And there's actually
physiology in your brain.
00:07:11.280 --> 00:07:13.390
The cells in your brain
are called neurons.
00:07:13.390 --> 00:07:14.470
And when we learn new things,
00:07:14.470 --> 00:07:17.530
it makes new connections to new neurons.
00:07:17.530 --> 00:07:21.000
And that in itself then helps you remember
00:07:21.000 --> 00:07:22.350
the things that you've learned.
00:07:22.350 --> 00:07:25.040
It makes you a stronger, better learner.
00:07:25.040 --> 00:07:28.930
All of that is better in a better message.
00:07:28.930 --> 00:07:30.150
And research shows,
00:07:30.150 --> 00:07:32.820
kids who understand and get
some of that understanding
00:07:32.820 --> 00:07:34.520
of how their brain works
00:07:34.520 --> 00:07:37.607
actually do persist more
than students who just say,
00:07:37.607 --> 00:07:41.020
"Hey, keep trying, hey, keep going."
00:07:41.020 --> 00:07:43.210
And so actually at Khan Academy,
00:07:43.210 --> 00:07:45.630
we have a growth mindset course
00:07:45.630 --> 00:07:47.440
where we have a couple of videos
00:07:47.440 --> 00:07:50.070
that explain some of
this in language for kids
00:07:50.070 --> 00:07:53.450
to understand that can
be good to just, again,
00:07:53.450 --> 00:07:56.350
start thinking of those
messages that your brain
00:07:56.350 --> 00:07:58.750
is like other muscles and
it needs to keep practicing
00:07:58.750 --> 00:07:59.940
and keep learning new things.
00:07:59.940 --> 00:08:02.703
That'll actually make you
better and a better learner.
00:08:03.560 --> 00:08:04.940
So that's the fourth tip,
00:08:04.940 --> 00:08:07.183
thinking about effort leading to success.
00:08:08.470 --> 00:08:11.210
The fifth one is to
engage their curiosity.
00:08:11.210 --> 00:08:14.631
So lots of kids are curious
about different things
00:08:14.631 --> 00:08:17.300
that happen in the world.
00:08:17.300 --> 00:08:19.930
It could be when they're
riding their bikes
00:08:19.930 --> 00:08:21.910
and they're thinking, "How does, you know,
00:08:21.910 --> 00:08:25.260
pushing on this pedal actually
make the wheels turn?"
00:08:25.260 --> 00:08:27.650
any of those kinds of questions.
00:08:27.650 --> 00:08:30.070
It's okay if you don't know the answer.
00:08:30.070 --> 00:08:32.210
Think about how you can find out answers
00:08:32.210 --> 00:08:33.980
to those things together.
00:08:33.980 --> 00:08:35.310
And when we think about kids
00:08:35.310 --> 00:08:37.150
that are curious about the world,
00:08:37.150 --> 00:08:39.180
those are the kids that keep learning
00:08:39.180 --> 00:08:41.860
and keep trying to find new things.
00:08:41.860 --> 00:08:44.560
And so you want to encourage
those kinds of questions.
00:08:44.560 --> 00:08:47.460
You can also model asking
those kinds of questions.
00:08:47.460 --> 00:08:49.830
So as you're doing
things around the house,
00:08:49.830 --> 00:08:52.150
or as you're doing things outside,
00:08:52.150 --> 00:08:54.790
asking questions about how the world works
00:08:54.790 --> 00:08:57.130
and thinking about, "Hey,
did you ever wonder,"
00:08:57.130 --> 00:08:59.620
and "How can you find
the answers to those?"
00:08:59.620 --> 00:09:02.440
All of those help build up
that internal motivation
00:09:02.440 --> 00:09:04.963
to find answers and understand the world.
00:09:07.720 --> 00:09:10.610
The sixth tip I have is
to establish relevance.
00:09:10.610 --> 00:09:12.540
So it relates to what I was just saying
00:09:12.540 --> 00:09:15.120
about linking things to the world.
00:09:15.120 --> 00:09:17.160
But the other way to do this is
00:09:17.160 --> 00:09:19.210
think about what your kids are learning
00:09:19.210 --> 00:09:21.780
and help them link that to things
00:09:21.780 --> 00:09:23.040
that are of interest to them.
00:09:23.040 --> 00:09:25.470
You know your kid's
interests better, really,
00:09:25.470 --> 00:09:27.200
than even their teachers do.
00:09:27.200 --> 00:09:30.990
So if you can think about
how do I help them see
00:09:30.990 --> 00:09:34.010
how this relates to a hobby
that they're interested in?
00:09:34.010 --> 00:09:35.950
How does this relate to
something they want to be
00:09:35.950 --> 00:09:37.140
when they grow up?
00:09:37.140 --> 00:09:40.210
How does this relate to something
we talked about yesterday?
00:09:40.210 --> 00:09:44.330
All of those things help
students establish the value
00:09:44.330 --> 00:09:45.590
of what they're learning.
00:09:45.590 --> 00:09:47.080
So if we go back to that equation,
00:09:47.080 --> 00:09:50.100
that second piece of
why should I learn this,
00:09:50.100 --> 00:09:52.420
what is this going to help me do,
00:09:52.420 --> 00:09:54.790
how does this relate to
things I'm interested in,
00:09:54.790 --> 00:09:57.380
if you can help make those connections,
00:09:57.380 --> 00:09:59.020
kids will value the activity more
00:09:59.020 --> 00:10:01.170
and be more likely to
want to engage in it.
00:10:02.380 --> 00:10:04.550
And finally, the seventh tip.
00:10:04.550 --> 00:10:07.647
I hear lots of concerns and we
get lots of questions about,
00:10:07.647 --> 00:10:09.490
"Should I use rewards?
00:10:09.490 --> 00:10:12.730
I don't want to be bribing
my student to work."
00:10:12.730 --> 00:10:17.650
And I would say rewards are
absolutely a part of what we do
00:10:17.650 --> 00:10:19.360
and how we reward ourselves.
00:10:19.360 --> 00:10:21.280
Even those of us who, you know,
00:10:21.280 --> 00:10:23.834
are successful and are
good students have tricks
00:10:23.834 --> 00:10:26.670
to keep ourselves motivated.
00:10:26.670 --> 00:10:31.555
I often say and do, when
I'm writing, I will say,
00:10:31.555 --> 00:10:34.380
"If I write one page here,
00:10:34.380 --> 00:10:36.554
I'll reward myself with
a piece of chocolate."
00:10:36.554 --> 00:10:38.420
You know, all of that is fine,
00:10:38.420 --> 00:10:40.420
but you want to think about
how to do this wisely.
00:10:40.420 --> 00:10:43.880
So the danger of rewards is sometimes
00:10:43.880 --> 00:10:47.580
that if a kid is already
interested in doing something,
00:10:47.580 --> 00:10:50.290
like it's already bringing
them happiness and joy,
00:10:50.290 --> 00:10:54.580
and you start rewarding it
with external things like candy
00:10:54.580 --> 00:10:56.150
and those kinds of things,
00:10:56.150 --> 00:10:57.850
they start to lose, actually,
00:10:57.850 --> 00:11:00.227
some of their internal
motivation and start thinking,
00:11:00.227 --> 00:11:02.930
"Oh, I'm just doing this for the reward."
00:11:02.930 --> 00:11:04.880
So that's what we want to avoid.
00:11:04.880 --> 00:11:07.240
But rewards can be really good for things
00:11:07.240 --> 00:11:10.120
that students just
don't want to do at all,
00:11:10.120 --> 00:11:13.350
but need a little bit of
kickstart to get going,
00:11:13.350 --> 00:11:15.580
and then maybe experience
some of the success,
00:11:15.580 --> 00:11:17.770
experience meeting a goal in it,
00:11:17.770 --> 00:11:19.600
to get from thinking about
00:11:19.600 --> 00:11:22.300
how we can use those extrinsic rewards
00:11:22.300 --> 00:11:24.457
to getting to more of those intrinsic,
00:11:24.457 --> 00:11:26.770
"Oh, actually I am good at this.
00:11:26.770 --> 00:11:28.440
I can learn math."
00:11:28.440 --> 00:11:30.900
Those extrinsic rewards
are really good at that.
00:11:30.900 --> 00:11:33.280
And they don't have to be things.
00:11:33.280 --> 00:11:35.680
They can be picking what's for dinner.
00:11:35.680 --> 00:11:39.120
They can be picking
which TV show you watch,
00:11:39.120 --> 00:11:42.840
spending, you know, another
15 minutes of screen time,
00:11:42.840 --> 00:11:44.800
taking a walk with you,
00:11:44.800 --> 00:11:47.150
having some of your time individually,
00:11:47.150 --> 00:11:49.576
all of those things are good rewards.
00:11:49.576 --> 00:11:52.940
And it's also good to ask your kids
00:11:52.940 --> 00:11:54.120
what's rewarding to them,
00:11:54.120 --> 00:11:56.600
what would they like to
be rewards for things
00:11:56.600 --> 00:12:00.100
that meeting goals and making progress.
00:12:00.100 --> 00:12:01.050
And that way, again,
00:12:01.050 --> 00:12:02.600
you're making sure you've got something
00:12:02.600 --> 00:12:06.220
that's meaningful to them
and helping them learn
00:12:06.220 --> 00:12:08.860
how to think about rewarding themselves.
00:12:08.860 --> 00:12:11.470
And when they need to
get a little extra kick
00:12:11.470 --> 00:12:14.799
to get something done,
to be able to think about
00:12:14.799 --> 00:12:18.160
how to use rewards wisely for themselves.
00:12:18.160 --> 00:12:22.320
So that said, that
gives us our seven tips,
00:12:22.320 --> 00:12:26.450
thinking about setting goals
and monitoring progress,
00:12:26.450 --> 00:12:31.450
celebrating success, help your
kids manage those roadblocks,
00:12:31.562 --> 00:12:35.350
emphasize that effort leads to success,
00:12:35.350 --> 00:12:39.620
encourage curiosity, establish relevance,
00:12:39.620 --> 00:12:41.853
and use rewards wisely.
00:12:42.700 --> 00:12:44.660
So with that,
00:12:44.660 --> 00:12:45.670
I'm going to open it up,
00:12:45.670 --> 00:12:48.240
because I'm sure there are
specific questions that you have
00:12:48.240 --> 00:12:49.870
about your situations
00:12:49.870 --> 00:12:52.320
and how to deal with some of the things,
00:12:52.320 --> 00:12:54.320
the specifics that you're facing.
00:12:54.320 --> 00:12:57.643
So would be glad to
hear some of those, Dan?
00:12:58.510 --> 00:13:00.380
- Yeah, well, so before we get to that,
00:13:00.380 --> 00:13:02.930
just a couple of things
that we'd all ask you to do.
00:13:02.930 --> 00:13:06.250
First, there's, in the handout
section of the webinar,
00:13:06.250 --> 00:13:09.910
you can download a printable
version of these seven tips.
00:13:09.910 --> 00:13:12.000
That's available in the download section.
00:13:12.000 --> 00:13:13.090
And again, if you registered
00:13:13.090 --> 00:13:15.190
and you're actually
watching this live now,
00:13:15.190 --> 00:13:18.320
once this video, this webinar's over,
00:13:18.320 --> 00:13:20.980
you'll get an email with the
recording of this webinar,
00:13:20.980 --> 00:13:23.420
as well as a link to the downloadable.
00:13:23.420 --> 00:13:24.970
So again, if you want to go back
00:13:24.970 --> 00:13:28.530
and both watch any of
the tips in particular
00:13:28.530 --> 00:13:31.390
or read about them, that'll
be available to you.
00:13:31.390 --> 00:13:32.440
And then secondly,
00:13:32.440 --> 00:13:34.970
go ahead and start putting in
any of the questions you have.
00:13:34.970 --> 00:13:36.840
Even specific examples would be great.
00:13:36.840 --> 00:13:37.970
And we'll try to get through
00:13:37.970 --> 00:13:40.540
as many of them as possible.
00:13:40.540 --> 00:13:41.740
So with that, Kristen,
00:13:41.740 --> 00:13:44.680
the first question we
have is from Rebecca.
00:13:44.680 --> 00:13:46.640
And I think you mentioned
this in terms of tip,
00:13:46.640 --> 00:13:48.580
I believe it's tip number six.
00:13:48.580 --> 00:13:51.280
How can you help kids feel
like what they're learning
00:13:51.280 --> 00:13:54.160
in school and what they
do is really relevant
00:13:54.160 --> 00:13:55.393
to their lives?
00:13:57.370 --> 00:14:02.370
- So the biggest thing here is
to think about understanding
00:14:03.470 --> 00:14:06.150
what is interesting to your kids.
00:14:06.150 --> 00:14:08.800
So what are things that
they're interested in
00:14:08.800 --> 00:14:11.710
is the first piece and then
relating things to them.
00:14:11.710 --> 00:14:15.620
So the most common place
we hear this is in math.
00:14:15.620 --> 00:14:16.850
And so there's some things
00:14:16.850 --> 00:14:20.930
that are pretty easy relatable to math.
00:14:20.930 --> 00:14:22.880
So one thing is cooking.
00:14:22.880 --> 00:14:25.360
Cooking, it turns out,
involves a lot of math,
00:14:25.360 --> 00:14:27.640
specifically, a lot of fractions.
00:14:27.640 --> 00:14:30.550
There can be, you know, if
you're doing a double batch,
00:14:30.550 --> 00:14:33.050
how do you think about
doubling a fraction?
00:14:33.050 --> 00:14:34.680
What does that look like?
00:14:34.680 --> 00:14:38.210
Thinking about how that actually applies,
00:14:38.210 --> 00:14:42.480
the things that they're doing
apply to their daily life.
00:14:42.480 --> 00:14:45.750
So cooking is always a good example
00:14:45.750 --> 00:14:48.520
for a lot of math issues.
00:14:48.520 --> 00:14:51.630
There are also things
that you can think about.
00:14:51.630 --> 00:14:54.430
What do they want to be when they grow up?
00:14:54.430 --> 00:14:57.140
Maybe they don't know. That's okay, too.
00:14:57.140 --> 00:15:00.360
You can think about what kinds of careers
00:15:00.360 --> 00:15:04.550
are the skills they're learning good for.
00:15:04.550 --> 00:15:06.470
So, hey, these are the kinds of things,
00:15:06.470 --> 00:15:10.130
I know we don't know what you
want to be when you grow up.
00:15:10.130 --> 00:15:12.213
You haven't decided what you
want to be when you grow up.
00:15:12.213 --> 00:15:15.380
It's a good idea to kind of
experience a bunch of different,
00:15:15.380 --> 00:15:18.140
find out about a bunch of
different possibilities.
00:15:18.140 --> 00:15:21.368
So, "Hey, this thing
that we're learning now,
00:15:21.368 --> 00:15:23.300
it turns out that this is something
00:15:23.300 --> 00:15:24.530
that accountants use a lot,"
00:15:24.530 --> 00:15:28.933
or "This is something that
someone who's doing a lot of,
00:15:30.450 --> 00:15:34.850
who's an oceanographer learns
a lot about these topics
00:15:34.850 --> 00:15:37.154
that you're learning
about in science today,
00:15:37.154 --> 00:15:40.090
thinking about those,
the kinds of careers,
00:15:40.090 --> 00:15:42.950
that link to the different
things that they're learning
00:15:42.950 --> 00:15:46.590
is another way to bring
some of this to life.
00:15:46.590 --> 00:15:48.960
And I would also not hesitate to reach out
00:15:48.960 --> 00:15:51.967
to your kids' teachers for
help in thinking about,
00:15:51.967 --> 00:15:55.720
"Hey, can you give us a
preview of what's coming?"
00:15:55.720 --> 00:15:58.420
And what do they think
are good ways to help them
00:15:58.420 --> 00:16:01.430
relate that to things
they see in their lives?
00:16:01.430 --> 00:16:03.620
But there's lots of things
in our everyday lives.
00:16:03.620 --> 00:16:05.520
I gave the bicycle example.
00:16:05.520 --> 00:16:08.570
It turns out that's all about
simple machines and pulleys
00:16:08.570 --> 00:16:09.920
and chains and all of that.
00:16:09.920 --> 00:16:13.820
So all of those kinds of
examples of how the world works,
00:16:13.820 --> 00:16:16.240
we can find things that kids are learning
00:16:16.240 --> 00:16:17.587
that relate to them.
00:16:17.587 --> 00:16:20.040
But it takes some work, I will admit.
00:16:20.040 --> 00:16:20.930
- No, that's great, Kristen.
00:16:20.930 --> 00:16:23.100
I would say like one thing, as well, is
00:16:23.100 --> 00:16:25.330
use all of your senses as a parent.
00:16:25.330 --> 00:16:27.530
Like there are things that
the child might not tell you,
00:16:27.530 --> 00:16:29.110
like they want to do this,
they want to do that.
00:16:29.110 --> 00:16:30.890
But you know, your child best.
00:16:30.890 --> 00:16:33.850
And if you know that they love
doing this activity, yeah,
00:16:33.850 --> 00:16:35.900
and just be observant of
that and try to relate that
00:16:35.900 --> 00:16:38.643
back to the, again, back to the subject.
00:16:39.960 --> 00:16:40.793
Cool.
00:16:40.793 --> 00:16:44.090
So Kristen, we have a
question from Jay Tinder.
00:16:44.090 --> 00:16:46.590
Apologies if I mispronounce the name.
00:16:46.590 --> 00:16:49.280
Any tips for helping motivate
elementary kids transitioning
00:16:49.280 --> 00:16:51.580
to middle school in a
distance learning environment?
00:16:51.580 --> 00:16:54.750
So really that transition
period, meeting new friends,
00:16:54.750 --> 00:16:55.583
those types of things.
00:16:55.583 --> 00:16:57.333
So any advice you have there.
00:16:58.840 --> 00:17:01.310
- So there's a number of
things that go on when kids
00:17:01.310 --> 00:17:02.810
transition to middle school.
00:17:02.810 --> 00:17:04.870
So you mentioned, Dan,
meeting new friends.
00:17:04.870 --> 00:17:08.490
There's also kids that are
taking on and required to take on
00:17:08.490 --> 00:17:10.490
a little bit more ownership,
00:17:10.490 --> 00:17:12.840
a little bit more self responsibility.
00:17:12.840 --> 00:17:14.030
And it's in,
00:17:14.030 --> 00:17:15.610
when we talk about distance learning,
00:17:15.610 --> 00:17:17.710
one of the things we know
about distance learning is
00:17:17.710 --> 00:17:19.300
that kids who are best at it
00:17:19.300 --> 00:17:22.630
are kids who are what we
call self-regulated learners.
00:17:22.630 --> 00:17:23.463
So those are kids
00:17:23.463 --> 00:17:25.680
that are actually
capable of setting goals,
00:17:25.680 --> 00:17:28.930
capable of monitoring their own progress,
00:17:28.930 --> 00:17:33.563
kids that can create, organize
schedules for themselves.
00:17:35.080 --> 00:17:38.470
Those are all skills that
you can help your child with.
00:17:38.470 --> 00:17:40.870
So think about helping them set up,
00:17:40.870 --> 00:17:43.880
what is their schedule for the day.
00:17:43.880 --> 00:17:46.330
Because the other piece that
often happens in middle school
00:17:46.330 --> 00:17:48.220
is you start switching teachers.
00:17:48.220 --> 00:17:50.450
Where in elementary
school, you just had one,
00:17:50.450 --> 00:17:52.200
now you have multiple teachers.
00:17:52.200 --> 00:17:53.610
So help your child think about
00:17:53.610 --> 00:17:56.100
how do they set out a schedule
of what the day looks like
00:17:56.100 --> 00:17:59.500
so they make sure to know
what the expectations are.
00:17:59.500 --> 00:18:04.440
Help them think about and let
them be part of the process.
00:18:04.440 --> 00:18:05.790
Let them, you know,
00:18:05.790 --> 00:18:08.820
you can maybe give them a
skeleton and let them fill it out.
00:18:08.820 --> 00:18:11.250
And next time they create what the,
00:18:11.250 --> 00:18:13.640
next week they create what
the schedule looks like.
00:18:13.640 --> 00:18:17.260
So kind of gradually
pulling back from the things
00:18:17.260 --> 00:18:19.737
that you're doing and letting
them have some ownership
00:18:19.737 --> 00:18:21.410
and some agency.
00:18:21.410 --> 00:18:24.480
And it turns out that a lot of kids
00:18:24.480 --> 00:18:25.690
are really motivated by that.
00:18:25.690 --> 00:18:27.790
If they know that you've
kind of got them there
00:18:27.790 --> 00:18:31.417
as a safety net and that you're
there to kind of catch them
00:18:31.417 --> 00:18:33.410
if things get too rough.
00:18:33.410 --> 00:18:36.180
So I would say, give them
a little bit more agency.
00:18:36.180 --> 00:18:38.750
They're going to then find more ownership
00:18:38.750 --> 00:18:40.210
in valuing the activities
00:18:40.210 --> 00:18:43.440
because they're driving
them and choosing them.
00:18:43.440 --> 00:18:46.150
And help them see that
00:18:46.150 --> 00:18:48.700
and take on a little bit
more of that ownership.
00:18:48.700 --> 00:18:50.329
Dan, you mentioned, you know,
00:18:50.329 --> 00:18:53.730
the pieces about making new friends,
00:18:53.730 --> 00:18:55.700
and often middle schools
are bringing together
00:18:55.700 --> 00:18:57.220
a bunch of elementary schools.
00:18:57.220 --> 00:18:58.650
And now that we're at distance,
00:18:58.650 --> 00:19:02.790
it's so difficult to create
some of those peer connections.
00:19:02.790 --> 00:19:05.250
And peers start to become
more and more important
00:19:05.250 --> 00:19:07.480
for kids at this age level.
00:19:07.480 --> 00:19:10.880
So the more you can help facilitate things
00:19:10.880 --> 00:19:12.610
in this distance environment,
00:19:12.610 --> 00:19:15.690
we're really limited, but
facilitating, you know,
00:19:15.690 --> 00:19:18.570
at least calls or Hangouts,
00:19:18.570 --> 00:19:22.300
ways for kids to informally
connect with each other
00:19:22.300 --> 00:19:26.000
and be able to do some
activities together online
00:19:26.000 --> 00:19:29.420
that maybe they wouldn't be
able to do in person these days,
00:19:29.420 --> 00:19:33.020
but to help keep some of
those peer relationships going
00:19:33.020 --> 00:19:36.440
and to try to build them
in these new places.
00:19:36.440 --> 00:19:39.164
But understand the other piece you may do
00:19:39.164 --> 00:19:41.927
is to empathize with your kids and say,
00:19:41.927 --> 00:19:44.060
"I know this is tough right now,
00:19:44.060 --> 00:19:47.270
and this is going to be difficult
as we're moving forward.
00:19:47.270 --> 00:19:48.660
I know you miss your friends,"
00:19:48.660 --> 00:19:52.170
and just give them a
chance to share with you
00:19:52.170 --> 00:19:54.380
and to express some of
what they're feeling, too,
00:19:54.380 --> 00:19:57.063
as they're kind of making
some of these transitions.
00:19:57.930 --> 00:19:59.630
- Yeah, I think that's
a great point, Kristen,
00:19:59.630 --> 00:20:00.463
great points.
00:20:00.463 --> 00:20:02.200
I think when you transition
to middle school,
00:20:02.200 --> 00:20:03.720
not only do you have more teachers,
00:20:03.720 --> 00:20:06.420
but you have to control
your schedules more,
00:20:06.420 --> 00:20:08.110
you know, which classrooms
are you going to when.
00:20:08.110 --> 00:20:10.340
So you're learning a lot of like agency
00:20:10.340 --> 00:20:12.960
and being responsible and
getting to class on time.
00:20:12.960 --> 00:20:13.793
And like you said,
00:20:13.793 --> 00:20:16.260
you're meeting like tons of
new kids from different schools
00:20:16.260 --> 00:20:19.020
that you're going to at the same time.
00:20:19.020 --> 00:20:22.763
So I do think there's a lot
of challenges for those kids.
00:20:23.750 --> 00:20:24.583
- Absolutely.
00:20:24.583 --> 00:20:27.420
And if you can pinpoint which
things your kid is good at
00:20:27.420 --> 00:20:28.530
and highlight those
00:20:28.530 --> 00:20:31.010
and find out where some
of the weaknesses are
00:20:31.010 --> 00:20:32.860
and help support those,
00:20:32.860 --> 00:20:36.670
that's a good way for
you to help support them
00:20:36.670 --> 00:20:38.570
and tailor it to what their needs are.
00:20:39.920 --> 00:20:41.550
- So we have a question from Dora.
00:20:41.550 --> 00:20:42.650
I think we get,
00:20:42.650 --> 00:20:44.000
we hear this question a lot,
00:20:44.000 --> 00:20:45.700
is how do you manage roadblocks?
00:20:45.700 --> 00:20:47.720
So when your child has self-doubt
00:20:47.720 --> 00:20:50.090
or developing low self esteem,
00:20:50.090 --> 00:20:52.600
especially in this distance
learning environment,
00:20:52.600 --> 00:20:53.900
how do you manage those
00:20:53.900 --> 00:20:56.000
and help the child overcome those moments?
00:20:57.160 --> 00:21:00.760
- Yeah, so kids who are, you know,
00:21:00.760 --> 00:21:03.450
not feeling like they're learners
00:21:03.450 --> 00:21:05.900
or they're feeling like,
"Math is not for me.
00:21:05.900 --> 00:21:09.250
I'm not, you know, not
good at these things.
00:21:09.250 --> 00:21:10.900
I don't know how to do this,"
00:21:10.900 --> 00:21:15.390
all of those are things
where kids can really benefit
00:21:15.390 --> 00:21:19.280
from things like the growth mindset piece
00:21:19.280 --> 00:21:20.360
that I was talking about.
00:21:20.360 --> 00:21:24.840
This idea that none of us
is fixed in our ability
00:21:24.840 --> 00:21:25.960
to do things.
00:21:25.960 --> 00:21:30.433
We can always get better and
getting better takes work.
00:21:30.433 --> 00:21:34.677
But it's actually pretty
rewarding when you start to see,
00:21:34.677 --> 00:21:39.040
"Hey, I used to be able to do
this and now I can do this.
00:21:39.040 --> 00:21:40.650
Here's a new thing that I can do now
00:21:40.650 --> 00:21:42.250
that I couldn't do before."
00:21:42.250 --> 00:21:46.550
So one, give them the
messages about thinking about
00:21:46.550 --> 00:21:48.170
we can always improve.
00:21:48.170 --> 00:21:51.790
Our brains improve. Our brains
change as we try new things.
00:21:51.790 --> 00:21:53.370
That's really important.
00:21:53.370 --> 00:21:56.260
But also thinking about helping them
00:21:56.260 --> 00:21:57.880
experience some success.
00:21:57.880 --> 00:22:01.340
So those small goals and thinking about
00:22:01.340 --> 00:22:05.330
how to get them to see
a little bit of progress
00:22:05.330 --> 00:22:06.163
that they're making.
00:22:06.163 --> 00:22:08.357
And even a little bit of progress is good.
00:22:08.357 --> 00:22:10.290
"Yesterday you couldn't do
00:22:10.290 --> 00:22:14.440
the two-digit by minus two-digit problems.
00:22:14.440 --> 00:22:17.370
And today you did three
of them. That's great."
00:22:17.370 --> 00:22:19.313
Like legitimately, that's progress.
00:22:20.320 --> 00:22:21.220
That's very good.
00:22:21.220 --> 00:22:23.910
So helping them see, again,
00:22:23.910 --> 00:22:25.980
that they can have a little bit of success
00:22:25.980 --> 00:22:27.733
and that really does build on itself
00:22:27.733 --> 00:22:31.600
and help kids start to see
themselves as learners.
00:22:31.600 --> 00:22:34.953
And that's really the key that
then will kick things off.
00:22:35.900 --> 00:22:38.120
- Great. So Kristen, we
have a lot of questions.
00:22:38.120 --> 00:22:40.420
And it goes back to the very first tip,
00:22:40.420 --> 00:22:41.470
which is setting goals.
00:22:41.470 --> 00:22:45.210
We have a couple of questions
around goals, first from Sue.
00:22:45.210 --> 00:22:46.670
She loves the idea of setting goals,
00:22:46.670 --> 00:22:48.660
but they're already
being set by the school.
00:22:48.660 --> 00:22:50.640
So how do you match what your,
00:22:50.640 --> 00:22:52.650
the goals that your schools are setting?
00:22:52.650 --> 00:22:55.570
Another question from Flavio is like,
00:22:55.570 --> 00:22:57.600
how do we know we're setting
goals at the appropriate level?
00:22:57.600 --> 00:23:00.890
And you know, whether
it's too challenging,
00:23:00.890 --> 00:23:02.570
not challenging enough.
00:23:02.570 --> 00:23:03.950
And then the third is from Ed,
00:23:03.950 --> 00:23:06.290
who's asking for very specific examples
00:23:06.290 --> 00:23:09.090
for their grade school kid.
00:23:09.090 --> 00:23:11.750
They're having challenges
with getting their child
00:23:11.750 --> 00:23:13.663
to help set their own goals.
00:23:14.690 --> 00:23:17.650
- Got it. So, yeah, lots
of, lots of good stuff.
00:23:17.650 --> 00:23:20.240
So the first thing I
would say that underlies
00:23:20.240 --> 00:23:22.370
all of those is,
00:23:22.370 --> 00:23:25.720
think about talking to
your child's teacher,
00:23:25.720 --> 00:23:27.250
even in this distance world,
00:23:27.250 --> 00:23:29.920
keeping those lines of communication open.
00:23:29.920 --> 00:23:32.937
So if a teacher starts hearing, like,
00:23:32.937 --> 00:23:36.350
"All of the things that you're
asking us to do every day
00:23:36.350 --> 00:23:37.290
is too much.
00:23:37.290 --> 00:23:40.200
Like, the kids can't handle that much."
00:23:40.200 --> 00:23:42.420
And they start hearing that from parents,
00:23:42.420 --> 00:23:44.250
they're gonna adjust what they're doing.
00:23:44.250 --> 00:23:45.330
Or they're gonna, you know,
00:23:45.330 --> 00:23:47.740
start to find ways to help the students
00:23:47.740 --> 00:23:50.800
and provide more support,
one or the other.
00:23:50.800 --> 00:23:53.810
But if the teacher doesn't know
that the kids are struggling
00:23:53.810 --> 00:23:54.643
to do this,
00:23:54.643 --> 00:23:56.600
and it can be difficult to know that
00:23:56.600 --> 00:24:00.226
when they are in a distance
learning situation,
00:24:00.226 --> 00:24:04.050
then they don't know that
the kids need extra help
00:24:04.050 --> 00:24:06.220
or that they need to think about
00:24:06.220 --> 00:24:08.290
how much they're putting on kids.
00:24:08.290 --> 00:24:11.650
Because a lot of teachers
may have tons of experience
00:24:11.650 --> 00:24:14.400
doing all of this in
the regular classroom,
00:24:14.400 --> 00:24:17.480
but it's not clear how
much kids can take on
00:24:17.480 --> 00:24:19.340
in these distance learning situations.
00:24:19.340 --> 00:24:24.340
So that's my first piece of
advice is to think about how to,
00:24:25.287 --> 00:24:27.120
you know, talk to your teacher
00:24:27.120 --> 00:24:28.969
about if the goals are too much,
00:24:28.969 --> 00:24:32.720
or if they're thinking about, you know,
00:24:32.720 --> 00:24:36.230
if they're not meeting them
or where they need to go.
00:24:36.230 --> 00:24:37.350
And Dan, I have lost,
00:24:37.350 --> 00:24:38.850
there were a bunch of questions there,
00:24:38.850 --> 00:24:42.630
and I lost, (giggles)
in my short term memory,
00:24:42.630 --> 00:24:43.900
a couple of the other points.
00:24:43.900 --> 00:24:45.677
Could you remind me of what those were?
00:24:45.677 --> 00:24:49.430
- So the other one is, how do we know when
00:24:49.430 --> 00:24:52.390
it's like the right level
of goal for the child,
00:24:52.390 --> 00:24:55.291
in addition to your teacher one.
00:24:55.291 --> 00:24:57.700
And then I think the third one was,
00:24:57.700 --> 00:25:00.491
how do you get your kids to
kind of play into goal setting
00:25:00.491 --> 00:25:02.880
if your kid's reluctant to kind of engage
00:25:02.880 --> 00:25:04.380
with the goal setting exercise, right?
00:25:04.380 --> 00:25:07.340
So if they're not happy to
share with you what they think,
00:25:07.340 --> 00:25:10.090
like, how do you pull that out of them?
00:25:10.090 --> 00:25:11.200
- Great. Yep.
00:25:11.200 --> 00:25:16.200
So the level of goals
piece is another one to,
00:25:17.020 --> 00:25:19.670
it's really good to talk
to your student's teacher,
00:25:19.670 --> 00:25:22.080
talk to your kid's
teacher about, you know,
00:25:22.080 --> 00:25:24.690
what kinds of levels that they're at,
00:25:24.690 --> 00:25:27.500
because it is going to
be individual for kids.
00:25:27.500 --> 00:25:30.320
But then it should be as
something that you're looking for,
00:25:30.320 --> 00:25:34.210
you want kids to, if you're
kind of observing them do work,
00:25:34.210 --> 00:25:36.960
you want to think about there's
something where they have to
00:25:36.960 --> 00:25:38.020
put in effort.
00:25:38.020 --> 00:25:39.330
And there's something that we talked about
00:25:39.330 --> 00:25:41.280
that's called productive struggle.
00:25:41.280 --> 00:25:43.130
And it means that kids are,
00:25:43.130 --> 00:25:45.250
they're having to put in
some cognitive efforts,
00:25:45.250 --> 00:25:48.437
like think hard about this
and reason through it.
00:25:48.437 --> 00:25:50.620
And it's not just coming easy to them.
00:25:50.620 --> 00:25:53.540
If it's coming really easy,
it's probably too low a goal.
00:25:53.540 --> 00:25:55.000
If they're getting really frustrated,
00:25:55.000 --> 00:25:56.510
it's probably too high a goal.
00:25:56.510 --> 00:25:58.770
So something kind of in between there
00:25:58.770 --> 00:26:00.590
is what you're looking to hit,
00:26:00.590 --> 00:26:03.320
where there is a little
bit of struggle going on.
00:26:03.320 --> 00:26:04.940
Maybe they're a little bit confused.
00:26:04.940 --> 00:26:06.740
Maybe they're not sure how to do this.
00:26:06.740 --> 00:26:10.050
Maybe they need a little bit
of help. That is all okay.
00:26:10.050 --> 00:26:12.620
Those are all signs
that they're right about
00:26:12.620 --> 00:26:13.610
at the right place.
00:26:13.610 --> 00:26:15.320
They don't need to be
doing it independently.
00:26:15.320 --> 00:26:17.160
If they could just breeze
through it independently,
00:26:17.160 --> 00:26:18.083
probably too easy.
00:26:19.400 --> 00:26:21.930
So that's kind of what you're
looking for in terms of
00:26:21.930 --> 00:26:24.360
where the step, what that is.
00:26:24.360 --> 00:26:26.543
But a good guide is looking at the things
00:26:26.543 --> 00:26:28.003
that your teachers,
00:26:28.003 --> 00:26:30.440
that your child's teacher's assigning
00:26:30.440 --> 00:26:33.080
and thinking about,
you know, how that can,
00:26:33.080 --> 00:26:35.120
how you can help break that down.
00:26:35.120 --> 00:26:36.980
The other piece to that
first question was, you know,
00:26:36.980 --> 00:26:39.670
it seems to be too much,
that's being assigned.
00:26:39.670 --> 00:26:42.380
Again, think about breaking
down into small pieces.
00:26:42.380 --> 00:26:45.627
So you can a little bit of
progress even after an hour.
00:26:45.627 --> 00:26:47.980
"What are we going to
try to do in this hour?
00:26:47.980 --> 00:26:49.880
I know it's a whole bunch of stuff.
00:26:49.880 --> 00:26:52.250
Let's just focus on this
thing we can get done now,
00:26:52.250 --> 00:26:54.810
and then we can worry about
the rest of it later."
00:26:54.810 --> 00:26:56.580
So all of that is good goal setting.
00:26:56.580 --> 00:26:58.630
And then if you've got kids that are just,
00:26:58.630 --> 00:27:00.620
that are not engaging
00:27:00.620 --> 00:27:03.997
and are not that good at setting goals,
00:27:03.997 --> 00:27:07.660
we can think about, again,
00:27:07.660 --> 00:27:12.660
that idea of rewards and
thinking about engaging them,
00:27:13.000 --> 00:27:17.480
and maybe if you're
initially setting a goal
00:27:17.480 --> 00:27:19.320
and then having them in the conversation
00:27:19.320 --> 00:27:22.110
about what they think maybe
would be a good reward
00:27:22.110 --> 00:27:25.750
for getting into that, reaching that goal.
00:27:25.750 --> 00:27:29.810
So all of that can kind of help
bring them into the process
00:27:29.810 --> 00:27:30.643
and what that is.
00:27:30.643 --> 00:27:33.086
So maybe they're not
interested in setting the goal
00:27:33.086 --> 00:27:34.580
the first time.
00:27:34.580 --> 00:27:38.120
'Cause then you can think about
what's the reward for that.
00:27:38.120 --> 00:27:41.600
Or you can think about
rewards for helping set goals.
00:27:41.600 --> 00:27:43.870
We're getting very kind of meta there.
00:27:43.870 --> 00:27:47.127
But then again, rewards can
be good for helping kids
00:27:47.127 --> 00:27:50.790
start doing something that
they're not interested in doing.
00:27:50.790 --> 00:27:53.137
So think about, you know,
00:27:53.137 --> 00:27:56.470
"Hey, let's set this goal and
then we can go and, you know,
00:27:56.470 --> 00:27:59.340
chase around in the backyard
with the dog for 30 minutes,
00:27:59.340 --> 00:28:02.100
and then we can get back
to work on a meeting."
00:28:02.100 --> 00:28:05.410
Those kinds of things, you
know, are all good ways
00:28:05.410 --> 00:28:07.713
to start to kind of
encourage that behavior.
00:28:08.950 --> 00:28:09.783
- That's great.
00:28:09.783 --> 00:28:10.740
And we have a question,
00:28:10.740 --> 00:28:12.810
we have a couple questions around feedback
00:28:12.810 --> 00:28:15.040
and that portion of the tips.
00:28:15.040 --> 00:28:16.600
So Rebecca asks,
00:28:16.600 --> 00:28:18.627
what type of feedback
is most helpful for kids
00:28:18.627 --> 00:28:21.950
and does it depend on the stage
of where they're learning?
00:28:21.950 --> 00:28:25.733
So things like the frequency
of the feedback, the timing,
00:28:25.733 --> 00:28:28.239
when to acknowledge, you know,
00:28:28.239 --> 00:28:32.180
basically effort versus
results, things like that?
00:28:32.180 --> 00:28:35.730
- Yup, yup. All good, excellent questions.
00:28:35.730 --> 00:28:36.840
This is actually some place
00:28:36.840 --> 00:28:40.080
where there's a pretty good
amount of research out there.
00:28:40.080 --> 00:28:43.420
So when you were just
learning a new thing,
00:28:43.420 --> 00:28:46.326
you want to give immediate feedback
00:28:46.326 --> 00:28:49.700
that is both about whether
it's correct or not,
00:28:49.700 --> 00:28:52.820
but also why it's correct or not.
00:28:52.820 --> 00:28:55.570
So that's what we call elaborated feedback
00:28:55.570 --> 00:28:58.410
because it's not just the
correctness, but it's the why.
00:28:58.410 --> 00:29:01.750
And so you want that to
be specific to the task
00:29:01.750 --> 00:29:03.070
that they're doing.
00:29:03.070 --> 00:29:05.417
You don't want to give
that general feedback like,
00:29:05.417 --> 00:29:06.560
"Oh, you're so smart."
00:29:06.560 --> 00:29:10.490
You want to keep it as "You
got that question right.
00:29:10.490 --> 00:29:11.677
Good job."
00:29:11.677 --> 00:29:15.517
"That answer is right because XYZ."
00:29:17.040 --> 00:29:19.970
or "You didn't get that
one right that time.
00:29:19.970 --> 00:29:24.580
That answer's not correct
because of XYZ. Let's try again."
00:29:24.580 --> 00:29:28.610
Again, don't make it about
characteristics of the child.
00:29:28.610 --> 00:29:31.330
You want to think about
trying to give feedback.
00:29:31.330 --> 00:29:32.950
So feedback on correctness
00:29:32.950 --> 00:29:35.890
and about why it's correct or not is good.
00:29:35.890 --> 00:29:38.080
And you can also then combine that
00:29:38.080 --> 00:29:40.320
with feedback about effort.
00:29:40.320 --> 00:29:42.630
So something like, "Wow,"
00:29:42.630 --> 00:29:44.380
if you're seeing that productive struggle
00:29:44.380 --> 00:29:45.340
that I was talking about,
00:29:45.340 --> 00:29:48.187
like they've worked pretty hard
to get to this answer, like,
00:29:48.187 --> 00:29:51.320
"Wow, I saw you really
thinking hard about that.
00:29:51.320 --> 00:29:52.900
That's great.
00:29:52.900 --> 00:29:55.470
Let's take a look at whether
we got it right or wrong,
00:29:55.470 --> 00:29:57.030
or whether we want to try again."
00:29:57.030 --> 00:30:00.090
And then you can move into
the correctness feedback.
00:30:00.090 --> 00:30:02.670
As kids are more advanced
00:30:02.670 --> 00:30:05.400
and they're getting into
more advanced topics
00:30:05.400 --> 00:30:08.090
and are kind of more
comfortable with things,
00:30:08.090 --> 00:30:11.370
it's actually good to
have them have a chance
00:30:11.370 --> 00:30:15.210
to reflect on whether they think
something's correct or not.
00:30:15.210 --> 00:30:16.977
So we do things like saying,
00:30:16.977 --> 00:30:18.990
"How confident are you in that answer?
00:30:18.990 --> 00:30:19.830
How sure are you,
00:30:19.830 --> 00:30:21.902
how sure are you that that's right?"
00:30:21.902 --> 00:30:25.970
And get them to actually start
building some of those skills
00:30:25.970 --> 00:30:29.170
where they're kind of mentally
checking their own work,
00:30:29.170 --> 00:30:32.340
which is a good skill
to have and think about,
00:30:32.340 --> 00:30:34.180
and then give them the feedback.
00:30:34.180 --> 00:30:35.700
It can be a little bit more delayed.
00:30:35.700 --> 00:30:37.416
It doesn't need to be quite as immediate
00:30:37.416 --> 00:30:39.766
as kids are getting a
little bit more advanced.
00:30:40.800 --> 00:30:43.330
- So perhaps we have time
for one more question.
00:30:43.330 --> 00:30:44.920
Unfortunately, we have
a lot more questions
00:30:44.920 --> 00:30:45.753
than we have time for.
00:30:45.753 --> 00:30:48.170
So we'll try to, you know,
00:30:48.170 --> 00:30:50.790
potentially address it in the
future in a future webinar.
00:30:50.790 --> 00:30:54.340
But Melissa asks, and it's a
little bit related to feedback,
00:30:54.340 --> 00:30:57.630
which is, when should you
step back and allow a break,
00:30:57.630 --> 00:31:00.823
if your child's just really
reluctant or really frustrated.
00:31:02.400 --> 00:31:05.910
When you recognize that and
then when do you actually engage
00:31:05.910 --> 00:31:07.880
or when do you disengage?
00:31:07.880 --> 00:31:09.710
- Yeah. Excellent question.
00:31:09.710 --> 00:31:11.360
So first I would say,
00:31:11.360 --> 00:31:16.360
we want to prioritize our
kids' emotional wellbeing
00:31:16.526 --> 00:31:17.900
in all of this.
00:31:17.900 --> 00:31:19.900
We don't want to let kids get to the point
00:31:19.900 --> 00:31:20.770
where they're, you know,
00:31:20.770 --> 00:31:22.750
breaking down in tears about things,
00:31:22.750 --> 00:31:26.310
because that's going to
take a lot to then walk back
00:31:26.310 --> 00:31:29.940
and get down and get
settled and where that is.
00:31:29.940 --> 00:31:34.810
So the more you can be proactive
in scheduling in breaks
00:31:34.810 --> 00:31:37.090
and taking a step away
00:31:37.090 --> 00:31:40.638
even before they're showing
signs of being upset,
00:31:40.638 --> 00:31:43.330
that's actually good too.
00:31:43.330 --> 00:31:45.270
So don't be hesitant to take breaks.
00:31:45.270 --> 00:31:47.220
Breaks are good for everybody.
00:31:47.220 --> 00:31:50.130
But if you've kind of
gotten through there,
00:31:50.130 --> 00:31:52.910
but your child is still
like really frustrated,
00:31:52.910 --> 00:31:54.433
absolutely take a break.
00:31:55.490 --> 00:31:57.607
Go back to those strategies.
00:31:57.607 --> 00:32:00.810
"Okay, let's take a
break, do something else."
00:32:00.810 --> 00:32:02.140
And then I tend to go back,
00:32:02.140 --> 00:32:03.470
have a little bit of discussion
00:32:03.470 --> 00:32:06.600
about what's really frustrating them.
00:32:06.600 --> 00:32:08.220
Where is that road block?
00:32:08.220 --> 00:32:10.870
Is it they don't know what to do next?
00:32:10.870 --> 00:32:14.170
They can't get this right?
They can't understand it?
00:32:14.170 --> 00:32:17.160
You know, then you can start
to problem solve about,
00:32:17.160 --> 00:32:21.440
okay, if you understand what
it is that's so frustrating.
00:32:21.440 --> 00:32:24.610
Is it that it's just too much
that they're thinking about?
00:32:24.610 --> 00:32:25.830
Is it that, you know,
00:32:25.830 --> 00:32:29.310
they're worried about all
of the other things going on
00:32:29.310 --> 00:32:32.100
in the world, or they,
where are those things?
00:32:32.100 --> 00:32:34.740
So the more you can have a
conversation, take a break,
00:32:34.740 --> 00:32:35.610
get away from it,
00:32:35.610 --> 00:32:40.070
then have a conversation
about how are they feeling,
00:32:40.070 --> 00:32:41.370
what are the things that
they're worried about?
00:32:41.370 --> 00:32:44.310
What are the things that are
frustrating them and see if you
00:32:44.310 --> 00:32:46.050
can problem solve some of those together.
00:32:46.050 --> 00:32:49.740
But absolutely look for
those body language signs
00:32:49.740 --> 00:32:53.440
that kids are getting
really upset and frustrated
00:32:53.440 --> 00:32:55.310
and try to cut things off if you can,
00:32:55.310 --> 00:32:57.810
before it gets too far down that road.
00:32:57.810 --> 00:32:59.860
- Well, I think that's
great advice for adults
00:32:59.860 --> 00:33:00.700
as much as kids.
00:33:00.700 --> 00:33:03.403
I think that's some good
advice for us all to follow.
00:33:04.240 --> 00:33:07.373
So huge apologies. We have
so many more questions.
00:33:08.220 --> 00:33:11.700
Like I said, perhaps we can
tackle more in a future webinar.
00:33:11.700 --> 00:33:12.533
But with that,
00:33:12.533 --> 00:33:15.640
I'd like to thank Kristen for
her sharing her expert advice
00:33:15.640 --> 00:33:16.780
with our audience.
00:33:16.780 --> 00:33:18.190
And we want to thank you, our audience,
00:33:18.190 --> 00:33:21.040
for taking time out of your
busy schedule to be with us.
00:33:21.040 --> 00:33:23.197
We know you're incredibly
busy during this time.
00:33:23.197 --> 00:33:26.110
And so we really appreciate
you investing your time
00:33:26.110 --> 00:33:27.360
to this session.
00:33:27.360 --> 00:33:30.020
If you missed anything or want
to go back and review again,
00:33:30.020 --> 00:33:31.850
this is being recorded.
00:33:31.850 --> 00:33:33.880
And not only are we going to post it,
00:33:33.880 --> 00:33:35.840
but for those of you who have registered,
00:33:35.840 --> 00:33:38.610
this will automatically be emailed to you.
00:33:38.610 --> 00:33:39.590
And in addition to that,
00:33:39.590 --> 00:33:42.180
as well as the downloadable
with the seven tips
00:33:42.180 --> 00:33:43.630
that Kristen mentioned before.
00:33:43.630 --> 00:33:44.740
So don't miss, you know,
00:33:44.740 --> 00:33:46.460
don't worry if you missed anything.
00:33:46.460 --> 00:33:49.900
And we also have quite a few
resources at khanacademy.org
00:33:49.900 --> 00:33:52.410
if you need more information.
00:33:52.410 --> 00:33:53.440
And before we sign off,
00:33:53.440 --> 00:33:55.890
we want to ask that you
do two things for us.
00:33:55.890 --> 00:34:00.680
First, please answer the
poll that happens at the end,
00:34:00.680 --> 00:34:02.630
that pops up at the end of this webinar.
00:34:02.630 --> 00:34:03.530
We want to ask, you know,
00:34:03.530 --> 00:34:06.580
how can we make future
iterations of this session
00:34:06.580 --> 00:34:07.920
even better for you?
00:34:07.920 --> 00:34:09.870
And then secondly, what
kind of other sessions
00:34:09.870 --> 00:34:12.240
would you like to see us
develop in the future?
00:34:12.240 --> 00:34:13.220
And we're here to help you.
00:34:13.220 --> 00:34:15.630
So please let us know
how we can best do that.
00:34:15.630 --> 00:34:18.050
And so from all of us at
Khan Academy, thank you.
00:34:18.050 --> 00:34:18.993
And goodbye.
|
Types of studies | https://www.youtube.com/watch?v=zmXBbHDUgY4 | vtt | https://www.youtube.com/api/timedtext?v=zmXBbHDUgY4&ei=91WUZZPCFPWsmLAPhYuekA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E1BCA9F08D562D0E328146568FC35FB47C38038D.64A580BF2CD354BBE615A0ED0A555E4460C51885&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.840 --> 00:00:02.520
- [Instructor] In this video,
we're gonna get our bearings
00:00:02.520 --> 00:00:04.610
on the different types of studies
00:00:04.610 --> 00:00:08.820
you might statistically
analyze or statistical studies.
00:00:08.820 --> 00:00:11.250
So first of all, it's
worth differentiating
00:00:11.250 --> 00:00:16.250
between an experiment and
an observational study.
00:00:16.790 --> 00:00:19.200
I encourage you pause this video
00:00:19.200 --> 00:00:20.600
and think about what the difference is,
00:00:20.600 --> 00:00:22.750
at least in your head
between an experiment
00:00:22.750 --> 00:00:24.980
and an observational.
00:00:24.980 --> 00:00:27.963
Observational study.
00:00:30.130 --> 00:00:33.130
Well, you might already be
familiar with experiments.
00:00:33.130 --> 00:00:35.450
You oftentimes have a hypothesis
00:00:35.450 --> 00:00:38.000
that if you do something to one group,
00:00:38.000 --> 00:00:40.800
that it might have some type
of statistically significant
00:00:40.800 --> 00:00:42.960
impact on them relative to a group
00:00:42.960 --> 00:00:44.450
that you did not do it to.
00:00:44.450 --> 00:00:46.270
And you would be generally right.
00:00:46.270 --> 00:00:48.770
That is the flavor of
what we're talking about
00:00:48.770 --> 00:00:50.470
when we're talking about an experiment.
00:00:50.470 --> 00:00:53.410
An experiment we're
actively putting people
00:00:53.410 --> 00:00:57.010
or things into a control
versus treatment group.
00:00:57.010 --> 00:01:01.250
In the treatment group, you put the people
00:01:01.250 --> 00:01:03.510
and you usually would want
to randomly select people
00:01:03.510 --> 00:01:04.343
into the treatment group.
00:01:04.343 --> 00:01:06.060
Maybe it's a new type of medication.
00:01:06.060 --> 00:01:07.730
And maybe in the treatment group,
00:01:07.730 --> 00:01:11.240
they actually get the medication
while in the control group,
00:01:11.240 --> 00:01:14.250
which you would put people into randomly,
00:01:14.250 --> 00:01:16.030
whether they're in control or treatment,
00:01:16.030 --> 00:01:18.210
here they might get a placebo
00:01:18.210 --> 00:01:20.370
where they get a pill that
looks just like the medication,
00:01:20.370 --> 00:01:22.140
but it really doesn't do anything.
00:01:22.140 --> 00:01:24.460
And then you wait some
time and you can see,
00:01:24.460 --> 00:01:26.900
is there a statistically
significant difference
00:01:26.900 --> 00:01:29.070
between the treatment group on average
00:01:29.070 --> 00:01:30.800
and the control group.
00:01:30.800 --> 00:01:32.370
So that's what an experiment does.
00:01:32.370 --> 00:01:34.520
It's kind of this act of
sorting and figuring out
00:01:34.520 --> 00:01:39.250
whether some type of stimulus
is able to show a difference
00:01:39.250 --> 00:01:41.190
while an observational study,
00:01:41.190 --> 00:01:43.870
you don't actively put into groups.
00:01:43.870 --> 00:01:46.760
Instead, you just collect data
00:01:46.760 --> 00:01:49.100
and see if you can have some insights
00:01:49.100 --> 00:01:50.400
from that data.
00:01:50.400 --> 00:01:54.660
If you can say, okay, the data,
there's a population here,
00:01:54.660 --> 00:01:56.110
can I come up with some statistics
00:01:56.110 --> 00:01:57.800
that are indicative of the population?
00:01:57.800 --> 00:01:59.620
I might just wanna look at averages,
00:01:59.620 --> 00:02:03.800
or I might wanna find some
correlations between variables.
00:02:03.800 --> 00:02:06.580
But even when we're talking
about an observational study,
00:02:06.580 --> 00:02:07.880
there are different types of it,
00:02:07.880 --> 00:02:10.360
depending on what type
of data we're looking at,
00:02:10.360 --> 00:02:13.420
whether the data is
backward-looking, forward-looking
00:02:13.420 --> 00:02:16.320
or it's data that we are
collecting right now,
00:02:16.320 --> 00:02:19.750
based on what people
think or say right now.
00:02:19.750 --> 00:02:22.560
So if we're thinking about
an observational study
00:02:22.560 --> 00:02:24.603
that is looking at past data,
00:02:25.940 --> 00:02:27.890
and I could imagine
doing something like this
00:02:27.890 --> 00:02:28.723
at Khan Academy,
00:02:28.723 --> 00:02:32.550
where we could look at
maybe usage of Khan Academy
00:02:32.550 --> 00:02:33.383
over time.
00:02:33.383 --> 00:02:35.560
We have these things in our server logs,
00:02:35.560 --> 00:02:38.150
and we're able to make
do some analysis there.
00:02:38.150 --> 00:02:41.010
Maybe we're able to analyze and say,
00:02:41.010 --> 00:02:45.660
on average students are
spending two hours per month
00:02:45.660 --> 00:02:49.500
on Khan Academy over in 2019.
00:02:49.500 --> 00:02:51.340
That would be past data.
00:02:51.340 --> 00:02:54.750
And that type of observational
study would be called
00:02:54.750 --> 00:02:57.690
a retrospective study.
00:02:57.690 --> 00:03:02.330
Retro for backwards and spective, looking.
00:03:02.330 --> 00:03:05.290
So retrospective observational study
00:03:05.290 --> 00:03:08.810
would sample past data
in order to come up with
00:03:08.810 --> 00:03:10.370
some insights.
00:03:10.370 --> 00:03:12.590
Now you can imagine there
might be the other side.
00:03:12.590 --> 00:03:16.970
What if we are trying to
observe things into the future?
00:03:16.970 --> 00:03:19.790
Well, here you might
take a sample of folks
00:03:19.790 --> 00:03:22.560
who you think are
indicative of a population
00:03:22.560 --> 00:03:25.830
and you might want to
just track their data.
00:03:25.830 --> 00:03:29.730
So you could even consider
that to be future data.
00:03:29.730 --> 00:03:32.030
So you pick the group,
the sample ahead of time,
00:03:32.030 --> 00:03:34.980
and then you track their data over time.
00:03:34.980 --> 00:03:37.630
I'm just gonna try these little arrows
00:03:37.630 --> 00:03:39.050
that you're tracking their data,
00:03:39.050 --> 00:03:40.760
and then you see what happens.
00:03:40.760 --> 00:03:43.890
For example, you might
randomly select hopefully
00:03:45.403 --> 00:03:47.340
a random sample of a hundred women,
00:03:47.340 --> 00:03:49.980
and you wanna see in the coming year,
00:03:49.980 --> 00:03:54.570
how many eggs do they
eat on average per day?
00:03:54.570 --> 00:03:57.310
Well, what you would do is
you selected those folks
00:03:57.310 --> 00:03:59.010
and then you would track that data
00:03:59.010 --> 00:04:00.590
for each of them every day.
00:04:00.590 --> 00:04:02.480
And then once you have the data,
00:04:02.480 --> 00:04:04.380
you could actually do it
while you're collecting it.
00:04:04.380 --> 00:04:05.310
But at the end of the study,
00:04:05.310 --> 00:04:07.740
you'll be able to see
what those averages are.
00:04:07.740 --> 00:04:09.090
But you can also keep track of it
00:04:09.090 --> 00:04:11.250
while you're taking that data.
00:04:11.250 --> 00:04:13.670
And you could imagine
what this was called.
00:04:13.670 --> 00:04:16.350
Instead of retrospective,
we're now looking forward.
00:04:16.350 --> 00:04:21.350
So it is prospective, forward
looking observational study.
00:04:22.961 --> 00:04:24.800
Last but not least, some of
y'all are probably thinking,
00:04:24.800 --> 00:04:27.430
what about if we're doing something now?
00:04:27.430 --> 00:04:32.080
If we go out there and we were
to survey a bunch of people
00:04:32.080 --> 00:04:34.800
and say, how many eggs did you eat today?
00:04:34.800 --> 00:04:37.410
Or who are you going to vote for?
00:04:37.410 --> 00:04:38.930
What might we call that?
00:04:38.930 --> 00:04:40.980
It's tempting to call it
something with a prefix
00:04:40.980 --> 00:04:41.980
and then spective.
00:04:41.980 --> 00:04:43.200
So it all matches,
00:04:43.200 --> 00:04:45.680
but it turns out that the
terminology that statisticians
00:04:45.680 --> 00:04:50.680
will typically use is a sample survey.
00:04:52.520 --> 00:04:55.740
That right now you're gonna
take a hopefully random sample
00:04:55.740 --> 00:04:58.840
of individuals from the
population that you care about.
00:04:58.840 --> 00:05:01.170
And you are just gonna
serve them right now
00:05:01.170 --> 00:05:03.030
and ask them, say some questions
00:05:03.030 --> 00:05:06.610
or observe some data about them right now.
00:05:06.610 --> 00:05:07.770
So I'll leave you there.
00:05:07.770 --> 00:05:09.870
This video is to just
give you a little bit of
00:05:09.870 --> 00:05:12.620
the vocabulary and a
little bit of a taxonomy
00:05:12.620 --> 00:05:14.880
on the types of studies
that you'll see in general,
00:05:14.880 --> 00:05:16.560
which is especially useful to know
00:05:16.560 --> 00:05:19.170
when you're exploring
the world of statistics.
|
Influential points in regression | https://www.youtube.com/watch?v=jHHPGhrcMOY | vtt | https://www.youtube.com/api/timedtext?v=jHHPGhrcMOY&ei=91WUZfeHHaaep-oP-smQ0AE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B2BBA7263EEFA43E8B5881CF19719D4AA5202754.918D10A791B3215A3C9A1A299CC4C5CDECE8B31E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.670 --> 00:00:01.860
- [Instructor] I'm pretty sure I just tore
00:00:01.860 --> 00:00:03.240
my calf muscle this morning
00:00:03.240 --> 00:00:05.370
while sprinting with my son.
00:00:05.370 --> 00:00:07.304
But the math must not stop,
00:00:07.304 --> 00:00:09.980
(chuckles) so I'm here to help us
00:00:09.980 --> 00:00:13.060
think about what we could
call influential points
00:00:13.060 --> 00:00:14.550
when we're thinking about regressions.
00:00:14.550 --> 00:00:15.430
And to help us here,
00:00:15.430 --> 00:00:18.990
I have this tool from BFW Publishing.
00:00:18.990 --> 00:00:22.200
I encourage you to go here
and use this tool yourself.
00:00:22.200 --> 00:00:25.020
But what it allows us to
do is to draw some points.
00:00:25.020 --> 00:00:28.470
So just like that, let
me draw some points.
00:00:28.470 --> 00:00:31.360
And then fit a least-squares line.
00:00:31.360 --> 00:00:33.470
So that's the least-squares
line right over there.
00:00:33.470 --> 00:00:35.650
And you can not only see the line,
00:00:35.650 --> 00:00:37.520
we can see our correlation coefficient.
00:00:37.520 --> 00:00:40.610
It's pretty good, 0.8156.
00:00:40.610 --> 00:00:41.720
It's pretty close to one.
00:00:41.720 --> 00:00:44.910
So we have a pretty good
fit right over here.
00:00:44.910 --> 00:00:47.720
But we're gonna think about our points
00:00:47.720 --> 00:00:51.070
that might influence, or it
might be overly influential,
00:00:51.070 --> 00:00:55.160
we could say, to different
aspects of this regression line.
00:00:55.160 --> 00:00:58.950
So one type of influential
point is known as an outlier.
00:00:58.950 --> 00:01:01.210
And a good way of identifying an outlier
00:01:01.210 --> 00:01:03.720
is it's a very bad fit to the line,
00:01:03.720 --> 00:01:06.280
or it has a very large residual.
00:01:06.280 --> 00:01:10.460
And so if I put a point right
over here, that is an outlier.
00:01:10.460 --> 00:01:13.330
So what happens when we
have an outlier like that?
00:01:13.330 --> 00:01:18.330
So before we had a correlation
coefficient of 0.8 something,
00:01:18.710 --> 00:01:20.960
you put one outlier like that out of,
00:01:20.960 --> 00:01:23.520
it's now one out of 16 points,
00:01:23.520 --> 00:01:25.970
it dramatically lowered
our correlation coefficient
00:01:25.970 --> 00:01:29.060
because we have a really large
residual right over here.
00:01:29.060 --> 00:01:32.210
So an outlier like this
has been very influential
00:01:32.210 --> 00:01:33.920
on the correlation coefficient.
00:01:33.920 --> 00:01:38.630
It didn't impact the slope of
the line a tremendous amount.
00:01:38.630 --> 00:01:39.633
It did a little bit.
00:01:40.710 --> 00:01:42.910
Actually, when I put it
there, it didn't impact
00:01:42.910 --> 00:01:44.270
the slope much at all.
00:01:44.270 --> 00:01:48.210
And it does impact the
Y-intercept a little bit.
00:01:48.210 --> 00:01:49.550
Actually, when I put it out here,
00:01:49.550 --> 00:01:51.520
it doesn't impact the
Y-intercept much at all.
00:01:51.520 --> 00:01:53.320
If I put it a little bit more to the left,
00:01:53.320 --> 00:01:54.870
it impacts it a little bit.
00:01:54.870 --> 00:01:58.100
But these outliers that are at least close
00:01:58.100 --> 00:02:00.830
to the mean X value,
00:02:00.830 --> 00:02:03.020
these seem to be most relevant
00:02:03.020 --> 00:02:05.610
in terms of impacting, or most influential
00:02:05.610 --> 00:02:08.720
in terms of the correlation coefficient.
00:02:08.720 --> 00:02:11.140
Now, what about an outlier
00:02:11.140 --> 00:02:14.040
that's further away from the mean X value?
00:02:14.040 --> 00:02:16.760
And something, a point whose X value
00:02:16.760 --> 00:02:19.810
is further away from the mean X value
00:02:19.810 --> 00:02:21.480
is considered a high leverage point.
00:02:21.480 --> 00:02:22.313
And the way you could think
00:02:22.313 --> 00:02:23.760
about that is if you imagine
00:02:23.760 --> 00:02:26.100
this as being some type of a seesaw
00:02:26.100 --> 00:02:28.730
somehow pivoted on the mean X value,
00:02:28.730 --> 00:02:30.730
well, if you put a point out here,
00:02:30.730 --> 00:02:32.090
it looks like it's pivoting down.
00:02:32.090 --> 00:02:34.510
It's like someone's sitting
at this end of the seesaw.
00:02:34.510 --> 00:02:37.330
And so that's where I think
the term leverage comes from.
00:02:37.330 --> 00:02:39.820
And you can see what I put an outlier,
00:02:39.820 --> 00:02:42.830
if I put a high leverage outlier out here
00:02:42.830 --> 00:02:44.600
that does many things.
00:02:44.600 --> 00:02:47.750
It definitely drops the
correlation coefficient.
00:02:47.750 --> 00:02:52.310
It changes the slope and
it changes the Y-intercept.
00:02:52.310 --> 00:02:53.850
So it does a lot of things.
00:02:53.850 --> 00:02:56.310
So it's highly influential for everything
00:02:56.310 --> 00:02:57.720
I just talked about.
00:02:57.720 --> 00:02:59.430
And if I have a high leverage point
00:02:59.430 --> 00:03:02.710
that's maybe a little
bit less of an outlier,
00:03:02.710 --> 00:03:03.880
something like this,
00:03:03.880 --> 00:03:05.240
based on the points that I happen to have,
00:03:05.240 --> 00:03:07.240
it didn't hurt the
correlation coefficient.
00:03:07.240 --> 00:03:08.880
In fact, in that example,
it's actually improved
00:03:08.880 --> 00:03:12.820
it a little bit, but it did
change the Y intercept a bit,
00:03:12.820 --> 00:03:14.440
and it did change the slope a bit.
00:03:14.440 --> 00:03:15.940
Although, obviously, not as dramatic
00:03:15.940 --> 00:03:17.360
as when you do something like that.
00:03:17.360 --> 00:03:20.820
And that kills the correlation
coefficient as well.
00:03:20.820 --> 00:03:22.720
Let's see what happens if
we do things over here.
00:03:22.720 --> 00:03:27.060
So if I have a high
leverage outlier over here,
00:03:27.060 --> 00:03:28.330
you see the same thing.
00:03:28.330 --> 00:03:32.270
A high leverage outliers
seems to influence everything.
00:03:32.270 --> 00:03:34.070
If it is a high leverage point
00:03:34.070 --> 00:03:35.680
that is less of an outlier.
00:03:35.680 --> 00:03:37.370
Actually, once again, it improved
00:03:37.370 --> 00:03:39.140
the correlation coefficient.
00:03:39.140 --> 00:03:40.760
You could say that it's still influential
00:03:40.760 --> 00:03:42.820
on the correlation
coefficient in this case,
00:03:42.820 --> 00:03:46.170
it's improving it, but
it's less influential
00:03:46.170 --> 00:03:48.250
in terms of the slope and the Y-intercept,
00:03:48.250 --> 00:03:50.280
although it is making a difference there.
00:03:50.280 --> 00:03:51.810
So I encourage you to play with this.
00:03:51.810 --> 00:03:53.750
Think about different points.
00:03:53.750 --> 00:03:57.680
How far they are away
from the mean X value,
00:03:57.680 --> 00:03:59.230
how large of a residual they have,
00:03:59.230 --> 00:04:00.540
are they an outlier?
00:04:00.540 --> 00:04:04.420
And how influential they
are to the various aspects
00:04:04.420 --> 00:04:07.410
of a least-squares line,
the slope, the Y-intercept,
00:04:07.410 --> 00:04:08.570
or the correlation coefficient.
00:04:08.570 --> 00:04:10.210
When we're talking about
correlation coefficient,
00:04:10.210 --> 00:04:11.680
also known as the R value,
00:04:11.680 --> 00:04:14.080
which is of course the
square root of R squared.
|
Systematic random sampling | https://www.youtube.com/watch?v=TrOS8OnM1u4 | vtt | https://www.youtube.com/api/timedtext?v=TrOS8OnM1u4&ei=91WUZdTEJvKyvdIPrtmimAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=CB74A2537B3D2607A136F81F6253FDB52B7E4BFD.AD4561E159E610C2C186982581FDF2BCA7765CE6&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.430 --> 00:00:02.460
- [Instructor] In this video,
we're going to talk about
00:00:02.460 --> 00:00:05.240
random sampling, which
we've already talked about
00:00:05.240 --> 00:00:06.500
in other videos.
00:00:06.500 --> 00:00:08.620
And we're going to compare
what we already know
00:00:08.620 --> 00:00:11.670
about simple random sampling to a new type
00:00:11.670 --> 00:00:13.670
of random sampling that
we're going to introduce
00:00:13.670 --> 00:00:14.503
in this video.
00:00:14.503 --> 00:00:19.140
And that is systematic random sampling.
00:00:19.140 --> 00:00:20.810
So let's look at an example.
00:00:20.810 --> 00:00:24.750
Let's say that there is a
concert that is happening
00:00:24.750 --> 00:00:29.370
and we expect approximately 10,000 people
00:00:29.370 --> 00:00:31.110
to attend the concert.
00:00:31.110 --> 00:00:34.020
And we want to randomly
sample people at the concert.
00:00:34.020 --> 00:00:36.740
Maybe we wanna do a study on how do people
00:00:36.740 --> 00:00:38.090
get to the concert.
00:00:38.090 --> 00:00:43.090
How do people get to the concert?
00:00:45.100 --> 00:00:48.820
Do they drive and park? Do
they ride with a friend?
00:00:48.820 --> 00:00:52.550
Do they take an Uber
or a cab of some kind?
00:00:52.550 --> 00:00:57.180
And so we wanna find a random
sample, ideally without bias,
00:00:57.180 --> 00:00:58.880
to survey people.
00:00:58.880 --> 00:01:00.490
So there's a couple of
ways you could do it.
00:01:00.490 --> 00:01:04.980
You could try to do a
simple random sample.
00:01:04.980 --> 00:01:07.670
And that might be a case
of if you could somehow
00:01:07.670 --> 00:01:10.620
get the names of all
10,000 people and put them
00:01:10.620 --> 00:01:12.830
into a big bowl like this.
00:01:12.830 --> 00:01:15.830
And then let's say you
want to sample 100 people.
00:01:15.830 --> 00:01:20.830
Let's say you want to sample
approximately 100 people.
00:01:22.750 --> 00:01:25.290
You could just mix up all the names
00:01:25.290 --> 00:01:28.660
that may be on these little
pieces of paper, 10,000 of them,
00:01:28.660 --> 00:01:31.900
and then pull them out and
pull out a random sample
00:01:31.900 --> 00:01:33.080
of 100 of them.
00:01:33.080 --> 00:01:36.440
That would be a simple random sample.
00:01:36.440 --> 00:01:38.420
But you could already
imagine there might be some
00:01:38.420 --> 00:01:40.170
logistic difficulties of doing this.
00:01:40.170 --> 00:01:41.970
How are you going to get the 10,000 names?
00:01:41.970 --> 00:01:43.840
You're gonna write 'em
on a piece of paper.
00:01:43.840 --> 00:01:46.290
That's gonna be a you'd
have to really mix 'em good
00:01:46.290 --> 00:01:49.120
so it's truly random
who you're picking out.
00:01:49.120 --> 00:01:51.480
So are there other ways
of doing a random sample?
00:01:51.480 --> 00:01:53.090
And as you can imagine, yes, there are.
00:01:53.090 --> 00:01:56.920
And that's where systematic
random sampling is useful.
00:01:56.920 --> 00:01:59.370
One way to think about
systematic random sampling
00:01:59.370 --> 00:02:03.430
is you're going to randomly
sample a subset of the people
00:02:03.430 --> 00:02:06.080
who are maybe walking into the concert.
00:02:06.080 --> 00:02:08.760
So let's say people get to
the concert and they start
00:02:08.760 --> 00:02:12.930
forming a line to get into the concert.
00:02:12.930 --> 00:02:15.860
What you wanna do in
systematic random sampling
00:02:15.860 --> 00:02:18.130
is randomly pick your first person.
00:02:18.130 --> 00:02:20.300
There's a bunch of ways
that you could do that.
00:02:20.300 --> 00:02:22.070
Let's say you have a
random number generator
00:02:22.070 --> 00:02:24.770
that'll generate a number from one to 100.
00:02:24.770 --> 00:02:26.800
And that's going to be the
first person you survey.
00:02:26.800 --> 00:02:29.470
If that random number
generator generates a 37,
00:02:29.470 --> 00:02:32.870
then you're going to start
with the 37th person in line.
00:02:32.870 --> 00:02:36.950
So you pick that first person
randomly. You survey them.
00:02:36.950 --> 00:02:39.930
And remember, our goal is
to sample about 100 people
00:02:39.930 --> 00:02:40.763
out of 10,000.
00:02:40.763 --> 00:02:43.970
So we wanna roughly sample
one out of every 100 people.
00:02:43.970 --> 00:02:47.440
And so what you do there is
once you have that first person
00:02:47.440 --> 00:02:49.610
that you're sampling, you then sample
00:02:49.610 --> 00:02:51.640
every 100th person after that.
00:02:51.640 --> 00:02:53.800
That's called sometimes
the sample interval.
00:02:53.800 --> 00:02:56.300
And the reason why 100 people
is because if you sample
00:02:56.300 --> 00:02:59.110
every 100th person after
that, you're gonna roughly get
00:02:59.110 --> 00:03:02.850
100 people in your sample
out of a total of 10,000.
00:03:02.850 --> 00:03:04.560
So this is going to be after 100,
00:03:04.560 --> 00:03:06.660
you're going to sample someone else.
00:03:06.660 --> 00:03:07.820
And then after another 100, you're going
00:03:07.820 --> 00:03:09.930
to sample someone else.
00:03:09.930 --> 00:03:13.000
Now, the reason why this
is useful is you could say
00:03:13.000 --> 00:03:14.630
okay, that first person was random.
00:03:14.630 --> 00:03:16.410
And then every person after that.
00:03:16.410 --> 00:03:18.410
It doesn't seem like there'd be any bias
00:03:18.410 --> 00:03:19.960
for why they would be the 100th person
00:03:19.960 --> 00:03:21.820
after that first person.
00:03:21.820 --> 00:03:23.660
You don't wanna just
do the first 100 people
00:03:23.660 --> 00:03:25.370
because those might be the early birds,
00:03:25.370 --> 00:03:28.200
the people who may be
disproportionately went parking
00:03:28.200 --> 00:03:30.650
or planned earlier or had
some bias in some way.
00:03:30.650 --> 00:03:32.690
So you do wanna make sure
that you're getting, you know,
00:03:32.690 --> 00:03:35.190
both the beginning, the middle,
and the end of the line,
00:03:35.190 --> 00:03:36.490
which this thing helps.
00:03:36.490 --> 00:03:38.140
Now, we have to be careful.
00:03:38.140 --> 00:03:41.750
Even systematic random
sampling is not foolproof.
00:03:41.750 --> 00:03:43.870
There's a situation where inadvertently
00:03:43.870 --> 00:03:45.830
even this system has bias.
00:03:45.830 --> 00:03:47.720
Let's say that this is the arena.
00:03:47.720 --> 00:03:50.550
This is a top view of the
arena right over here.
00:03:50.550 --> 00:03:54.580
And this is the line of people coming in.
00:03:54.580 --> 00:03:58.780
And this is where you are
standing and you are counting
00:03:58.780 --> 00:04:00.220
every 100th person.
00:04:00.220 --> 00:04:04.430
But maybe, and let's say
there's a tree right over here.
00:04:04.430 --> 00:04:09.000
And maybe there's a road. I'm
making this quite elaborate.
00:04:09.000 --> 00:04:11.940
So maybe there is a road right over here.
00:04:11.940 --> 00:04:15.560
And a lot of people, maybe all
of the people who are walking
00:04:15.560 --> 00:04:19.180
or taking a cab are coming
from this direction.
00:04:19.180 --> 00:04:21.670
And maybe all of the
people from the parking lot
00:04:21.670 --> 00:04:24.070
are coming from this direction.
00:04:24.070 --> 00:04:26.770
And maybe you have a police
officer right over here
00:04:26.770 --> 00:04:30.360
who is doing crowd control,
who lets 50 people,
00:04:30.360 --> 00:04:34.510
50 of these people in, followed
by 50 of these people in.
00:04:34.510 --> 00:04:37.590
Well, in that situation,
every 100th, you might end up
00:04:37.590 --> 00:04:40.170
just sampling one side or the other.
00:04:40.170 --> 00:04:42.340
So you have to make sure
that there isn't some bias
00:04:42.340 --> 00:04:44.840
that's being introduced
into this line somehow
00:04:44.840 --> 00:04:46.433
that might distort your sample.
|
Analyzing mosaic plots | https://www.youtube.com/watch?v=2sHkluggZp8 | vtt | https://www.youtube.com/api/timedtext?v=2sHkluggZp8&ei=91WUZYzDHvagp-oPn9CxoAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E5C6581DC4F84A78C351DAAE81AE53C6C29F6211.C4F73BB8E6879AC9FD1A677271660B8ADF3464D3&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.220 --> 00:00:02.050
- [Instructor] We're told that
administrators at a school
00:00:02.050 --> 00:00:04.190
are considering a policy change.
00:00:04.190 --> 00:00:06.850
They survey a group of
students, staff members,
00:00:06.850 --> 00:00:09.630
and parents about
whether or not they agree
00:00:09.630 --> 00:00:11.180
with the new policy.
00:00:11.180 --> 00:00:15.300
The following mosaic plot
summarizes their results.
00:00:15.300 --> 00:00:17.780
Which of the following
statements can we justify
00:00:17.780 --> 00:00:19.810
from the mosaic plot?
00:00:19.810 --> 00:00:22.720
So pause this video and try to
figure this out on your own.
00:00:22.720 --> 00:00:25.030
Pick which of these
statements can be justified
00:00:25.030 --> 00:00:28.963
and there could be more than
one based on this mosaic plot.
00:00:30.310 --> 00:00:32.500
All right, now let's work
through this together.
00:00:32.500 --> 00:00:33.880
So before I even look at the choices,
00:00:33.880 --> 00:00:35.890
let me see if I can interpret this.
00:00:35.890 --> 00:00:36.930
So this mosaic plot,
00:00:36.930 --> 00:00:39.780
what it does above and
beyond a segmented bar chart,
00:00:39.780 --> 00:00:43.040
is it gives us the width
that shows us how many,
00:00:43.040 --> 00:00:45.750
for example, students
versus staff versus parents
00:00:45.750 --> 00:00:47.630
were sampled or surveyed.
00:00:47.630 --> 00:00:50.520
And it looks like more than half
00:00:50.520 --> 00:00:52.620
of the people surveyed were students.
00:00:52.620 --> 00:00:55.160
And then staff and parents seem similar.
00:00:55.160 --> 00:00:58.020
In terms of who is
agreeing with the policy,
00:00:58.020 --> 00:00:59.600
so that's that light blue color.
00:00:59.600 --> 00:01:02.950
It seems like students are
not very likely to agree
00:01:02.950 --> 00:01:03.783
with the policy.
00:01:03.783 --> 00:01:07.060
It looks like staff is very
likely to agree with the policy,
00:01:07.060 --> 00:01:09.250
that the bulk of staff
is agreeing with it.
00:01:09.250 --> 00:01:12.330
And parents are kind of on both sides.
00:01:12.330 --> 00:01:14.980
So let's see which of these
statements are consistent
00:01:14.980 --> 00:01:16.530
with what we just looked at.
00:01:16.530 --> 00:01:19.840
Parents were the least likely
to agree with the new policy.
00:01:19.840 --> 00:01:21.460
No, that's not true.
00:01:21.460 --> 00:01:24.600
The least likely to
agree with the new policy
00:01:24.600 --> 00:01:27.150
that's students, right over here.
00:01:27.150 --> 00:01:28.730
They were definitely the least likely.
00:01:28.730 --> 00:01:30.750
The lowest percentage of students
00:01:30.750 --> 00:01:32.010
are agreeing with the policy.
00:01:32.010 --> 00:01:35.260
So I don't like that choice.
00:01:35.260 --> 00:01:38.600
More than half of the total
responses came from students.
00:01:38.600 --> 00:01:40.330
And that does look like the case.
00:01:40.330 --> 00:01:43.700
'Cause if you view this entire
width as the total responses,
00:01:43.700 --> 00:01:46.190
it looks like the student
width right over here,
00:01:46.190 --> 00:01:47.870
that is more than half of it.
00:01:47.870 --> 00:01:50.070
It looks like it's about
50 something percent
00:01:50.070 --> 00:01:51.370
or even 60 percent.
00:01:51.370 --> 00:01:55.270
So I like this choice right over here.
00:01:55.270 --> 00:01:57.070
And then last but not least,
00:01:57.070 --> 00:02:01.880
there were more total "No"
responses from students
00:02:01.880 --> 00:02:04.370
than from staff and parents combined.
00:02:04.370 --> 00:02:07.360
So let's look at the no
responses from students.
00:02:07.360 --> 00:02:09.300
No, that's that darker blue color.
00:02:09.300 --> 00:02:14.300
The no responses for students
is this area right over here.
00:02:15.780 --> 00:02:19.400
And then the nos, so I can,
maybe I'll shade all of that in,
00:02:19.400 --> 00:02:22.490
and then the no responses from staff
00:02:22.490 --> 00:02:27.490
and parents combined, that
is this area right over here.
00:02:28.590 --> 00:02:32.900
And it does look like indeed
the total no responses
00:02:32.900 --> 00:02:35.400
from students, this area is much larger
00:02:35.400 --> 00:02:37.040
than this area right over here.
00:02:37.040 --> 00:02:39.373
So I like this choice as well.
|
Mosaic plots and segmented bar charts | https://www.youtube.com/watch?v=b9G5pWuxb1Y | vtt | https://www.youtube.com/api/timedtext?v=b9G5pWuxb1Y&ei=91WUZZSWI5S2mLAP9YKVCA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6DC8CD7B308157468587A51FA4924E5C6FDC47BA.9DD01702A65140EB869B07CECCE0FA0F5958C64D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.280 --> 00:00:01.113
- [Instructor] Let's say we're looking
00:00:01.113 --> 00:00:02.550
at some type of disease
00:00:02.550 --> 00:00:05.100
and we want to see if
there's any relationship
00:00:05.100 --> 00:00:09.080
between people having
antibodies for that disease
00:00:09.080 --> 00:00:12.880
and whether they are
adults, children or infants.
00:00:12.880 --> 00:00:14.870
And if you don't know what antibodies are,
00:00:14.870 --> 00:00:17.670
these are things that your
immune system keeps around
00:00:17.670 --> 00:00:20.970
so it's very easy to
recognize future infection.
00:00:20.970 --> 00:00:22.680
But you don't have to
worry too much about that
00:00:22.680 --> 00:00:23.700
for this video.
00:00:23.700 --> 00:00:25.010
In this video, we're just
trying to think about
00:00:25.010 --> 00:00:28.000
how we can visualize data to understand
00:00:28.000 --> 00:00:31.040
if there's a relationship
between having antibodies
00:00:31.040 --> 00:00:33.500
and the age of the individual.
00:00:33.500 --> 00:00:35.980
So let's say we go out and
collect a bunch of data.
00:00:35.980 --> 00:00:37.990
So we test 120 adults
00:00:37.990 --> 00:00:40.660
and 114 have antibodies, six don't.
00:00:40.660 --> 00:00:41.960
We test 60 children,
00:00:41.960 --> 00:00:44.400
54 have antibodies, six don't.
00:00:44.400 --> 00:00:46.530
We test 20 infants, and then eight
00:00:46.530 --> 00:00:49.590
have antibodies and 12 don't.
00:00:49.590 --> 00:00:51.110
So we can just look at this data,
00:00:51.110 --> 00:00:52.540
but this really still doesn't give us
00:00:52.540 --> 00:00:55.630
a visual representation
of what's going on.
00:00:55.630 --> 00:00:57.590
One step we can take,
what's still doesn't give us
00:00:57.590 --> 00:00:59.380
a fully visual representation,
00:00:59.380 --> 00:01:01.130
is to just think about percentages
00:01:01.130 --> 00:01:03.110
that might help us think
about the likelihood
00:01:03.110 --> 00:01:04.790
of having antibodies.
00:01:04.790 --> 00:01:06.510
So if we calculate the percentages,
00:01:06.510 --> 00:01:08.530
we might see something like this.
00:01:08.530 --> 00:01:12.400
For example, 114 over 120
00:01:12.400 --> 00:01:17.090
is 95%, or 95% have antibodies.
00:01:17.090 --> 00:01:19.900
That 114 over one 20 is 95%.
00:01:19.900 --> 00:01:22.820
And then the number that
don't have antibodies,
00:01:22.820 --> 00:01:24.370
this six right over here,
00:01:24.370 --> 00:01:27.360
that is 5%, six over 120.
00:01:27.360 --> 00:01:30.040
And you can do that for
each of the categories.
00:01:30.040 --> 00:01:34.470
54 over 60 is 90%.
00:01:34.470 --> 00:01:36.760
While six over 60,
00:01:36.760 --> 00:01:39.570
you can do that math in your head, is 10%.
00:01:39.570 --> 00:01:41.870
And we can do the same
thing for the infants.
00:01:41.870 --> 00:01:45.370
Eight out of 20 is 40%
00:01:45.370 --> 00:01:50.210
while 12 out of 20 is 60%.
00:01:50.210 --> 00:01:51.500
So that helps us a little bit.
00:01:51.500 --> 00:01:52.750
It helps us think about,
00:01:52.750 --> 00:01:54.490
well, what's the percentage of adults
00:01:54.490 --> 00:01:57.540
that have the antibody
or children or infants?
00:01:57.540 --> 00:01:58.990
But if we really want to visualize it,
00:01:58.990 --> 00:02:02.260
we can look at two different
types of visualizations.
00:02:02.260 --> 00:02:06.200
One we can call a segmented bar chart,
00:02:06.200 --> 00:02:08.640
and I will show a segmented bar chart
00:02:08.640 --> 00:02:10.670
for this data right over here.
00:02:10.670 --> 00:02:13.370
Now in a segmented bar chart, we group,
00:02:13.370 --> 00:02:16.070
we have a bar for each category here
00:02:16.070 --> 00:02:18.570
and we're making adults,
children and infants
00:02:18.570 --> 00:02:20.610
the different categories
because we're thinking
00:02:20.610 --> 00:02:23.230
maybe that has something
to do with the likelihood
00:02:23.230 --> 00:02:24.720
of having antibodies.
00:02:24.720 --> 00:02:28.020
And then for each bar, for
example, this adult bar,
00:02:28.020 --> 00:02:31.090
you can see the percentage
that have the antibodies
00:02:31.090 --> 00:02:32.220
and the percentage that don't.
00:02:32.220 --> 00:02:36.050
So 95% of the adult bar is filled in blue.
00:02:36.050 --> 00:02:38.140
That's for yes, they have the antibodies.
00:02:38.140 --> 00:02:41.060
And 5% is filled in red.
00:02:41.060 --> 00:02:42.250
And then for children,
00:02:42.250 --> 00:02:45.330
you can see that 90% is filled in blue
00:02:45.330 --> 00:02:46.760
and 10% is filled in red
00:02:46.760 --> 00:02:48.720
because 10% don't have the antibodies.
00:02:48.720 --> 00:02:50.890
And then for infants, you can see
00:02:50.890 --> 00:02:53.300
that 40% is filled in blue
00:02:53.300 --> 00:02:56.630
and 60% don't have the antibodies.
00:02:56.630 --> 00:02:58.550
Now, this by itself is pretty useful
00:02:58.550 --> 00:03:00.850
to visually see, alright,
it looks like adults
00:03:00.850 --> 00:03:03.240
are much more likely
to have the antibodies
00:03:03.240 --> 00:03:05.580
than children, and children
are far more likely
00:03:05.580 --> 00:03:08.240
to have the antibodies than infants.
00:03:08.240 --> 00:03:11.390
And so it looks like
this idea of making a bar
00:03:11.390 --> 00:03:13.700
for each of adults, children or infants
00:03:13.700 --> 00:03:16.490
was a good way to start to understand
00:03:16.490 --> 00:03:18.620
the likelihood of having antibodies.
00:03:18.620 --> 00:03:20.280
You could have done it other ways.
00:03:20.280 --> 00:03:23.170
You could have had a
bar for have antibodies
00:03:23.170 --> 00:03:25.000
and another bar for not have antibodies.
00:03:25.000 --> 00:03:26.980
And then you could have
segmented the bar chart
00:03:26.980 --> 00:03:29.410
by whether they are adults,
children, or infants.
00:03:29.410 --> 00:03:30.440
But if you did that,
00:03:30.440 --> 00:03:31.870
that would have been trying to understand
00:03:31.870 --> 00:03:34.330
whether having antibodies
or not having antibodies
00:03:34.330 --> 00:03:37.140
is predictive of whether you're
an adult, child or infant
00:03:37.140 --> 00:03:39.030
while this one makes, at least to me,
00:03:39.030 --> 00:03:40.760
a little bit more sense that
whether you're an adult,
00:03:40.760 --> 00:03:42.900
child or infant might be predictive
00:03:42.900 --> 00:03:45.070
of whether or not you have antibodies.
00:03:45.070 --> 00:03:46.940
But there is some information lost
00:03:46.940 --> 00:03:48.900
in this segmented bar chart.
00:03:48.900 --> 00:03:50.820
For example, we have lost the fact
00:03:50.820 --> 00:03:53.390
that we have sampled, or we have tested
00:03:53.390 --> 00:03:54.820
a lot more adults than children
00:03:54.820 --> 00:03:57.540
and far more children than infants.
00:03:57.540 --> 00:03:59.710
So one way to incorporate that data
00:03:59.710 --> 00:04:01.460
back into a visualization
00:04:01.460 --> 00:04:03.360
to essentially show how many people
00:04:03.360 --> 00:04:05.660
you sampled in each of these categories,
00:04:05.660 --> 00:04:09.253
we can generate what's
known as a mosaic plot.
00:04:09.253 --> 00:04:11.920
So this is a mosaic plot right over here.
00:04:11.920 --> 00:04:13.750
And one way to think about it is
00:04:13.750 --> 00:04:15.600
we have just adjusted the width
00:04:15.600 --> 00:04:17.320
of each of these bars
00:04:17.320 --> 00:04:19.910
based on how many people we tested.
00:04:19.910 --> 00:04:21.870
So we tested 200 people.
00:04:21.870 --> 00:04:24.770
And so you can view this
width right over here
00:04:24.770 --> 00:04:26.800
as being 200.
00:04:26.800 --> 00:04:30.840
And you can see that we tested 120 adults.
00:04:30.840 --> 00:04:32.990
So the width of this first bar,
00:04:32.990 --> 00:04:33.823
I guess you could say,
00:04:33.823 --> 00:04:35.750
although now we're dealing
with a mosaic plot,
00:04:35.750 --> 00:04:38.150
this width right over here would be
00:04:38.150 --> 00:04:40.400
60% of this entire width,
00:04:40.400 --> 00:04:42.000
which you can see that it is.
00:04:42.000 --> 00:04:45.680
And then the children are 60
of the 200 that we tested.
00:04:45.680 --> 00:04:47.970
And so this width right over here
00:04:47.970 --> 00:04:51.380
would be 60 over the entire 200,
00:04:51.380 --> 00:04:54.040
or it would be about
30% of the entire width.
00:04:54.040 --> 00:04:55.880
And we can see that we tested
00:04:55.880 --> 00:04:57.240
the fewest number of infants.
00:04:57.240 --> 00:04:59.760
And so this 20 right over here
00:04:59.760 --> 00:05:02.890
represents the 20 infants we tested.
00:05:02.890 --> 00:05:04.810
And the reason why this mosaic plot
00:05:04.810 --> 00:05:06.010
conveys more information,
00:05:06.010 --> 00:05:07.980
it conveys all the same information
00:05:07.980 --> 00:05:10.010
that our segmented bar chart does.
00:05:10.010 --> 00:05:12.630
But it also gives us
a sense that we tested
00:05:12.630 --> 00:05:13.717
more adults than children
00:05:13.717 --> 00:05:16.370
and far more children than infants.
00:05:16.370 --> 00:05:19.200
And it's also easy to then
look at it and say, okay,
00:05:19.200 --> 00:05:22.440
of the total number of people
who don't have the antibodies,
00:05:22.440 --> 00:05:25.490
so that would be the red
area right over here,
00:05:25.490 --> 00:05:28.450
even though we tested the
fewest number of infants,
00:05:28.450 --> 00:05:31.100
it looks like infants
make up a large chunk
00:05:31.100 --> 00:05:32.650
of the total number of folks
00:05:32.650 --> 00:05:35.000
who don't have antibodies.
00:05:35.000 --> 00:05:36.020
So I'll leave you there.
00:05:36.020 --> 00:05:38.460
The whole point of this
video is to just understand
00:05:38.460 --> 00:05:41.170
why a segmented bar chart or a mosaic plot
00:05:41.170 --> 00:05:42.640
will be useful in future videos.
00:05:42.640 --> 00:05:45.473
We'll get more practice analyzing them.
|
Thin-layer chromatography (TLC) | https://www.youtube.com/watch?v=GOWUw0-SEDE | vtt | https://www.youtube.com/api/timedtext?v=GOWUw0-SEDE&ei=91WUZfD5FcPNp-oP7vWJ-Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=68D9DFB8976467ABB7F4681A32AAA8553CC7195D.E913DF8854D08B9C61E45F6EF314FBC39B8957E4&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.290 --> 00:00:01.620
- [Instructor] So let's
say that I have a vial
00:00:01.620 --> 00:00:03.840
of some mystery liquid right over here,
00:00:03.840 --> 00:00:06.080
and I want to start figuring
out what's going on there.
00:00:06.080 --> 00:00:08.070
And the first step is to think about,
00:00:08.070 --> 00:00:09.730
is it just one substance
00:00:09.730 --> 00:00:12.210
or is it a mixture of multiple substances?
00:00:12.210 --> 00:00:15.230
And the focus of this video is a technique
00:00:15.230 --> 00:00:17.540
to separate out the substances
00:00:17.540 --> 00:00:19.860
to understand at least how many there are,
00:00:19.860 --> 00:00:23.030
and this technique generally
is called chromatography,
00:00:23.030 --> 00:00:25.680
but we'll focus on thin
layer chromatography
00:00:25.680 --> 00:00:27.570
which is the most common
that you might see,
00:00:27.570 --> 00:00:29.590
but other variations of chromatography
00:00:29.590 --> 00:00:31.150
like paper chromatography
00:00:31.150 --> 00:00:33.890
operate on very similar principles.
00:00:33.890 --> 00:00:37.780
So what we're going to do is set up
00:00:37.780 --> 00:00:40.790
on top of something like glass or plastic,
00:00:40.790 --> 00:00:45.790
we're going to put a thin layer
of a solid polar substance.
00:00:46.800 --> 00:00:48.040
Now, what you typically do
00:00:48.040 --> 00:00:50.650
is put a thin layer of silica gel,
00:00:50.650 --> 00:00:55.140
that's the most common solid
polar substance that folks use.
00:00:55.140 --> 00:00:56.430
And it's also porous.
00:00:56.430 --> 00:00:58.500
And the fact that it's
porous is really important
00:00:58.500 --> 00:01:01.290
because we're going to want
liquid to have capillary action
00:01:01.290 --> 00:01:03.480
and travel up through it.
00:01:03.480 --> 00:01:05.600
Now, the silica gel, as I mentioned,
00:01:05.600 --> 00:01:08.983
this thing is very polar.
00:01:10.440 --> 00:01:11.273
Now, what we're going to do
00:01:11.273 --> 00:01:12.970
is take some of our mystery substance,
00:01:12.970 --> 00:01:14.900
let's say it's this color right over here,
00:01:14.900 --> 00:01:19.900
and we're going to place a
dot of it on that silica gel.
00:01:19.940 --> 00:01:21.370
You then want to take this plate
00:01:21.370 --> 00:01:23.180
that has the silica gel on it
00:01:23.180 --> 00:01:25.670
and that little dot of
our mystery substance,
00:01:25.670 --> 00:01:30.060
and then you want to dip just
one end of it in a solution.
00:01:30.060 --> 00:01:31.077
And what's really important is that
00:01:31.077 --> 00:01:35.120
the solution is less
polar than the silica gel.
00:01:35.120 --> 00:01:37.430
Less polar here.
00:01:37.430 --> 00:01:39.620
And we'll talk a little
bit about what happens
00:01:39.620 --> 00:01:41.600
depending on how polar this is.
00:01:41.600 --> 00:01:44.810
Now, usually this is going
to be a very shallow amount
00:01:44.810 --> 00:01:47.530
of this solution, which, as we'll see,
00:01:47.530 --> 00:01:49.360
will be something of a solvent.
00:01:49.360 --> 00:01:51.940
And you usually want to put
it in a closed container
00:01:51.940 --> 00:01:52.773
like this
00:01:52.773 --> 00:01:55.980
so that this fluid down
here doesn't evaporate out.
00:01:55.980 --> 00:01:58.160
And then what do you
think is going to happen?
00:01:58.160 --> 00:02:00.970
Well, as I mentioned, this
is a porous substance here.
00:02:00.970 --> 00:02:03.160
And so you're going to
have capillary action.
00:02:03.160 --> 00:02:05.960
This fluid at the bottom
is going to move upwards
00:02:05.960 --> 00:02:07.260
through the silica gel,
00:02:07.260 --> 00:02:09.320
through those little
pores in the silica gel.
00:02:09.320 --> 00:02:11.570
This is the stationary phase.
Why do we call it that?
00:02:11.570 --> 00:02:12.670
Well, 'cause it's not moving.
00:02:12.670 --> 00:02:16.270
And you can imagine we would
call this less polar solvent
00:02:17.170 --> 00:02:18.610
the mobile phase,
00:02:18.610 --> 00:02:21.970
because that is traveling
through the silica gel
00:02:21.970 --> 00:02:25.010
and it's picking up some
of this mystery substance
00:02:25.010 --> 00:02:26.700
and it's transporting it.
00:02:26.700 --> 00:02:28.280
And let's say this mystery substance
00:02:28.280 --> 00:02:30.610
is made up of two different things.
00:02:30.610 --> 00:02:33.200
If something is more polar,
00:02:33.200 --> 00:02:35.210
that means it's going to be more attracted
00:02:35.210 --> 00:02:37.600
to the stationary phase
which is very polar.
00:02:37.600 --> 00:02:40.490
And so it's not going to travel that far,
00:02:40.490 --> 00:02:42.210
while the parts of our mystery substance
00:02:42.210 --> 00:02:43.450
that are less polar,
00:02:43.450 --> 00:02:46.500
they're not going to be attracted
to the silica gel as much.
00:02:46.500 --> 00:02:49.410
So they're going to travel
further with the solvent.
00:02:49.410 --> 00:02:51.910
So maybe it might go like that.
00:02:51.910 --> 00:02:53.530
And you would run this
until your mobile phase
00:02:53.530 --> 00:02:56.940
makes a good way to the
top of your silica gel
00:02:56.940 --> 00:02:58.190
right over here.
00:02:58.190 --> 00:02:59.380
Now, just looking at this,
00:02:59.380 --> 00:03:01.160
and the reason why it was
called chromatography is
00:03:01.160 --> 00:03:02.280
when they originally did this,
00:03:02.280 --> 00:03:04.760
they were actually separating
out various tissues
00:03:04.760 --> 00:03:07.610
in vegetation that had different colors.
00:03:07.610 --> 00:03:10.160
The chroma is referring
to the various colors,
00:03:10.160 --> 00:03:11.960
but it doesn't necessarily
even have to refer to things
00:03:11.960 --> 00:03:13.040
that have different colors
00:03:13.040 --> 00:03:15.630
or sometimes you might need
a UV light to see them.
00:03:15.630 --> 00:03:17.440
But when you run thin
layer chromatography,
00:03:17.440 --> 00:03:20.780
you will see that your
original dot will have traveled
00:03:20.780 --> 00:03:22.660
to various degrees with your solvent
00:03:22.660 --> 00:03:24.860
and then will now be multiple dots
00:03:24.860 --> 00:03:28.520
depending on how many things
were in your original mixture.
00:03:28.520 --> 00:03:31.670
And as I just mentioned,
this thing right over here,
00:03:31.670 --> 00:03:35.520
this is the less polar thing
is going to travel further
00:03:35.520 --> 00:03:40.380
than the more polar thing, more
polar constituent substance,
00:03:40.380 --> 00:03:42.850
because the more polar
thing is more attractive
00:03:42.850 --> 00:03:45.570
to the silica gel, which is stationary,
00:03:45.570 --> 00:03:49.440
and there is a way to quantify
how far these things traveled
00:03:49.440 --> 00:03:51.660
relative to your solvent.
00:03:51.660 --> 00:03:54.700
And that's called a retention factor.
00:03:54.700 --> 00:03:57.853
Retention factor.
00:03:59.010 --> 00:04:02.780
Which the shorthand is R subscript f.
00:04:02.780 --> 00:04:07.200
And it's just defined
as the distance traveled
00:04:08.170 --> 00:04:13.170
by the solute divided
by the distance traveled
00:04:18.690 --> 00:04:22.080
by the solvent.
00:04:22.080 --> 00:04:23.090
And we need to be clear.
00:04:23.090 --> 00:04:26.000
It's not the distance traveled
by the solvent in total,
00:04:26.000 --> 00:04:29.810
it's the distance traveled by
the solvent from this origin,
00:04:29.810 --> 00:04:32.750
from where we applied
this dot right over here.
00:04:32.750 --> 00:04:36.353
So, past the origin.
00:04:37.320 --> 00:04:39.893
And let me label that as the origin.
00:04:40.730 --> 00:04:42.730
So what would it be in this situation?
00:04:42.730 --> 00:04:46.930
Well, to help us there, we
would have to get out a ruler.
00:04:46.930 --> 00:04:51.930
So the retention factor for
substance A right over here,
00:04:52.400 --> 00:04:54.890
so I'll put that dot there, label that A,
00:04:54.890 --> 00:04:58.560
would be equal to the distance
traveled by the solute,
00:04:58.560 --> 00:05:03.340
which we can see, it
traveled one centimeter,
00:05:03.340 --> 00:05:05.040
one centimeter,
00:05:05.040 --> 00:05:09.110
over the distance traveled by
the solvent past the origin.
00:05:09.110 --> 00:05:11.810
And so that is going to be,
00:05:11.810 --> 00:05:15.110
we see it traveled five
centimeters past the origin.
00:05:15.110 --> 00:05:17.810
So one centimeter over five centimeters,
00:05:17.810 --> 00:05:19.813
which is the same thing as 0.2.
00:05:20.700 --> 00:05:24.630
And then the retention
factor for substance B
00:05:26.190 --> 00:05:29.750
is going to be equal to,
how far did it travel?
00:05:29.750 --> 00:05:31.850
Well, it traveled three centimeters
00:05:33.300 --> 00:05:36.480
out of a total of five
centimeters for the solvent,
00:05:36.480 --> 00:05:37.820
past this origin,
00:05:37.820 --> 00:05:40.470
past where we put the
sample right over there.
00:05:40.470 --> 00:05:45.410
Five centimeters, which is equal to 0.6.
00:05:45.410 --> 00:05:47.240
So notice, in this situation,
00:05:47.240 --> 00:05:50.660
the more polar substance
had a lower retention factor
00:05:50.660 --> 00:05:54.550
than the less polar substance,
and that makes sense.
00:05:54.550 --> 00:05:59.490
Because our stationary phase
is more polar than our solvent,
00:05:59.490 --> 00:06:03.500
and so the things that are
more polar were harder to move
00:06:03.500 --> 00:06:06.253
by the less polar solvent.
|
Hands off My Phone! (An ELA audio drama) | https://www.youtube.com/watch?v=wV7e7IGQ0zc | vtt | https://www.youtube.com/api/timedtext?v=wV7e7IGQ0zc&ei=91WUZebtLO2Hp-oPh5qYwAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7DAFB53A314BCA9ABD2B42DD5ACBD0494DDE8E95.065167C5338B2D0ADEB90DE74D4DAC765AADF4AC&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:02.362 --> 00:00:05.300
(bell ringing)
00:00:05.300 --> 00:00:07.842
- [Boy] Oh no he didn't, that is so harsh!
00:00:07.842 --> 00:00:08.675
- [Valentina] Right?
00:00:08.675 --> 00:00:09.770
- [Boy] Your dad took your phone away
00:00:09.770 --> 00:00:11.560
just for getting a D on the history test?
00:00:11.560 --> 00:00:12.410
- [Valentina] Yep.
00:00:12.410 --> 00:00:13.820
- [Boy] My mind is blown.
00:00:13.820 --> 00:00:14.890
- [Valentina] Mine too.
00:00:14.890 --> 00:00:16.580
- [Boy] I mean that was an easy test.
00:00:16.580 --> 00:00:17.413
- [Valentina] What?
00:00:17.413 --> 00:00:18.410
- [Boy] I can't believe you got a D.
00:00:18.410 --> 00:00:19.597
- [Valentina] Hey that's not really the-
00:00:19.597 --> 00:00:21.174
- [Boy] And your dad is
the school principal,
00:00:21.174 --> 00:00:23.610
and he took your phone away, whoa.
00:00:23.610 --> 00:00:26.710
- [Valentina] You know,
this isn't really helping.
00:00:26.710 --> 00:00:29.380
- [Boy] Your life is so bleak right now.
00:00:29.380 --> 00:00:31.800
- [Valentina] Well, thank you so much
00:00:31.800 --> 00:00:33.853
for your encouraging words.
00:00:36.170 --> 00:00:37.984
- [Boy] What did I say?
00:00:37.984 --> 00:00:40.567
(upbeat music)
00:00:45.530 --> 00:00:46.800
Hey Jamilla.
00:00:46.800 --> 00:00:48.120
- [Jamilla] Hey friends.
00:00:48.120 --> 00:00:50.470
What's with the face of doom, Valentina?
00:00:50.470 --> 00:00:52.190
Have you been eating
those poisonous apples
00:00:52.190 --> 00:00:53.990
from the tree behind the bleachers again?
00:00:53.990 --> 00:00:56.094
- [Valentina] My dad took my phone away.
00:00:56.094 --> 00:00:58.587
- [Jamilla] Yikes! Glad I'm not you.
00:00:58.587 --> 00:01:00.110
- [Valentina] (sighing)
What do I have to do
00:01:00.110 --> 00:01:02.725
to get some sympathy around here?
00:01:02.725 --> 00:01:04.114
(vibrating)
00:01:04.114 --> 00:01:06.400
(laughing)
00:01:06.400 --> 00:01:07.330
- [Jamilla] Sorry, what were you saying?
00:01:07.330 --> 00:01:09.283
- [Valentina] Ugh, never mind.
00:01:11.261 --> 00:01:13.330
- [Principal Rosario]
Attention Eagleton Huskies.
00:01:13.330 --> 00:01:15.370
Last night the school
board voted to regulate
00:01:15.370 --> 00:01:17.390
cell phone usage during school hours.
00:01:17.390 --> 00:01:18.960
Starting immediately, this lunch time.
00:01:18.960 --> 00:01:20.682
- [Boy] Uh, what?
00:01:20.682 --> 00:01:21.515
- [Principal Rosario] Research shows
00:01:21.515 --> 00:01:23.090
that cell phones are distracting,
00:01:23.090 --> 00:01:25.720
isolating, and can get in the way of work.
00:01:25.720 --> 00:01:28.120
To this end, we will be
imposing a new policy
00:01:28.120 --> 00:01:29.220
here at school.
00:01:29.220 --> 00:01:30.560
- [Jamilla] Did you know about this?
00:01:30.560 --> 00:01:31.972
- [Valentina] What? No!
00:01:31.972 --> 00:01:33.480
- [Principal Rosario] In
order to maximize learning,
00:01:33.480 --> 00:01:34.910
and eliminate distractions,
00:01:34.910 --> 00:01:39.070
there will be no cell phone
usage during class or lunch.
00:01:39.070 --> 00:01:41.080
All teachers are in line
on this new approach,
00:01:41.080 --> 00:01:43.461
and the policy will be strictly enforced.
00:01:43.461 --> 00:01:46.233
- [Valentina] Well this
just gets better and better.
00:01:47.124 --> 00:01:48.380
- [Principal Rosario]
Thank you for listening,
00:01:48.380 --> 00:01:49.653
now put your phones away.
00:01:51.492 --> 00:01:54.450
- [Jamilla] Unbelievable, did he just?
00:01:54.450 --> 00:01:55.283
- [Valentina] He did.
00:01:55.283 --> 00:01:56.610
- [Boy] I'm calling my lawyer.
00:01:56.610 --> 00:01:59.100
- [Jamilla] You don't have a
lawyer, you're 12 years old.
00:01:59.100 --> 00:02:01.370
- [Boy] Oh yeah, but the point is,
00:02:01.370 --> 00:02:04.260
this is America, land of the free.
00:02:04.260 --> 00:02:05.960
What kind of freedom is this?
00:02:05.960 --> 00:02:07.250
- [Jamilla] Well, Valentina?
00:02:07.250 --> 00:02:08.310
- [Valentina] Well, what?
00:02:08.310 --> 00:02:10.030
- [Jamilla] What are you going to do?
00:02:10.030 --> 00:02:10.863
- [Valentina] Me?
00:02:10.863 --> 00:02:12.090
- [Jamilla] Last time I checked,
00:02:12.090 --> 00:02:14.400
Mr. Rosario was still your dad.
00:02:14.400 --> 00:02:16.160
And it was you flunking the history test
00:02:16.160 --> 00:02:18.690
that gave him this idea
in the first place.
00:02:18.690 --> 00:02:21.543
Your problem, you figure it out.
00:02:24.648 --> 00:02:26.981
(sad music)
00:02:37.120 --> 00:02:38.510
Can you believe it?
00:02:38.510 --> 00:02:40.580
They confiscated my phone
because I took it out
00:02:40.580 --> 00:02:44.210
for literally four seconds
to check a text from my mom.
00:02:44.210 --> 00:02:45.830
- [Boy] Ugh, that's just wrong.
00:02:45.830 --> 00:02:48.740
I mean what if it was a
serious emergency or something?
00:02:48.740 --> 00:02:49.770
- [Jamilla] Right?
00:02:49.770 --> 00:02:51.530
I don't know how much
longer I can take it.
00:02:51.530 --> 00:02:54.810
It's such an inconvenience
to wait until after school
00:02:54.810 --> 00:02:57.680
to check my texts or contact my friends.
00:02:57.680 --> 00:03:00.300
Plus now I have to write
down my assignments,
00:03:00.300 --> 00:03:01.300
which takes forever.
00:03:02.425 --> 00:03:05.090
It was so much faster
to just take a picture.
00:03:05.090 --> 00:03:06.820
- [Boy] Like do they want us
to go back to the Stone Age,
00:03:06.820 --> 00:03:07.653
or what?
00:03:08.700 --> 00:03:12.250
- [Valentina] Hey, hey, I figured it out.
00:03:12.250 --> 00:03:13.083
- [Boy] What?
00:03:13.083 --> 00:03:15.380
- [Valentina] Jamilla
said this was my problem,
00:03:15.380 --> 00:03:18.820
so I came up with a plan.
00:03:18.820 --> 00:03:20.170
- [Jamilla] This had better be good.
00:03:20.170 --> 00:03:21.520
- [Valentina] Oh it's good.
00:03:22.800 --> 00:03:25.050
You know how my dad said
he was banning cell phones
00:03:25.050 --> 00:03:27.420
because research said
they were distracting?
00:03:27.420 --> 00:03:29.200
- [Jamilla] How could I forget?
00:03:29.200 --> 00:03:32.921
- [Valentina] But what was
he doing when he said that?
00:03:32.921 --> 00:03:34.850
- [Boy] Being an evil dictator.
00:03:34.850 --> 00:03:38.880
- [Valentina] No, he was
using reasons and evidence.
00:03:38.880 --> 00:03:42.000
And that is what we're going to do too.
00:03:42.000 --> 00:03:42.833
- [Boy] You mean?
00:03:42.833 --> 00:03:44.320
- [Valentina] That's right.
00:03:44.320 --> 00:03:48.773
We're going to write
an argumentative essay.
00:03:49.850 --> 00:03:51.480
- [Jamilla] Is this a joke?
00:03:51.480 --> 00:03:53.590
- [Boy] No, it's genius.
00:03:53.590 --> 00:03:55.150
You're a genius Valentina.
00:03:55.150 --> 00:03:56.720
We'll turn their own weapons against them,
00:03:56.720 --> 00:03:58.630
and crush them mercilessly.
00:03:58.630 --> 00:03:59.463
- [Jamilla] With what?
00:03:59.463 --> 00:04:00.910
A topic sentence?
00:04:00.910 --> 00:04:02.130
- [Valentina] Exactly!
00:04:02.130 --> 00:04:04.220
But first, we've got to come up with
00:04:04.220 --> 00:04:05.473
our full list of points.
00:04:06.380 --> 00:04:09.573
So, are you guys going to help me or not?
00:04:11.060 --> 00:04:11.893
- [Boy] I'm in.
00:04:12.850 --> 00:04:13.950
- [Valentina] Jamilla?
00:04:16.164 --> 00:04:17.700
- [Jamilla] (sighing) Fine.
00:04:17.700 --> 00:04:18.880
But if this doesn't work,
00:04:18.880 --> 00:04:21.540
you're doing my homework
for the next decade.
00:04:21.540 --> 00:04:22.720
- [Valentina] It's a deal!
00:04:22.720 --> 00:04:24.860
Now let's do this.
00:04:24.860 --> 00:04:27.443
(upbeat music)
|
Distillation curves | https://www.youtube.com/watch?v=Aaz99lyLBf8 | vtt | https://www.youtube.com/api/timedtext?v=Aaz99lyLBf8&ei=91WUZciCGt_2xN8P75aXgAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1711E3B71DD6119467C04482925D4EB18FBB2547.DF358726CA44FB039B7CA4767280BD0CC0FCCFF9&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.480 --> 00:00:01.313
- [Instructor] In this video,
00:00:01.313 --> 00:00:03.270
we're gonna dig a little bit
deeper into distillation,
00:00:03.270 --> 00:00:05.840
and in particular, we're
gonna learn how to construct
00:00:05.840 --> 00:00:09.320
and interpret distillation curves.
00:00:09.320 --> 00:00:14.320
So let's say we're trying to
distill roughly 50 milliliters.
00:00:15.370 --> 00:00:19.820
That is 50% methyl acetate
and 50% propyl acetate.
00:00:19.820 --> 00:00:22.750
If you don't know what methyl
acetate or propyl acetate are
00:00:22.750 --> 00:00:25.100
not a big deal, but what's interesting
00:00:25.100 --> 00:00:26.890
is the difference in their boiling points.
00:00:26.890 --> 00:00:31.530
The boiling point of methyl
acetate is 56.9 degrees Celsius.
00:00:31.530 --> 00:00:35.540
While the boiling point of
propyl acetate is a lot higher,
00:00:35.540 --> 00:00:38.410
101.5 degrees Celsius.
00:00:38.410 --> 00:00:39.700
And so you can imagine,
00:00:39.700 --> 00:00:43.290
as we have this fractional
distillation setup,
00:00:43.290 --> 00:00:45.760
we're going to be able to
separate these quite readily
00:00:45.760 --> 00:00:48.750
because of those differences
in boiling point.
00:00:48.750 --> 00:00:50.430
So what you do, you have the solution,
00:00:50.430 --> 00:00:52.070
you begin to heat it up.
00:00:52.070 --> 00:00:53.530
Now you're going to have to heat it up
00:00:53.530 --> 00:00:55.480
to the boiling point of the mixture,
00:00:55.480 --> 00:00:57.160
which is going to be someplace in between
00:00:57.160 --> 00:00:58.140
these two boiling points.
00:00:58.140 --> 00:01:01.600
It's probably going to be
70-something degrees Celsius.
00:01:01.600 --> 00:01:04.290
Now once you get this thing boiling,
00:01:04.290 --> 00:01:07.520
you're going to start having
a lot more vapors form.
00:01:07.520 --> 00:01:09.310
Now those vapors are
going to be a combination
00:01:09.310 --> 00:01:12.360
of methyl acetate and propyl acetate.
00:01:12.360 --> 00:01:15.110
Because methyl acetate
has a lower boiling point
00:01:15.110 --> 00:01:16.500
than propyl acetate,
00:01:16.500 --> 00:01:18.670
a disproportionate number of those vapors
00:01:18.670 --> 00:01:20.240
are gonna be methyl acetate.
00:01:20.240 --> 00:01:22.950
And then, because this is
fractional distillation,
00:01:22.950 --> 00:01:26.610
that mixture of vapors is
going to have multiple cycles
00:01:26.610 --> 00:01:29.480
of condensing and then revaporizing.
00:01:29.480 --> 00:01:31.390
And as we get higher and higher,
00:01:31.390 --> 00:01:34.590
every time you condense
and then revaporize,
00:01:34.590 --> 00:01:37.190
those revaporized vapors are going to have
00:01:37.190 --> 00:01:40.050
even a higher proportion
of methyl acetate.
00:01:40.050 --> 00:01:40.883
And what you see
00:01:40.883 --> 00:01:43.190
as you gradually increase
the temperature here,
00:01:43.190 --> 00:01:45.820
you're going to have
this condensation ring,
00:01:45.820 --> 00:01:47.470
and you can view that as the boundary
00:01:47.470 --> 00:01:51.780
between where it's hot enough
for enough vapors to form
00:01:51.780 --> 00:01:53.370
and where it's not hot enough
00:01:53.370 --> 00:01:55.850
for enough vapors to
form and they condense.
00:01:55.850 --> 00:02:00.210
And so when this temperature
is having fairly low readings,
00:02:00.210 --> 00:02:01.620
maybe right at the beginning,
00:02:01.620 --> 00:02:05.760
you're not going to be
generating a lot of distillate.
00:02:05.760 --> 00:02:08.650
You're not really gonna be
generating a lot of distillate
00:02:08.650 --> 00:02:12.310
until this condensation
ring gets pretty close
00:02:12.310 --> 00:02:14.730
to where the bulb of this thermometer is,
00:02:14.730 --> 00:02:16.630
and those vapors can start entering
00:02:16.630 --> 00:02:19.050
into this condensation tube.
00:02:19.050 --> 00:02:21.120
And now you can imagine by the time
00:02:21.120 --> 00:02:24.520
that the ring gets up here,
that means that the vapors,
00:02:24.520 --> 00:02:25.560
the mixture of vapors,
00:02:25.560 --> 00:02:29.330
have had multiple cycles of
condensation and vaporization,
00:02:29.330 --> 00:02:33.090
which is equivalent to multiple
simple distillation cycles.
00:02:33.090 --> 00:02:36.110
So by the time the
vapor ring gets up here,
00:02:36.110 --> 00:02:39.400
we're going to have mainly
methyl acetate vapors.
00:02:39.400 --> 00:02:40.700
And the temperature here,
00:02:40.700 --> 00:02:43.300
the boiling point of the vapors up here,
00:02:43.300 --> 00:02:46.970
are gonna be roughly the
boiling point of methyl acetate.
00:02:46.970 --> 00:02:47.803
But that's the point
00:02:47.803 --> 00:02:50.040
at which you start seeing
a lot of those vapors
00:02:50.040 --> 00:02:52.000
being able to enter into
the condensation ring
00:02:52.000 --> 00:02:52.833
and get condensed,
00:02:52.833 --> 00:02:55.820
and we're starting to
produce a lot of distillate.
00:02:55.820 --> 00:03:00.820
So right at around 56.9
degrees Celsius, roughly,
00:03:01.930 --> 00:03:05.630
we now start producing
a lot of distillate.
00:03:05.630 --> 00:03:07.790
Now you can imagine the
whole time we're doing this,
00:03:07.790 --> 00:03:10.680
you have to slowly increase
the temperature of the mixture.
00:03:10.680 --> 00:03:11.740
Why is that?
00:03:11.740 --> 00:03:13.590
Well, as we start losing
00:03:13.590 --> 00:03:16.340
more and more methyl acetate vapors,
00:03:16.340 --> 00:03:20.120
then the boiling point of the
solution is going to increase.
00:03:20.120 --> 00:03:22.750
As we said, this original
solution's about 50 milliliters.
00:03:22.750 --> 00:03:25.880
So once you get about
20-something milliliters
00:03:25.880 --> 00:03:28.660
of your methyl acetate distilled,
00:03:28.660 --> 00:03:31.040
you are not going to be able to produce
00:03:31.040 --> 00:03:33.910
a lot more distillate at that temperature.
00:03:33.910 --> 00:03:36.350
You're gonna have to keep
increasing that temperature
00:03:36.350 --> 00:03:39.860
until the bulb here
gets to the temperature
00:03:39.860 --> 00:03:42.800
of the boiling point of propyl acetate.
00:03:42.800 --> 00:03:45.610
So the temperature of the
bulb keeps increasing.
00:03:45.610 --> 00:03:49.180
You're not seeing a lot of new distillate,
00:03:49.180 --> 00:03:50.830
maybe a little bit more form,
00:03:50.830 --> 00:03:54.330
and you are getting more and
more of the propyl acetate.
00:03:54.330 --> 00:03:58.010
So this especially is going
to be a mixture of vapors.
00:03:58.010 --> 00:04:00.220
You're kind of getting the
last of the methyl acetate,
00:04:00.220 --> 00:04:02.690
but you're getting an increase
amount of propyl acetate.
00:04:02.690 --> 00:04:03.800
But once you're hot enough
00:04:03.800 --> 00:04:06.560
at the boiling point of propyl acetate,
00:04:06.560 --> 00:04:10.430
so about 101 degrees Celsius,
00:04:10.430 --> 00:04:14.630
then you start producing a
lot more of your distillate.
00:04:14.630 --> 00:04:16.960
And this is essentially
the condensing vapors
00:04:16.960 --> 00:04:19.330
of propyl acetate.
00:04:19.330 --> 00:04:21.340
And so if you wanted
to separate these two,
00:04:21.340 --> 00:04:23.700
what you would do is, in this first phase,
00:04:23.700 --> 00:04:25.170
when you see this plateau
00:04:25.170 --> 00:04:27.260
and you're seeing a lot
of this volume happen
00:04:27.260 --> 00:04:29.530
at the boiling point of methyl acetate,
00:04:29.530 --> 00:04:32.770
you could have one little
tube here or one little jar,
00:04:32.770 --> 00:04:35.030
and then you can swap them in this phase.
00:04:35.030 --> 00:04:36.930
Before you raise the temperature too much,
00:04:36.930 --> 00:04:38.810
you can then collect the condensation
00:04:38.810 --> 00:04:41.130
of the propyl acetate.
00:04:41.130 --> 00:04:43.180
Now you can also go the other way around.
00:04:43.180 --> 00:04:47.440
People will oftentimes present
to you a distillation curve
00:04:47.440 --> 00:04:49.990
that looks something like that.
00:04:49.990 --> 00:04:51.120
And they might say, okay,
00:04:51.120 --> 00:04:53.500
what were the boiling points
of the constituents there?
00:04:53.500 --> 00:04:56.580
And you'd say, okay, well the
lower boiling point substance,
00:04:56.580 --> 00:04:58.010
I can see that right over here.
00:04:58.010 --> 00:04:59.940
We were able to get a lot of distillate
00:04:59.940 --> 00:05:02.700
when the bulb right over
here was at that temperature,
00:05:02.700 --> 00:05:06.203
so that must be the boiling
point of substance one.
00:05:07.180 --> 00:05:09.330
And you might even be able to identify it
00:05:09.330 --> 00:05:11.520
if you know the boiling point
of different substances.
00:05:11.520 --> 00:05:13.770
And then you would identify this plateau
00:05:13.770 --> 00:05:18.750
as the boiling point of
substance number two.
00:05:18.750 --> 00:05:20.140
So some of you all might be thinking,
00:05:20.140 --> 00:05:24.210
this is all good and well
for fractional distillation,
00:05:24.210 --> 00:05:28.390
but what would simple distillation
curve actually look like?
00:05:28.390 --> 00:05:30.140
Well, remember, in simple distillation,
00:05:30.140 --> 00:05:32.230
you don't have multiple cycles
00:05:32.230 --> 00:05:35.260
of condensation and revaporization,
00:05:35.260 --> 00:05:37.270
which is equivalent to multiple cycles
00:05:37.270 --> 00:05:38.950
of simple distillation.
00:05:38.950 --> 00:05:42.270
So when you're hot enough for
the vapors to get up here,
00:05:42.270 --> 00:05:44.650
it's gonna be less pure methyl acetate.
00:05:44.650 --> 00:05:47.250
It's going to be a combination of the two.
00:05:47.250 --> 00:05:49.750
It still will be
disproportionally methyl acetate,
00:05:49.750 --> 00:05:52.060
but the boiling point of
that combination of mixtures
00:05:52.060 --> 00:05:53.460
is going to be higher.
00:05:53.460 --> 00:05:54.770
So what happens
00:05:54.770 --> 00:05:57.650
is that you start getting
significant distillate
00:05:57.650 --> 00:05:59.810
at a higher temperature
00:05:59.810 --> 00:06:04.730
and the whole notion is just
a little bit more gradual
00:06:04.730 --> 00:06:09.550
when you're doing simple
distillation versus fractional.
00:06:09.550 --> 00:06:11.390
And you could imagine if
someone were to present
00:06:11.390 --> 00:06:13.560
a simple distillation curve like this,
00:06:13.560 --> 00:06:15.890
it's much harder to pick
out the boiling points
00:06:15.890 --> 00:06:18.560
of the various substances,
because at any given point,
00:06:18.560 --> 00:06:20.803
you have more of a mixture of vapors
00:06:20.803 --> 00:06:23.003
than you do when you're doing fractional.
|
Measuring lengths in different units | https://www.youtube.com/watch?v=9dur4s-4lhk | vtt | https://www.youtube.com/api/timedtext?v=9dur4s-4lhk&ei=91WUZdHJGpSmp-oPg5OI0AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=274A5FA0CA0565E2CFE7379E8E74768C221B7F3E.E7EFDB853F9B22C041CA29AA6A93D77843388A95&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.800 --> 00:00:02.930
- [Instructor] So I have
the same green rectangle
00:00:02.930 --> 00:00:04.560
up here and down here
00:00:04.560 --> 00:00:07.120
and what I wanna do is measure its width
00:00:07.120 --> 00:00:10.210
but we're going to measure it's
with in two different ways.
00:00:10.210 --> 00:00:12.220
Up here, we're going to measure it's width
00:00:12.220 --> 00:00:15.490
in terms of how many of
these paper clips wide
00:00:15.490 --> 00:00:16.780
the rectangle is
00:00:16.780 --> 00:00:19.360
and down here, we're
going to measure its width
00:00:19.360 --> 00:00:23.330
in terms of how many centimeters
wide this rectangle is.
00:00:23.330 --> 00:00:24.490
So let's start on top.
00:00:24.490 --> 00:00:25.323
Pause the video.
00:00:25.323 --> 00:00:28.323
How many paper clips
wide is this rectangle?
00:00:29.730 --> 00:00:31.740
All right, now let's do this together.
00:00:31.740 --> 00:00:35.690
We can see that the rectangle
starts right over here
00:00:35.690 --> 00:00:38.420
and it ends right over here on the right
00:00:38.420 --> 00:00:39.800
if we're thinking about its width
00:00:39.800 --> 00:00:44.800
and so we have one,
two, three, four, five,
00:00:45.150 --> 00:00:50.150
six, seven, eight, nine, 10 paper clips.
00:00:50.630 --> 00:00:55.630
So this rectangle is we
could say 10 paper clips,
00:00:55.810 --> 00:00:59.133
paper clips wide.
00:00:59.980 --> 00:01:02.030
Now, if we wanna measure
it in terms of centimeters,
00:01:02.030 --> 00:01:04.530
we would do the same thing
but we would use this ruler.
00:01:04.530 --> 00:01:06.450
Let me do this in a different color.
00:01:06.450 --> 00:01:08.120
So the left edge is there.
00:01:08.120 --> 00:01:10.550
The right edge is right over there
00:01:10.550 --> 00:01:14.120
and it looks like this
rectangle is also one,
00:01:14.120 --> 00:01:19.020
two, three, four, five centimeters wide.
00:01:19.020 --> 00:01:22.553
Five centimeters wide.
00:01:23.400 --> 00:01:27.200
So notice 10, the same
rectangle has the same width.
00:01:27.200 --> 00:01:31.560
It's 10 paper clips wide and
it's five centimeters wide.
00:01:31.560 --> 00:01:35.090
So its width is more paper
clips than centimeters
00:01:35.090 --> 00:01:36.670
is one way to think about it.
00:01:36.670 --> 00:01:40.600
Now, based on that, what is
a larger unit of measurement,
00:01:40.600 --> 00:01:41.450
the paper clip,
00:01:41.450 --> 00:01:44.440
at least these paper
clips or the centimeter?
00:01:44.440 --> 00:01:46.240
Pause the video to think about that.
00:01:47.450 --> 00:01:49.513
Well, you might just see it naturally
00:01:49.513 --> 00:01:52.470
if you just look at a
centimeter right over here.
00:01:52.470 --> 00:01:55.100
It looks wider than a paper clip
00:01:55.100 --> 00:01:57.840
but you could also tell that
by looking at the measurement.
00:01:57.840 --> 00:02:00.000
We needed more paper clips
00:02:00.000 --> 00:02:02.360
to cover the width of this rectangle
00:02:02.360 --> 00:02:03.800
than we needed centimeters
00:02:03.800 --> 00:02:07.270
and so, because we
needed more paper clips,
00:02:07.270 --> 00:02:10.720
that means that this is
a smaller unit of measure
00:02:10.720 --> 00:02:13.000
because we needed more of them.
00:02:13.000 --> 00:02:18.000
So this is a smaller unit of measure
00:02:18.900 --> 00:02:20.450
or maybe actually I should make the arrow
00:02:20.450 --> 00:02:21.800
point right over here.
00:02:21.800 --> 00:02:24.930
The paper clip is a
smaller unit of measure
00:02:24.930 --> 00:02:29.930
and then the centimeter is
the larger unit of measure.
00:02:32.210 --> 00:02:34.280
We needed fewer centimeters
00:02:34.280 --> 00:02:37.050
to make up the width of the
rectangle than paper clips.
00:02:37.050 --> 00:02:40.020
So the centimeter is larger
and you could see that visually
00:02:40.020 --> 00:02:42.680
if you just look at that
with compared to that width.
00:02:42.680 --> 00:02:47.203
It's clear that a centimeter
is wider than this paper clip.
|
How to Keep Your Child Learning & Happy! at Home | https://www.youtube.com/watch?v=2XQdVMqAAsg | vtt | https://www.youtube.com/api/timedtext?v=2XQdVMqAAsg&ei=91WUZbSuGv2np-oPwsCdgAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245351&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9E41A388338433E26CF59D3513AD752C6513E7B9.D609B4B33910AF0AAA1E5C877D2987757F604373&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.672 --> 00:00:03.592
- Hello, thank you for joining us today,
00:00:03.592 --> 00:00:06.192
we know how busy you are as
parents of young children
00:00:06.192 --> 00:00:08.012
particularly during these times
00:00:08.012 --> 00:00:10.242
with so much going on in the world.
00:00:10.242 --> 00:00:12.522
We wanna make the session
a really valuable use
00:00:12.522 --> 00:00:15.722
of your time, so we're
gonna jump right in.
00:00:15.722 --> 00:00:19.652
I'm Caroline Huflexor and
I'm the CEO and co-founder
00:00:19.652 --> 00:00:21.602
of Khan Academy Kids,
00:00:21.602 --> 00:00:24.982
and today I am joined
by my colleague Dan Tu,
00:00:24.982 --> 00:00:27.782
who will be moderating
our questions later.
00:00:27.782 --> 00:00:31.042
And our special guest Renee Scott.
00:00:31.042 --> 00:00:34.252
Renee is a longtime early educator
00:00:34.252 --> 00:00:38.012
and is early education program director
00:00:38.012 --> 00:00:39.922
at Stanford University.
00:00:39.922 --> 00:00:42.882
She's been one of our
main curriculum advisors
00:00:42.882 --> 00:00:44.782
as we've developed Khan Kids.
00:00:44.782 --> 00:00:46.872
And Renee and I are both parents
00:00:46.872 --> 00:00:48.202
and we will be talking about
00:00:48.202 --> 00:00:50.312
how to keep young kids engaged
00:00:50.312 --> 00:00:53.132
and learning at home while
many schools are closed,
00:00:53.132 --> 00:00:54.182
and families are going through
00:00:54.182 --> 00:00:55.755
a lot of transition this fall.
00:00:57.142 --> 00:00:59.692
We're nonprofit, and I'd
like to thank our sponsors,
00:00:59.692 --> 00:01:04.122
Bank of America, AT&T,
google.org, Novartis and Fastly
00:01:04.122 --> 00:01:05.572
for their support of this webinar
00:01:05.572 --> 00:01:08.952
and our other distance learning resources.
00:01:08.952 --> 00:01:11.512
A few other notes, this
webinar will be recorded.
00:01:11.512 --> 00:01:15.632
And we'll be sending a copy to
you via email in a few hours.
00:01:15.632 --> 00:01:17.192
And if you have questions,
00:01:17.192 --> 00:01:19.642
please enter them in the question box.
00:01:19.642 --> 00:01:21.912
We'll save time at the
end for live Q and A.
00:01:23.102 --> 00:01:24.952
So, today we'll be focusing mostly
00:01:24.952 --> 00:01:27.622
on the youngest children
ages two through seven.
00:01:27.622 --> 00:01:30.152
So, preschool through grade one.
00:01:30.152 --> 00:01:31.502
Let's get started.
00:01:31.502 --> 00:01:34.722
I am thrilled to have
Renee with us here today.
00:01:34.722 --> 00:01:37.342
Can you share a little bit about yourself
00:01:37.342 --> 00:01:38.682
and your background?
00:01:38.682 --> 00:01:40.382
- Sure.
00:01:40.382 --> 00:01:41.382
Thanks, Caroline.
00:01:41.382 --> 00:01:43.882
I am a lifelong teacher.
00:01:43.882 --> 00:01:45.982
I started long ago as a swim instructor
00:01:45.982 --> 00:01:48.082
when I was in high school and just kept on
00:01:48.082 --> 00:01:49.562
that teaching path.
00:01:49.562 --> 00:01:53.622
So now I've taught kindergarten,
first grade, fourth grade,
00:01:53.622 --> 00:01:57.372
sixth grade, and I'm
currently teaching teachers
00:01:57.372 --> 00:02:00.792
how to engage in engage young children
00:02:00.792 --> 00:02:02.372
with reading and math,
00:02:02.372 --> 00:02:06.782
specifically in pre-k and
kindergarten and first grade.
00:02:06.782 --> 00:02:09.822
And as you mentioned, I'm also a mom,
00:02:09.822 --> 00:02:11.712
my kids are now a teen and preteen.
00:02:11.712 --> 00:02:13.845
So I've seen a lot of stages with them.
00:02:14.752 --> 00:02:16.135
- Wonderful, thanks Renee.
00:02:17.442 --> 00:02:20.962
Some parents of young children
are typically the ones
00:02:20.962 --> 00:02:24.382
who are the really stressed
then, even in the best of times.
00:02:24.382 --> 00:02:27.172
And right now, in this pandemic,
00:02:27.172 --> 00:02:30.482
they're juggling even more so
on top of work and childcare,
00:02:30.482 --> 00:02:35.199
their heightened health and
financial and medical concerns.
00:02:35.199 --> 00:02:37.112
And now with school closures,
00:02:37.112 --> 00:02:39.402
a lot of parents are managing
the distance learning
00:02:39.402 --> 00:02:40.822
for their young children.
00:02:40.822 --> 00:02:42.932
What's your big message to parents
00:02:42.932 --> 00:02:44.952
as they are getting through these times
00:02:44.952 --> 00:02:48.265
and wanna keep their children
learning and developing?
00:02:50.072 --> 00:02:51.652
- So you're exactly right.
00:02:51.652 --> 00:02:53.082
It is a stressful time right now
00:02:53.082 --> 00:02:55.832
trying to figure out how to
juggle things in a new way.
00:02:56.722 --> 00:02:59.282
And really, I think my big message is
00:02:59.282 --> 00:03:03.772
to all of you parents out there,
you're already doing a lot.
00:03:03.772 --> 00:03:07.155
Give yourself some grace and
give your kids some grace too.
00:03:08.542 --> 00:03:11.702
It's a lot to take on
and here's the thing,
00:03:11.702 --> 00:03:13.422
kids are learning all the time,
00:03:13.422 --> 00:03:15.612
whether you're teaching them something,
00:03:15.612 --> 00:03:18.122
or you're just hanging out
with them doing something.
00:03:18.122 --> 00:03:20.172
So, there's a pretty good chance that
00:03:20.172 --> 00:03:23.472
some of those things that
you're engaged in, for example,
00:03:23.472 --> 00:03:27.112
your bedtime routine,
that's engaging in learning.
00:03:27.112 --> 00:03:28.682
They're learning about time.
00:03:28.682 --> 00:03:31.312
They're learning about
how to reflect on the day,
00:03:31.312 --> 00:03:32.712
they're using language.
00:03:32.712 --> 00:03:34.092
So today, we're gonna spend some time
00:03:34.092 --> 00:03:36.852
talking a little bit about
what that might look like
00:03:36.852 --> 00:03:39.692
and how to insert some
intentional language
00:03:39.692 --> 00:03:41.885
into how to support your development.
00:03:42.972 --> 00:03:43.805
- That's great.
00:03:45.272 --> 00:03:48.312
Yeah, can you give me some examples of
00:03:48.312 --> 00:03:51.075
some of these everyday activities
00:03:51.075 --> 00:03:52.702
and how you could use language
00:03:52.702 --> 00:03:54.972
as you go through the second.
00:03:54.972 --> 00:03:55.805
- Definitely.
00:03:55.805 --> 00:03:58.992
So, one of the things that
I like to remind myself of
00:03:58.992 --> 00:04:02.252
is that when you go to
a preschool classroom,
00:04:02.252 --> 00:04:03.762
a lot of times you'll notice that kids
00:04:03.762 --> 00:04:05.422
are working in some sort of center
00:04:05.422 --> 00:04:08.512
and they're working with others.
00:04:08.512 --> 00:04:11.442
And there we call them
sort of workplace centers
00:04:11.442 --> 00:04:13.082
maybe they're working on a painting
00:04:13.082 --> 00:04:15.872
or they're working on listening to books
00:04:15.872 --> 00:04:18.045
with a friend or through a tape recorder.
00:04:19.182 --> 00:04:24.182
And so I like to think about
working with young children
00:04:24.232 --> 00:04:26.692
even at home in these ways
00:04:26.692 --> 00:04:30.682
to think about how to organize your day.
00:04:30.682 --> 00:04:31.942
So for example,
00:04:31.942 --> 00:04:35.452
just looking for opportunities
perhaps to use your language
00:04:35.452 --> 00:04:38.992
and language development and
ask really good questions,
00:04:38.992 --> 00:04:42.132
and just being intentionally
during an activity
00:04:42.132 --> 00:04:43.505
such as bath time,
00:04:44.572 --> 00:04:46.972
it's really a great time to talk about
00:04:46.972 --> 00:04:51.452
maybe sensory skills and
fine motor asking kids, hey,
00:04:51.452 --> 00:04:53.272
I wonder how do these bubbles feel?
00:04:53.272 --> 00:04:54.752
How do they feel to you,
00:04:54.752 --> 00:04:59.172
you can introduce words
like fluffy, wet, slippery,
00:04:59.172 --> 00:05:02.002
those are really great words to practice
00:05:02.002 --> 00:05:04.412
and it builds out their vocabulary.
00:05:04.412 --> 00:05:07.402
Bath times also really great
time to make up stories
00:05:07.402 --> 00:05:10.372
and making up stories
is brilliant for kids.
00:05:10.372 --> 00:05:12.962
It helps prep them for learning to read,
00:05:12.962 --> 00:05:15.252
for learning to write,
00:05:15.252 --> 00:05:18.342
for starting to understand
things like history
00:05:18.342 --> 00:05:19.332
and social studies.
00:05:19.332 --> 00:05:21.672
So, it's one of those activities
00:05:21.672 --> 00:05:23.112
that's really fun when they're little,
00:05:23.112 --> 00:05:25.542
that just has a ton of
payoff and benefits.
00:05:25.542 --> 00:05:27.662
So if your kids to hop into the bath,
00:05:27.662 --> 00:05:31.392
and they've got a fish
in a frog and just, say,
00:05:31.392 --> 00:05:35.092
some really great questions
to ask, or, oh, what happens,
00:05:35.092 --> 00:05:36.992
tell me a story about fish and frog,
00:05:36.992 --> 00:05:39.652
and then keep the conversation going.
00:05:39.652 --> 00:05:43.052
So what happens next,
and then what happens?
00:05:43.052 --> 00:05:44.892
And tell me more about that.
00:05:44.892 --> 00:05:48.432
So, if you can just keep
your kids talking about
00:05:48.432 --> 00:05:49.265
something like that,
00:05:49.265 --> 00:05:51.262
and perhaps use some of
that more difficult language
00:05:51.262 --> 00:05:53.322
they don't know yet and encourage them
00:05:53.322 --> 00:05:54.792
to use that in their speech.
00:05:54.792 --> 00:05:56.672
It works great.
00:05:56.672 --> 00:05:58.102
Another great example of something
00:05:58.102 --> 00:06:01.452
that you're gonna have to do
anyway, is brushing teeth.
00:06:01.452 --> 00:06:02.542
I know it can be a challenge,
00:06:02.542 --> 00:06:05.042
but it's also a great time
maybe to practice math.
00:06:06.632 --> 00:06:09.392
You can set a timer
that the kids can watch,
00:06:09.392 --> 00:06:11.132
they can count the timer down backwards.
00:06:11.132 --> 00:06:13.442
They keep track of each other
counting down backwards,
00:06:13.442 --> 00:06:16.812
counting forwards, maybe
they can see how many times
00:06:16.812 --> 00:06:19.577
they can hop on a foot before they're done
00:06:19.577 --> 00:06:21.202
with their brushing.
00:06:21.202 --> 00:06:23.562
It's also I've heard a lot
of kids sing their ABCs
00:06:23.562 --> 00:06:24.972
while they wash their hands.
00:06:24.972 --> 00:06:27.492
So these are just some really easy,
00:06:27.492 --> 00:06:31.392
but intentional ways to include a lot of
00:06:31.392 --> 00:06:33.812
the vocabulary language
and math type skills
00:06:33.812 --> 00:06:35.492
that are really gonna help them
00:06:35.492 --> 00:06:38.065
when they get back into the classroom.
00:06:39.592 --> 00:06:42.212
One that we love at my house is baking.
00:06:42.212 --> 00:06:43.852
And I think a lot of folks feel like oh,
00:06:43.852 --> 00:06:46.172
well, baking is obvious
because it involves
00:06:46.172 --> 00:06:49.092
measuring and pouring
and things like that.
00:06:49.092 --> 00:06:52.562
But I think it's easy
to forget things like,
00:06:52.562 --> 00:06:54.212
can you count how many blueberries
00:06:54.212 --> 00:06:58.462
we're gonna put into each of the muffins
00:06:58.462 --> 00:06:59.872
and put them into the cups,
00:06:59.872 --> 00:07:01.972
sorting things is amazing for kids.
00:07:01.972 --> 00:07:04.372
And that's a natural
way to get them sorting
00:07:04.372 --> 00:07:09.372
and get them thinking
about dividing and grouping
00:07:09.592 --> 00:07:11.682
and to use mathematical terms.
00:07:11.682 --> 00:07:12.762
But they're doing it right there
00:07:12.762 --> 00:07:14.222
at your kitchen counter, maybe.
00:07:14.222 --> 00:07:15.602
And something you have to do,
00:07:15.602 --> 00:07:18.312
maybe you're making muffins
for breakfast or your neighbor
00:07:18.312 --> 00:07:19.145
to help them out.
00:07:19.145 --> 00:07:22.012
So, those are easy ways to include that.
00:07:22.012 --> 00:07:23.822
Another one that's great
is get out the recipe
00:07:23.822 --> 00:07:24.932
and like kids look at it,
00:07:24.932 --> 00:07:26.812
if they can't read it, that's okay.
00:07:26.812 --> 00:07:29.002
They can look for words that start with M,
00:07:29.002 --> 00:07:31.412
they can look for how many ingredients,
00:07:31.412 --> 00:07:32.729
show them where the ingredient list is.
00:07:32.729 --> 00:07:34.922
And sometimes they have
numbers in front of them,
00:07:34.922 --> 00:07:37.282
have them count out all the ingredients.
00:07:37.282 --> 00:07:39.472
Those are just some quick ways to do
00:07:39.472 --> 00:07:42.682
to push these things into
what you're already doing.
00:07:42.682 --> 00:07:44.882
My daughter and I always
like to sing songs.
00:07:46.305 --> 00:07:47.138
The other day,
00:07:47.138 --> 00:07:48.262
we had a conversation
she's a little older now
00:07:48.262 --> 00:07:50.542
but we still like to
talk about song lyrics.
00:07:50.542 --> 00:07:53.445
And we were singing "The Method Man" song.
00:07:54.375 --> 00:07:56.002
♪ You know the method man, the method ♪
00:07:56.002 --> 00:07:57.992
and I was telling her, I
used to have this little boy
00:07:57.992 --> 00:08:00.682
when I taught kindergarten,
who just love that song.
00:08:00.682 --> 00:08:03.862
And I said, but I always wondered
about the word drury lane,
00:08:03.862 --> 00:08:05.692
I said it's a hard word to say.
00:08:05.692 --> 00:08:07.832
And drury sounds kind of dreary.
00:08:07.832 --> 00:08:09.972
And so we had this whole
conversation that included
00:08:09.972 --> 00:08:14.282
all this language and that's
the kind of silly conversation
00:08:14.282 --> 00:08:16.562
that ends up being something that
00:08:16.562 --> 00:08:18.215
includes a lot more vocabulary.
00:08:20.402 --> 00:08:24.522
So, one more example of
just integrating stuff
00:08:24.522 --> 00:08:27.615
into the everyday, one
of the things I love is,
00:08:28.592 --> 00:08:30.552
thinking about ways to be
intentional about eating
00:08:30.552 --> 00:08:32.292
maybe not always at the dinner table,
00:08:32.292 --> 00:08:33.752
but lunch table or breakfast table
00:08:33.752 --> 00:08:35.155
is a great time to do this.
00:08:37.643 --> 00:08:39.272
Using that time for counting
00:08:39.272 --> 00:08:42.422
is a great example of putting
something in there quickly.
00:08:42.422 --> 00:08:44.392
So, you're handing out grapes to the kids
00:08:44.392 --> 00:08:47.382
and ask them how many
grapes would you like
00:08:47.382 --> 00:08:51.302
and have them tell you and
then give them some grapes,
00:08:51.302 --> 00:08:53.232
you can mix this up,
00:08:53.232 --> 00:08:55.022
you can give them what they asked for
00:08:55.022 --> 00:08:56.892
and have them double check
and see if you're right
00:08:56.892 --> 00:08:58.962
or you can give them
what they didn't ask for
00:08:58.962 --> 00:09:01.392
and have them double check
and see if they catch you.
00:09:01.392 --> 00:09:06.152
So, kids really love that
aspect of there's a game in it,
00:09:06.152 --> 00:09:08.122
so and you can turn something into a game
00:09:08.122 --> 00:09:10.045
and make it playful, is great.
00:09:11.422 --> 00:09:14.132
- Great, I love hearing your examples
00:09:14.132 --> 00:09:16.952
because it's comforting to hear
00:09:16.952 --> 00:09:18.842
that there's so much learning
00:09:18.842 --> 00:09:20.652
in terms of language development
00:09:20.652 --> 00:09:23.112
and early numeracy that can just come up
00:09:23.112 --> 00:09:24.892
in everyday activities and things.
00:09:24.892 --> 00:09:27.512
So it's not like (mumbling)
00:09:27.512 --> 00:09:29.092
you don't have to sit your child down.
00:09:29.092 --> 00:09:29.925
And in fact,
00:09:29.925 --> 00:09:32.022
if you just sit your child
down and say, do this,
00:09:32.022 --> 00:09:35.072
it's probably not nearly as
fun and engaging for them.
00:09:35.072 --> 00:09:38.742
So, I love how you should
always be play base
00:09:38.742 --> 00:09:39.602
for young kids,
00:09:39.602 --> 00:09:42.499
which is how we approach
the learning in Khan Kids.
00:09:44.542 --> 00:09:45.662
So as an educator,
00:09:45.662 --> 00:09:48.382
what are some techniques
that teachers used
00:09:48.382 --> 00:09:50.632
to keep kids engaged and
learning through the day,
00:09:50.632 --> 00:09:54.602
especially as parents, we're
juggling work and multitasking
00:09:54.602 --> 00:09:57.842
and can't always be 100% focused on
00:09:57.842 --> 00:10:00.072
and playing with our kids all the time.
00:10:00.072 --> 00:10:02.202
- Yeah, definitely.
00:10:02.202 --> 00:10:03.462
One of the things I mean,
00:10:03.462 --> 00:10:05.942
the reality is there's gonna
be periods during the day
00:10:05.942 --> 00:10:08.482
when your kid, you can't sit
down and play with your child.
00:10:08.482 --> 00:10:10.002
You can't play a game with them.
00:10:10.002 --> 00:10:11.162
You maybe can't talk to them.
00:10:11.162 --> 00:10:12.162
You're on the phone.
00:10:13.092 --> 00:10:14.762
And the first thing again,
00:10:14.762 --> 00:10:16.782
I wanna reiterate, that's okay.
00:10:16.782 --> 00:10:20.022
Like, it's okay for your
kids to have to hang out
00:10:20.022 --> 00:10:21.762
and entertain themselves for a while,
00:10:21.762 --> 00:10:23.832
if that's what you need.
00:10:23.832 --> 00:10:26.132
Everyone's gonna be happier
if you're feeling better
00:10:26.132 --> 00:10:27.142
about what you're doing too.
00:10:27.142 --> 00:10:29.172
So give yourself grace there.
00:10:29.172 --> 00:10:32.482
But one thing that I do
like to keep in mind,
00:10:32.482 --> 00:10:34.312
and you were you kind of alluded to this
00:10:34.312 --> 00:10:37.082
just a second ago
Caroline, about motivation
00:10:37.082 --> 00:10:41.252
is sometimes the second you
ask a child to do something
00:10:41.252 --> 00:10:44.242
that they otherwise might do just for fun.
00:10:44.242 --> 00:10:46.622
It's not that fun to them anymore.
00:10:46.622 --> 00:10:48.402
It's a matter of trying to convince them
00:10:48.402 --> 00:10:50.352
that is their idea, right?
00:10:50.352 --> 00:10:54.032
So some of the things that
have been found, actually,
00:10:54.032 --> 00:10:56.392
this always makes me think of my mentor,
00:10:56.392 --> 00:10:58.932
Deborah Steinbeck because
she does a lot of research
00:10:58.932 --> 00:11:00.632
on motivation with young children.
00:11:00.632 --> 00:11:03.972
And she really highlighted
a few important things.
00:11:03.972 --> 00:11:06.542
And the ones that I wanna
talk about briefly today
00:11:06.542 --> 00:11:10.942
are competence, autonomy,
and care and connection.
00:11:10.942 --> 00:11:12.432
So, what are those mean, right?
00:11:12.432 --> 00:11:14.172
So, competence is just basically kids
00:11:14.172 --> 00:11:16.282
like to feel like they
know what they're doing.
00:11:16.282 --> 00:11:19.862
So going back to that
great example, if you,
00:11:19.862 --> 00:11:22.452
if they're able to catch
you giving them four grapes,
00:11:22.452 --> 00:11:26.312
when they asked for five,
they feel really competent.
00:11:26.312 --> 00:11:29.222
And also you get to see
that they know what,
00:11:29.222 --> 00:11:31.692
they know a skill and then you,
00:11:31.692 --> 00:11:32.982
it gives you that indication,
00:11:32.982 --> 00:11:34.092
okay, we can check,
00:11:34.092 --> 00:11:36.162
we can make this a little
more difficult for them
00:11:36.162 --> 00:11:37.842
and kids love the challenge.
00:11:37.842 --> 00:11:39.962
So, kind of up the challenge on them if
00:11:39.962 --> 00:11:41.942
when you get sense that
they're ready for it,
00:11:41.942 --> 00:11:43.762
they think that's exciting.
00:11:43.762 --> 00:11:45.892
The other thing is language
around that is important.
00:11:45.892 --> 00:11:49.582
So be careful not to always
say good job, good job,
00:11:49.582 --> 00:11:52.152
good job, because it's hard
to know what that means.
00:11:52.152 --> 00:11:55.642
So I really love the
response of you did it.
00:11:55.642 --> 00:11:57.262
Oh my gosh, you figured that out.
00:11:57.262 --> 00:11:58.962
You notice that?
00:11:58.962 --> 00:12:00.782
So just being really, specific.
00:12:00.782 --> 00:12:04.612
Oh, I saw that you put five
blocks all together in a pile.
00:12:04.612 --> 00:12:06.982
Wow, how did you put that together.
00:12:06.982 --> 00:12:09.082
So, rather than just saying good job,
00:12:09.082 --> 00:12:11.542
use it as a chance to
elicit more conversations.
00:12:11.542 --> 00:12:13.392
But also let them know that you observed
00:12:13.392 --> 00:12:15.935
that they did something
that was kind of cool.
00:12:16.788 --> 00:12:19.482
So, then getting back
to those other ideas,
00:12:19.482 --> 00:12:24.042
autonomy is just basically
giving them choices.
00:12:24.042 --> 00:12:26.702
I don't know if you've ever
heard a pre-k teacher do this,
00:12:26.702 --> 00:12:28.602
or if you've received the advice where
00:12:30.339 --> 00:12:32.742
you always run the risk of asking
00:12:32.742 --> 00:12:34.302
when you just don't give a child a choice,
00:12:34.302 --> 00:12:35.952
you say something like,
00:12:35.952 --> 00:12:39.702
do you wanna sit down and
color a picture with me,
00:12:39.702 --> 00:12:41.732
you run the risk of them saying, nope,
00:12:41.732 --> 00:12:43.105
and then you're right.
00:12:44.912 --> 00:12:46.212
Love to have choice.
00:12:46.212 --> 00:12:49.032
It makes them feel a little
bit more independent.
00:12:49.032 --> 00:12:50.302
It gives them some agency.
00:12:50.302 --> 00:12:52.792
So, offer a couple of things to them.
00:12:52.792 --> 00:12:55.532
If you know you're gonna be on
the phone for a few minutes,
00:12:55.532 --> 00:12:58.282
you can say here's three
things that you can do.
00:12:58.282 --> 00:12:59.732
What do you wanna start with?
00:13:00.672 --> 00:13:01.652
Do you wanna start with the puzzle
00:13:01.652 --> 00:13:03.132
or the blocks or the coloring
00:13:03.132 --> 00:13:04.492
and let them just pick the thing
00:13:04.492 --> 00:13:05.325
and then say when you're done,
00:13:05.325 --> 00:13:07.102
you can move to the next
thing that you want to do,
00:13:07.102 --> 00:13:10.492
but that way you're giving them
some specific things to do.
00:13:10.492 --> 00:13:12.452
So, you're still putting
boundaries around it,
00:13:12.452 --> 00:13:13.682
but they get to choose.
00:13:13.682 --> 00:13:14.635
And then finally,
00:13:15.642 --> 00:13:18.862
the caring connection piece
is really, really important.
00:13:18.862 --> 00:13:20.072
It's super hard right now
00:13:20.072 --> 00:13:22.952
'cause sometimes you're trying
to listen to a phone call
00:13:22.952 --> 00:13:24.022
and you've got your little one going
00:13:24.022 --> 00:13:25.342
mommy, mommy, mommy, right?
00:13:25.342 --> 00:13:28.362
And it feels like you just wanna,
00:13:28.362 --> 00:13:31.572
it's a lot sometimes to
handle all of that at once.
00:13:31.572 --> 00:13:35.142
And so, it's important
to maybe set aside time
00:13:35.142 --> 00:13:38.302
to make those points of
connection with your child.
00:13:38.302 --> 00:13:40.422
One of my favorite things to recommend
00:13:40.422 --> 00:13:43.572
and to do is to have a
moment at either at bedtime
00:13:43.572 --> 00:13:46.115
or bath time or even first
thing in the morning,
00:13:47.332 --> 00:13:48.732
where you ask them a few questions
00:13:48.732 --> 00:13:49.802
just to tap into their day.
00:13:49.802 --> 00:13:53.202
Our favorite thing at our house is to do
00:13:53.202 --> 00:13:56.472
what we call rose, thorn, and bird.
00:13:56.472 --> 00:13:57.782
And so with the rose,
00:13:57.782 --> 00:14:00.072
you ask them something
great that happened that day
00:14:00.072 --> 00:14:01.935
that made them feel beautiful.
00:14:02.972 --> 00:14:04.742
A thorn is maybe something that was ouchy
00:14:04.742 --> 00:14:05.902
that they didn't like very much
00:14:05.902 --> 00:14:08.692
and bird is something that
they're looking forward to.
00:14:08.692 --> 00:14:10.802
Some days we just do a bird, my kid Sam,
00:14:10.802 --> 00:14:12.032
oh, I'm really looking
forward to this thing,
00:14:12.032 --> 00:14:13.552
sometimes we just do an ouchy
00:14:13.552 --> 00:14:15.582
because we end up talking
about it for a while.
00:14:15.582 --> 00:14:18.722
And it's important to make
sure that your kids feel like
00:14:18.722 --> 00:14:21.592
all of how all of these things are okay.
00:14:21.592 --> 00:14:22.712
That you're here.
00:14:22.712 --> 00:14:23.732
You may not even want it,
00:14:23.732 --> 00:14:25.202
you don't wanna offer suggestions
00:14:25.202 --> 00:14:26.732
for how to fix it necessarily.
00:14:26.732 --> 00:14:30.072
You just want them to
have a chance to tell you
00:14:30.072 --> 00:14:32.232
what's going on and kind of
get stuff off their chest,
00:14:32.232 --> 00:14:33.912
little kids need to vent too.
00:14:33.912 --> 00:14:38.552
So, you're their most
comfortable person to vent to.
00:14:38.552 --> 00:14:39.762
So that's important,
00:14:39.762 --> 00:14:43.462
because then they know
that they can come to you
00:14:43.462 --> 00:14:44.295
when they need it,
00:14:44.295 --> 00:14:46.562
but that it's okay for
them to go a little further
00:14:46.562 --> 00:14:48.532
during the day and be
independent on their own
00:14:48.532 --> 00:14:49.762
when you're not always there.
00:14:49.762 --> 00:14:52.052
It helps that safety factor.
00:14:52.052 --> 00:14:54.035
So, it's very important.
00:14:56.555 --> 00:15:00.862
- Another part is that
maintaining routines
00:15:00.862 --> 00:15:02.402
is really important for young children.
00:15:02.402 --> 00:15:04.392
Why is that and how do you recommend
00:15:04.392 --> 00:15:06.192
that parents do that at home?
00:15:06.192 --> 00:15:08.442
- Yeah, yeah, good question.
00:15:08.442 --> 00:15:13.042
It's really, it can feel really daunting.
00:15:13.042 --> 00:15:15.372
And I wanna encourage parents
00:15:15.372 --> 00:15:17.482
that you don't feel like
you have to write up
00:15:17.482 --> 00:15:19.302
a separate lesson plan for your child
00:15:19.302 --> 00:15:22.212
on top of your own plans every day.
00:15:22.212 --> 00:15:24.762
But routine at the same
time routines are important.
00:15:24.762 --> 00:15:26.395
They help create a
sense of safety for kids
00:15:26.395 --> 00:15:29.962
that helps them know that
they're going to be fed
00:15:29.962 --> 00:15:31.932
at a certain time and
there's comfort in that,
00:15:31.932 --> 00:15:34.892
they know they're being taken
care of and looked after.
00:15:34.892 --> 00:15:36.272
It also helps you helps them to know
00:15:36.272 --> 00:15:38.822
what your expectations are of them.
00:15:38.822 --> 00:15:40.852
So if they know that after dinner,
00:15:40.852 --> 00:15:42.952
their job is to always
help clean up the dishes,
00:15:42.952 --> 00:15:43.785
there's comfort in that,
00:15:43.785 --> 00:15:46.012
they know that that's something
that they're supposed to do
00:15:46.012 --> 00:15:48.282
and it helps lower their anxiety levels,
00:15:48.282 --> 00:15:51.792
which ultimately helps
with things like meltdowns
00:15:51.792 --> 00:15:55.082
because they are aware
of what is coming up
00:15:55.082 --> 00:15:56.775
and what their expectations are.
00:15:58.752 --> 00:16:01.682
So one thing I wanna encourage you to do
00:16:01.682 --> 00:16:05.385
is to make your routine work for you.
00:16:06.432 --> 00:16:07.882
In the evening before you go to sleep
00:16:07.882 --> 00:16:09.442
or first thing in the
morning when you get up,
00:16:09.442 --> 00:16:11.372
take a look at your own schedule.
00:16:11.372 --> 00:16:13.652
Figure out when do you,
when are there times
00:16:13.652 --> 00:16:16.702
when you can maybe work with
your child on something?
00:16:16.702 --> 00:16:19.182
And where are the times
when you really do need
00:16:19.182 --> 00:16:20.452
to have alone time and you're gonna have
00:16:20.452 --> 00:16:22.152
to maybe put some things
out for your child
00:16:22.152 --> 00:16:24.862
to work on their own and
give them those directions,
00:16:24.862 --> 00:16:26.792
perfectly fine as well to prompt them,
00:16:26.792 --> 00:16:28.652
give them something and say, hey,
00:16:28.652 --> 00:16:31.052
I want you to build and when I come back,
00:16:31.052 --> 00:16:33.202
I want you to tell me
about what you built.
00:16:34.162 --> 00:16:36.862
So, that's a nice way to get it
00:16:36.862 --> 00:16:38.282
or maybe not I want you to build
00:16:38.282 --> 00:16:40.202
but here's some blocks, do you wanna build
00:16:40.202 --> 00:16:41.632
and then let them go with it again,
00:16:41.632 --> 00:16:43.175
you want it to be their idea,
00:16:44.206 --> 00:16:45.532
but making sure you go back
00:16:45.532 --> 00:16:47.602
and make that touch point when
you connect with them again,
00:16:47.602 --> 00:16:49.482
and always come back with a smile,
00:16:49.482 --> 00:16:52.322
let them know you're happy
to be there with them.
00:16:52.322 --> 00:16:54.872
And not add on a lot to them,
00:16:54.872 --> 00:16:56.815
but just let them just be with them.
00:16:58.212 --> 00:17:00.332
One thing yeah, that we've,
00:17:00.332 --> 00:17:02.402
I've been talking to
Caroline about a little bit
00:17:02.402 --> 00:17:04.582
is how to set up a schedule for your child
00:17:04.582 --> 00:17:07.762
and so I know that something Caroline that
00:17:08.842 --> 00:17:10.312
is really exciting right now
00:17:10.312 --> 00:17:13.172
on the Khan Academy Kid's programming.
00:17:13.172 --> 00:17:15.592
- Yeah, we just launched weekly planners
00:17:15.592 --> 00:17:17.042
for ages two through seven.
00:17:17.042 --> 00:17:21.392
And it's just the template, a
starting point for families.
00:17:21.392 --> 00:17:22.462
We worked with Renee
00:17:22.462 --> 00:17:24.752
and one of the most valuable parts of it,
00:17:24.752 --> 00:17:28.902
I think are just kind
of all the tips in there
00:17:28.902 --> 00:17:31.682
and ideas for how to fill your,
00:17:31.682 --> 00:17:34.982
how to build the time for
early literacy and math,
00:17:34.982 --> 00:17:36.642
social emotional development.
00:17:36.642 --> 00:17:38.772
And it's not that you have
to stick really rigidly
00:17:38.772 --> 00:17:39.852
to the planner
00:17:39.852 --> 00:17:43.982
but it's just a place where
parents can start with a routine
00:17:43.982 --> 00:17:44.932
and some structure.
00:17:46.562 --> 00:17:47.542
- And most importantly,
00:17:47.542 --> 00:17:49.032
be creative in how you're thinking
00:17:49.032 --> 00:17:53.042
remember that you may be using
math or language or literacy
00:17:53.042 --> 00:17:54.992
in places that you might not identify.
00:17:54.992 --> 00:17:58.462
So, think through what's
happening in your day
00:17:58.462 --> 00:18:01.532
and just identify that you
can write that on the planner
00:18:01.532 --> 00:18:05.162
as that's our we did it during
teeth brushing this morning
00:18:05.162 --> 00:18:07.452
and then you don't have to
feel like that's another check
00:18:07.452 --> 00:18:08.285
on your list.
00:18:08.285 --> 00:18:10.782
You can make that anything you want.
00:18:10.782 --> 00:18:11.615
- Exactly.
00:18:13.672 --> 00:18:14.505
Great.
00:18:14.505 --> 00:18:19.117
So should we shift now
to some of the questions
00:18:19.117 --> 00:18:19.950
from the audience?
00:18:19.950 --> 00:18:22.992
I think Dan from our team
is gonna be joining us.
00:18:22.992 --> 00:18:24.392
- Yep, thank you, Caroline.
00:18:24.392 --> 00:18:27.082
Before we get started
with the live questions
00:18:27.082 --> 00:18:28.122
and answer period,
00:18:28.122 --> 00:18:30.062
there's couple announcements
that I'd like to make.
00:18:30.062 --> 00:18:32.872
So first, as Caroline
mentioned at the start of this,
00:18:32.872 --> 00:18:34.652
this entire webinar is being recorded,
00:18:34.652 --> 00:18:36.222
so don't worry if you missed anything,
00:18:36.222 --> 00:18:37.372
or if you joined late,
00:18:37.372 --> 00:18:38.622
the recording will be made available.
00:18:38.622 --> 00:18:40.932
We'll be posting it after this session.
00:18:40.932 --> 00:18:43.672
And then also excitingly,
as Caroline mentioned,
00:18:43.672 --> 00:18:45.262
we did create the weekly planners
00:18:45.262 --> 00:18:46.622
and we've actually attached those
00:18:46.622 --> 00:18:48.322
as part of this webinar as well.
00:18:48.322 --> 00:18:50.932
So in our downloadable
sections, please go there.
00:18:50.932 --> 00:18:53.192
There are two things that
we wanna share with you,
00:18:53.192 --> 00:18:55.752
the weekly planners for
kids ages two to seven,
00:18:55.752 --> 00:18:57.922
and also one cheater quick tip sheet
00:18:57.922 --> 00:18:59.782
of some of the topics
that Renee and Caroline
00:18:59.782 --> 00:19:01.872
spoke to just now.
00:19:01.872 --> 00:19:02.705
And then finally,
00:19:02.705 --> 00:19:04.342
before we get started with
the live question and answers,
00:19:04.342 --> 00:19:06.752
please start putting your
questions in the question box.
00:19:06.752 --> 00:19:08.652
We have a team of moderators
00:19:08.652 --> 00:19:10.432
who are kind of surfacing up for me.
00:19:10.432 --> 00:19:13.052
I'll do my best job to get
through as many of them possible
00:19:13.052 --> 00:19:15.602
as possible with Renee and Caroline.
00:19:15.602 --> 00:19:17.432
Okay, so shall we get started?
00:19:18.450 --> 00:19:19.283
- Okay.
00:19:19.283 --> 00:19:20.952
- So, Caroline perhaps
this one's a good place
00:19:20.952 --> 00:19:21.785
to start with you.
00:19:21.785 --> 00:19:23.952
We have a great question from Laura.
00:19:23.952 --> 00:19:27.132
Laura asked when so much of
the interaction with school
00:19:27.132 --> 00:19:28.862
is through an iPad,
00:19:28.862 --> 00:19:31.842
how can I help my child
transition on and off,
00:19:31.842 --> 00:19:33.692
and so that she can more easily engage
00:19:33.692 --> 00:19:35.622
in the actual physical world?
00:19:35.622 --> 00:19:38.912
- Yes, I completely
understand that when I mean,
00:19:38.912 --> 00:19:40.382
I think it may be a starting point
00:19:40.382 --> 00:19:42.852
is what Renee was talking
about what the schedule
00:19:42.852 --> 00:19:46.252
is like, understanding,
what's coming from her school,
00:19:46.252 --> 00:19:48.765
and what's the schedule
that they're proposing?
00:19:49.682 --> 00:19:52.252
How much of that is on an iPad
00:19:52.252 --> 00:19:54.482
and then maybe you have some other time PE
00:19:54.482 --> 00:19:56.602
or something where it's not a live better,
00:19:56.602 --> 00:19:58.742
or maybe the teacher
is actually leading you
00:19:58.742 --> 00:19:59.792
through things there.
00:20:00.722 --> 00:20:03.772
But something visual is
often helpful for children
00:20:03.772 --> 00:20:06.952
so that they can kind of see
okay, I'm here right now.
00:20:06.952 --> 00:20:09.172
The next block, I'm gonna
be doing something else.
00:20:09.172 --> 00:20:10.402
I have to go find a book
00:20:10.402 --> 00:20:12.802
or I have to go find
something else in my house.
00:20:13.652 --> 00:20:16.682
And I think maybe giving them
a little advanced warning too,
00:20:16.682 --> 00:20:21.682
is you're about to transition
into the next period.
00:20:21.772 --> 00:20:23.772
Let's try this.
00:20:23.772 --> 00:20:26.112
Khan Kids, we also have some complimentary
00:20:26.112 --> 00:20:30.389
offline activities so that
they can use principles
00:20:32.372 --> 00:20:34.232
that reinforce the learning
that's in the app too.
00:20:34.232 --> 00:20:36.295
So that gets off the screen.
00:20:37.582 --> 00:20:38.892
- Those are great ideas, I.
00:20:38.892 --> 00:20:40.912
May I add one thing quickly,
00:20:40.912 --> 00:20:44.572
just that often in preschools
and kindergarten classrooms,
00:20:44.572 --> 00:20:47.322
teachers will use music
during transition times.
00:20:47.322 --> 00:20:50.372
So, I'll let you love you
could play it for a minute
00:20:50.372 --> 00:20:52.362
while it's time to put one thing away
00:20:52.362 --> 00:20:53.822
and take the next thing out.
00:20:53.822 --> 00:20:55.262
Sometimes that helps kids know,
00:20:55.262 --> 00:20:57.862
'cause it's, it goes
along with the schedule
00:20:57.862 --> 00:20:59.842
and it signals oh, we're gonna change.
00:20:59.842 --> 00:21:00.962
We're gonna shift gears here.
00:21:00.962 --> 00:21:02.292
Let's look at our schedule
00:21:02.292 --> 00:21:03.855
and see what's coming up next.
00:21:04.872 --> 00:21:06.332
- Great, thank you.
00:21:06.332 --> 00:21:08.392
We have a question from Ruth.
00:21:08.392 --> 00:21:10.642
The question is I have
a young kindergartener
00:21:10.642 --> 00:21:13.482
and a three year old,
and Ruth worries that
00:21:13.482 --> 00:21:16.162
when the kindergartner
potentially falling behind
00:21:16.162 --> 00:21:18.472
with the social skills
given the distance learning
00:21:18.472 --> 00:21:20.872
and our shelter in place rules.
00:21:20.872 --> 00:21:23.962
And also she worries that about
potential attachment issues
00:21:23.962 --> 00:21:26.442
once the kids have to go back to school.
00:21:26.442 --> 00:21:28.062
So Renee, perhaps this
is a good one for you
00:21:28.062 --> 00:21:30.672
to kind of address how do we
deal with attachment issues
00:21:30.672 --> 00:21:34.292
and the lack of kind
of social interactions
00:21:34.292 --> 00:21:37.066
or the limited interactions that we have?
00:21:37.066 --> 00:21:38.061
- Right, right.
00:21:38.061 --> 00:21:40.692
And I think that's
definitely a great question.
00:21:40.692 --> 00:21:44.202
It's something that even
the education community
00:21:44.202 --> 00:21:46.392
is trying to think a lot about.
00:21:46.392 --> 00:21:48.692
And this is actually one
area where I might recommend
00:21:48.692 --> 00:21:53.692
that you try to embrace
technology a little bit more even
00:21:53.692 --> 00:21:57.322
to get your kids maybe
communicating with family members,
00:21:57.322 --> 00:22:00.112
or if they have friends
that they might be able
00:22:00.112 --> 00:22:02.972
to communicate with the
help of another parent.
00:22:02.972 --> 00:22:04.982
And the parents can be there with you,
00:22:04.982 --> 00:22:07.322
but just to give them that
sense of being able to play,
00:22:07.322 --> 00:22:12.035
I've seen kids play games
over like a Facebook type
00:22:14.002 --> 00:22:19.002
or a Zoom type situation and they can play
00:22:20.332 --> 00:22:22.612
all sorts of games or they
can do jumping jacks together
00:22:22.612 --> 00:22:25.172
or something that you that
a parent models for them.
00:22:25.172 --> 00:22:27.092
But in that way they can start to interact
00:22:27.092 --> 00:22:29.402
and use some language back and forth.
00:22:29.402 --> 00:22:30.852
Admittedly, it's not the same
00:22:30.852 --> 00:22:33.232
as if they're playing
necessarily next to each other,
00:22:33.232 --> 00:22:34.302
but it is helpful.
00:22:34.302 --> 00:22:36.042
Another thing I love is,
00:22:36.042 --> 00:22:39.052
it's a great time to do some
reflecting with your child.
00:22:39.052 --> 00:22:41.062
There's some really wonderful books
00:22:42.192 --> 00:22:43.972
about social emotional learning.
00:22:43.972 --> 00:22:47.712
And so it might be a good time,
especially in kindergarten,
00:22:47.712 --> 00:22:50.182
might be a time when they
can reflect back on time,
00:22:50.182 --> 00:22:51.912
experiences that they've had before
00:22:51.912 --> 00:22:54.452
that align with what
they're reading in the book.
00:22:54.452 --> 00:22:55.285
And so you can say, oh,
00:22:55.285 --> 00:22:57.372
have you ever felt like
this at a certain time,
00:22:57.372 --> 00:23:00.482
and then you can actually share
your own experience as well.
00:23:00.482 --> 00:23:02.445
So, it's definitely a challenge.
00:23:03.652 --> 00:23:05.802
But I encourage you to
continue to be creative.
00:23:05.802 --> 00:23:09.532
And let your little one
kind of help each other out
00:23:09.532 --> 00:23:11.775
if they can, if they're
able to do that too.
00:23:13.642 --> 00:23:14.475
- Great.
00:23:14.475 --> 00:23:16.962
So the next one is quite a tough one.
00:23:16.962 --> 00:23:18.372
I'll let you both answer this.
00:23:18.372 --> 00:23:19.852
And Caroline, since probably good for you.
00:23:19.852 --> 00:23:21.612
And this is one that we hear a lot.
00:23:21.612 --> 00:23:24.512
And I'm sure this resonates
with a lot of our audience.
00:23:24.512 --> 00:23:27.752
So Cindy asks, I'm on day four of school
00:23:27.752 --> 00:23:31.392
and I'm already getting a
I don't wanna do school,
00:23:31.392 --> 00:23:33.452
what is a good way to help them?
00:23:33.452 --> 00:23:35.755
Get their kids excited to start the day?
00:23:36.732 --> 00:23:40.712
- Yeah, that is a tough
one, especially on day four.
00:23:40.712 --> 00:23:44.252
I might start with asking your child,
00:23:44.252 --> 00:23:48.422
why are you feeling that way today?
00:23:48.422 --> 00:23:51.112
And it could be a whole host of things.
00:23:51.112 --> 00:23:54.462
It could be that I don't like sitting here
00:23:54.462 --> 00:23:57.082
in front of my computer for so long.
00:23:57.082 --> 00:24:00.872
It could be I don't
know who's in my class.
00:24:00.872 --> 00:24:03.675
So, I think depending on that answer,
00:24:04.652 --> 00:24:07.732
you may have, you may
trigger some ideas for you.
00:24:07.732 --> 00:24:09.362
For example, if it is the screen,
00:24:09.362 --> 00:24:12.542
like maybe there's conversation
that you could have
00:24:12.542 --> 00:24:15.182
with a teacher to see
if there are parts where
00:24:16.692 --> 00:24:19.552
he or she does not need to be logged in
00:24:19.552 --> 00:24:22.875
and maybe she can do
something else offline, or.
00:24:24.032 --> 00:24:27.322
Yeah, I think it's not understanding why,
00:24:27.322 --> 00:24:28.155
I don't know, Renee,
00:24:28.155 --> 00:24:31.695
do you have other things to
add on this one, it's tough.
00:24:32.792 --> 00:24:34.032
- That is a tough one.
00:24:34.032 --> 00:24:36.082
That's a great place to start.
00:24:36.082 --> 00:24:39.002
It's really understandable
that little ones
00:24:39.002 --> 00:24:43.542
might need to move around a
little bit more than they are.
00:24:43.542 --> 00:24:46.882
I would also recommend that
you contact the teacher
00:24:46.882 --> 00:24:48.642
and explain that that's happening,
00:24:48.642 --> 00:24:51.312
not necessarily as a complaint,
00:24:51.312 --> 00:24:53.292
but it's a nice way for a teacher to gauge
00:24:53.292 --> 00:24:54.425
how things are going.
00:24:55.462 --> 00:24:58.972
Our teachers are working
really hard to develop classes
00:24:58.972 --> 00:25:00.572
that the kids will be interested in.
00:25:00.572 --> 00:25:03.342
But this is their time doing it as well.
00:25:03.342 --> 00:25:05.082
And so when you give them feedback,
00:25:05.082 --> 00:25:08.742
it lets them know how to that
they might want to adjust
00:25:08.742 --> 00:25:10.065
and change for your child.
00:25:11.332 --> 00:25:13.122
My other thought is if it's allowed,
00:25:13.122 --> 00:25:15.412
maybe let your child
bring a lovey to class,
00:25:15.412 --> 00:25:18.382
or something that makes
them feel comfortable
00:25:18.382 --> 00:25:19.632
depending on the age of the child.
00:25:19.632 --> 00:25:21.482
And if that's okay with the teacher,
00:25:21.482 --> 00:25:23.995
that might be a way to
help with that as well.
00:25:25.212 --> 00:25:26.442
Or perhaps you could sit with them
00:25:26.442 --> 00:25:28.532
for some of the class time.
00:25:28.532 --> 00:25:29.982
Maybe not all of it,
00:25:29.982 --> 00:25:31.552
but some of it just until they transition
00:25:31.552 --> 00:25:32.842
and start to feel better.
00:25:32.842 --> 00:25:33.882
But I agreed, Caroline,
00:25:33.882 --> 00:25:36.942
I think you have the right approach
00:25:36.942 --> 00:25:38.372
in terms of just trying to figure out
00:25:38.372 --> 00:25:42.305
what it might be that's
creating that pushback.
00:25:44.242 --> 00:25:47.212
- Well, I'd like to say
there's an easier question,
00:25:47.212 --> 00:25:49.432
but the next one's is
quite challenging as well.
00:25:49.432 --> 00:25:51.982
And I think a lot of parents
have this on their mind.
00:25:51.982 --> 00:25:55.662
Vivian says one thing
that she's struggling with
00:25:55.662 --> 00:25:57.232
is sort of that she's struggling with
00:25:57.232 --> 00:26:00.172
is that both parents
are working full time.
00:26:00.172 --> 00:26:02.812
They've got meetings on
Zoom at the same time.
00:26:02.812 --> 00:26:04.242
And so the gist of the question is like,
00:26:04.242 --> 00:26:06.052
how should they think about screen child,
00:26:06.052 --> 00:26:08.592
screen time for their child,
00:26:08.592 --> 00:26:10.152
especially when they are on Zoom calls
00:26:10.152 --> 00:26:11.982
two, three hours a day.
00:26:11.982 --> 00:26:13.602
What's the best way to think about it
00:26:13.602 --> 00:26:15.545
and the best way to control
the amount of screen time
00:26:15.545 --> 00:26:17.125
that they're exposing?
00:26:18.102 --> 00:26:19.762
- Yeah, I think,
00:26:19.762 --> 00:26:24.762
we're very cognizant of the
American Academy of Pediatrics,
00:26:25.412 --> 00:26:28.002
who guidelines around screen time,
00:26:28.002 --> 00:26:31.942
and have designed our app to fit
00:26:31.942 --> 00:26:34.362
within those constraints
on recommendations.
00:26:34.362 --> 00:26:37.652
But I'd also say,
especially during this time,
00:26:37.652 --> 00:26:41.192
when we're all really
challenged and stressed,
00:26:41.192 --> 00:26:45.792
give yourself some forgiveness
and grace in this area.
00:26:45.792 --> 00:26:49.592
And I may not look so
much at the screen time.
00:26:49.592 --> 00:26:51.612
I mean, you're talking about
two to three hours a day,
00:26:51.612 --> 00:26:53.335
so it's not like excessive,
00:26:54.442 --> 00:26:56.962
but look at the quality
of the screen time,
00:26:56.962 --> 00:27:00.862
what is the screen time
bringing to your child?
00:27:00.862 --> 00:27:03.482
And how is your child
engaging in that time?
00:27:03.482 --> 00:27:07.462
So it's there's a huge
array of options, obviously,
00:27:07.462 --> 00:27:10.632
and from very passive experiences
00:27:10.632 --> 00:27:13.082
where the child you can just
see them get glazed over.
00:27:13.082 --> 00:27:15.542
And also things that are not
developmentally appropriate
00:27:15.542 --> 00:27:19.562
where you're just gonna be
overstimulated or not learning.
00:27:19.562 --> 00:27:21.142
But if they're using time,
00:27:21.142 --> 00:27:22.792
screen time in a constructive way,
00:27:22.792 --> 00:27:24.572
so if it's a Zoom call with their teacher,
00:27:24.572 --> 00:27:28.282
and their teacher is
having them sing or dance
00:27:28.282 --> 00:27:30.512
or do activities,
00:27:30.512 --> 00:27:32.932
and they're also getting
some social interaction
00:27:32.932 --> 00:27:36.542
with their peers, that's
very active screen time,
00:27:36.542 --> 00:27:40.622
or if they're learning
particular skills on a program
00:27:40.622 --> 00:27:42.402
that's been designed by educators
00:27:42.402 --> 00:27:45.052
and has learning goals at the forefront.
00:27:45.052 --> 00:27:49.532
And it's really about
active minds on learning,
00:27:49.532 --> 00:27:50.712
which you'll be able to see
00:27:50.712 --> 00:27:52.802
as you observe your child's
learning the screen time,
00:27:52.802 --> 00:27:55.252
and that's those are healthy ways
00:27:55.252 --> 00:27:56.402
to be engaging in screen time.
00:27:56.402 --> 00:27:58.912
And I think,
00:27:58.912 --> 00:28:02.592
very good options for when you cannot be
00:28:02.592 --> 00:28:05.075
in front of your child 100% of the time,
00:28:06.222 --> 00:28:10.002
but it does sound like you
are trying to curb the time
00:28:10.002 --> 00:28:12.705
and I'd say also extending,
00:28:14.222 --> 00:28:17.052
if your child's really
interested in a certain app
00:28:17.052 --> 00:28:17.932
or something like that,
00:28:17.932 --> 00:28:20.722
maybe asking them to
take it offline and draw
00:28:20.722 --> 00:28:23.132
and tell a story about that character
00:28:23.132 --> 00:28:23.965
or something like that.
00:28:23.965 --> 00:28:26.065
Renee I don't know if you want to jump in.
00:28:27.202 --> 00:28:29.005
- Yeah, I think, I would one thing.
00:28:30.072 --> 00:28:33.542
This may be something parents
are already doing or aware of,
00:28:33.542 --> 00:28:37.532
but do try and have your
kiddo be somewhat near you
00:28:37.532 --> 00:28:38.852
when they're on screen time.
00:28:38.852 --> 00:28:40.322
So give them some headphones.
00:28:40.322 --> 00:28:42.422
So it's not disruptive
to what you're doing.
00:28:42.422 --> 00:28:45.152
But if it's possible, again,
00:28:45.152 --> 00:28:48.502
I recognize sometimes it's
not possible and that's okay.
00:28:48.502 --> 00:28:49.922
But it is, that way,
00:28:49.922 --> 00:28:52.642
you can kind of keep an eye on
just what they're what it is
00:28:52.642 --> 00:28:53.595
that they're doing.
00:28:54.822 --> 00:28:56.292
Especially in the case
that you have a kiddo
00:28:56.292 --> 00:28:58.742
who maybe can switch
screens or switch apps
00:28:58.742 --> 00:29:00.492
without you realizing it.
00:29:00.492 --> 00:29:03.222
And then yes, exactly.
00:29:03.222 --> 00:29:05.372
Like Caroline said, you always wanna have
00:29:05.372 --> 00:29:07.842
something ready for your kiddo to go
00:29:07.842 --> 00:29:09.712
if they want to transition off screens
00:29:09.712 --> 00:29:11.242
or you want to try and encourage them
00:29:11.242 --> 00:29:14.422
to transition off screen so
having something out a puzzle
00:29:14.422 --> 00:29:17.722
that's about that is partway
started, a Lego activity
00:29:17.722 --> 00:29:22.252
that's partway started, a paint
like the paint's ready to go
00:29:22.252 --> 00:29:24.692
so they can just get going on it.
00:29:24.692 --> 00:29:25.842
That kind of thing.
00:29:25.842 --> 00:29:27.932
At least that way when they look up,
00:29:27.932 --> 00:29:30.902
there's something else that
they can go to immediately
00:29:30.902 --> 00:29:33.265
and might be interesting to them.
00:29:34.962 --> 00:29:36.362
That's a tough one for sure.
00:29:37.712 --> 00:29:40.302
- So I think we have time
for one more question.
00:29:40.302 --> 00:29:42.382
And Renee perhaps you
could start with this one
00:29:42.382 --> 00:29:44.322
and Caroline if you have anything to add.
00:29:44.322 --> 00:29:47.322
Hilary asks, my five
year old doesn't choose
00:29:47.322 --> 00:29:48.972
the choices I give her.
00:29:48.972 --> 00:29:50.852
She says no, and that
she wants something else.
00:29:50.852 --> 00:29:53.642
Even if I tell her she
can't have something else.
00:29:53.642 --> 00:29:56.125
Any inspiring ideas that you have there.
00:29:57.172 --> 00:30:00.742
- Right, so this might be a good time
00:30:00.742 --> 00:30:03.532
to ask your child ahead of time,
00:30:03.532 --> 00:30:07.252
what are some choices that
you would like to have?
00:30:07.252 --> 00:30:10.552
So, without making the,
without promising that
00:30:10.552 --> 00:30:12.842
she'll get to have them say, hey,
00:30:12.842 --> 00:30:15.152
I wanted some new ideas for choices
00:30:15.152 --> 00:30:17.505
that you might like to
do or like to play with.
00:30:18.552 --> 00:30:21.672
That might help with just
coming up with new ideas.
00:30:21.672 --> 00:30:24.122
The other thing to keep
in mind and be aware of
00:30:24.122 --> 00:30:26.662
is it could be that she
wants something else entirely
00:30:26.662 --> 00:30:28.122
like to spend time with you.
00:30:28.122 --> 00:30:30.502
And so that might
require a little bit more
00:30:30.502 --> 00:30:32.772
of a conversation and just checking in
00:30:32.772 --> 00:30:34.632
maybe a few extra times during the day.
00:30:34.632 --> 00:30:37.752
So letting her know when
you're gonna check in with her
00:30:37.752 --> 00:30:39.372
and making sure to honor that time,
00:30:39.372 --> 00:30:41.362
so she knows when it's coming.
00:30:41.362 --> 00:30:44.462
So you might say, these
are your choices for now.
00:30:44.462 --> 00:30:46.952
I will be back in 15 minutes,
00:30:46.952 --> 00:30:49.662
and I wanna hear all about
what you've been working on.
00:30:49.662 --> 00:30:51.892
Or then we can read a story.
00:30:51.892 --> 00:30:53.592
Or then we can watch a show together,
00:30:53.592 --> 00:30:55.512
whatever is something
that she feels comfortable
00:30:55.512 --> 00:30:59.652
doing with you, could be more
than that she wants that time.
00:30:59.652 --> 00:31:02.812
I have to say my preteen
who's 11 right now
00:31:02.812 --> 00:31:04.822
has suddenly become really demanding
00:31:04.822 --> 00:31:06.152
about breakfast every day,
00:31:06.152 --> 00:31:08.382
which she's been making herself breakfast
00:31:08.382 --> 00:31:10.162
for a really long time and I really think
00:31:10.162 --> 00:31:12.042
it's her attach point for me,
00:31:12.042 --> 00:31:15.612
she wants to get up and she
wants to be able to be near me
00:31:15.612 --> 00:31:16.642
while she's eating breakfast.
00:31:16.642 --> 00:31:19.012
So even our older kids, I
think are looking for that.
00:31:19.012 --> 00:31:20.742
So keep that in mind,
that may be something
00:31:20.742 --> 00:31:22.765
happening with your little one as well.
00:31:26.742 --> 00:31:29.112
- Any other advice, Caroline or.
00:31:29.112 --> 00:31:31.452
- No, I just had a quick thought of like,
00:31:31.452 --> 00:31:33.162
building on Renee's idea
00:31:33.162 --> 00:31:35.812
of having the child come
up with a few choices,
00:31:35.812 --> 00:31:37.642
then maybe you put them all into a box,
00:31:37.642 --> 00:31:39.719
and then next time, you can pick one
00:31:39.719 --> 00:31:43.642
and maybe that element of
surprise would add some intrigue
00:31:43.642 --> 00:31:45.162
to the option.
00:31:45.162 --> 00:31:47.302
- That's a great idea,
that's a great idea.
00:31:47.302 --> 00:31:52.282
And similarly sometimes you
can rotate like a bucket,
00:31:52.282 --> 00:31:55.302
a few toy choices in and out.
00:31:55.302 --> 00:31:56.772
So, today these are your toy choices.
00:31:56.772 --> 00:31:59.622
But tomorrow we'll have these toy choices.
00:31:59.622 --> 00:32:00.962
Kind of put the other ones away
00:32:00.962 --> 00:32:02.412
so she can't see them or access them.
00:32:02.412 --> 00:32:05.329
So she is constantly changing up
00:32:05.329 --> 00:32:07.779
and it looks a little bit
different all the time.
00:32:08.982 --> 00:32:12.912
- Right, well, unfortunate
that's about all the time we have
00:32:12.912 --> 00:32:14.002
for the questions.
00:32:14.002 --> 00:32:16.422
And so Caroline I wanna
thank you and Renee
00:32:16.422 --> 00:32:18.272
for sharing your expertise
with our audience.
00:32:18.272 --> 00:32:21.102
And as you can see, thank you
the audience for submitting
00:32:21.102 --> 00:32:23.262
such great questions.
00:32:23.262 --> 00:32:25.172
And taking the time out
of your busy schedules
00:32:25.172 --> 00:32:26.005
to be with us,
00:32:26.005 --> 00:32:27.672
we really appreciate that.
00:32:27.672 --> 00:32:29.812
As I mentioned before, if you
miss anything, don't worry,
00:32:29.812 --> 00:32:31.732
we've recorded this entire session.
00:32:31.732 --> 00:32:33.602
And we'll be posting that available online
00:32:33.602 --> 00:32:35.252
shortly after this webinar.
00:32:35.252 --> 00:32:36.702
And in fact, when you register,
00:32:36.702 --> 00:32:38.942
you'll automatically be getting this email
00:32:38.942 --> 00:32:41.192
with the links to the recording.
00:32:41.192 --> 00:32:42.522
And then if you need more resources,
00:32:42.522 --> 00:32:43.502
or you wanna learn more,
00:32:43.502 --> 00:32:45.642
you can always go to khankids.org,
00:32:45.642 --> 00:32:48.282
which is our website
for Khan Academy Kids.
00:32:48.282 --> 00:32:50.002
And there, there's a
blue banner at the top
00:32:50.002 --> 00:32:53.002
that links to our distance
learning resources as well.
00:32:53.002 --> 00:32:54.992
And we update those
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00:32:54.992 --> 00:32:58.332
So, please come by and
check out, check by often.
00:32:58.332 --> 00:32:59.562
And then before we sign off,
00:32:59.562 --> 00:33:02.022
we wanna ask you to do us one favor.
00:33:02.022 --> 00:33:04.902
There's a poll that pops up at
the very end of this webinar
00:33:04.902 --> 00:33:07.132
and ask two important questions.
00:33:07.132 --> 00:33:09.962
The first is help us
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00:33:09.962 --> 00:33:11.512
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00:33:11.512 --> 00:33:13.252
So if you have any
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00:33:13.252 --> 00:33:14.552
please put that there.
00:33:14.552 --> 00:33:15.672
And then secondly,
00:33:15.672 --> 00:33:18.262
we're always looking to create
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00:33:18.262 --> 00:33:20.712
So if the, if you have
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00:33:20.712 --> 00:33:22.882
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00:33:22.882 --> 00:33:25.692
please add your suggestions there as well.
00:33:25.692 --> 00:33:28.112
So, from all of us at Khan Academy Kids,
00:33:28.112 --> 00:33:30.815
we just wanna thank you again and goodbye.
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