Frames of reference

WEBVTT
Kind: captions
Language: en

00:00:00.150 --> 00:00:02.140
- [Instructor] When we
make new discoveries

00:00:02.140 --> 00:00:04.330
we need to be able to
share them with others.

00:00:04.330 --> 00:00:06.570
And the first thing we
have to do is make sure

00:00:06.570 --> 00:00:08.620
everyone is on the same page.

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We do this by using units
and frames of reference,

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which are also called reference frames.

00:00:14.740 --> 00:00:16.930
We talk about units in another video,

00:00:16.930 --> 00:00:20.360
so let's look at what a
frame of reference is.

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Let's say this blue box thing is a car,

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and it's going 45 miles per hour.

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Someone standing on the side of the road

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would see it pass at 45 miles per hour.

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Now, if this yellow truck
is going 40 miles per hour

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someone sitting in the yellow truck

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would observe the blue traveling
at five miles per hour.

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How could the person
on the side of the road

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see the blue car traveling
at 45 miles per hour

00:00:50.350 --> 00:00:52.004
and a person in the yellow truck

00:00:52.004 --> 00:00:55.500
see the blue car moving
at five miles per hour?

00:00:55.500 --> 00:00:57.330
This is because both observers

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are using different frames of reference.

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So let's go ahead and take a look at that,

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starting with the speed of the blue car.

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The person on the side of the road

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is using their frame of
reference of being at rest.

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So relative to them,
the blue car is moving

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at 45 miles per hour.

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To the person in this yellow truck,

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which remember is already
going 40 miles per hour,

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the blue car is going five miles per hour.

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Now let's do the exact same thing

00:01:26.990 --> 00:01:29.550
for the speed of the yellow truck.

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So what is the speed of the yellow truck

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for the observer on the side of the road?

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It's 40 miles per hour.

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And what do you think
the speed of the truck is

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for the person using their blue
car as the reference frame?

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Well, the blue car is
moving at 45 miles per hour,

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and the truck is only
moving at 40 miles per hour.

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So the speed of the yellow truck

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is actually five miles per hour slower

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than this reference frame,
because the blue car

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is already moving at 45 miles per hour.

00:02:02.570 --> 00:02:05.627
Now you might be thinking, "But wait,

00:02:05.627 --> 00:02:08.897
"the person on the side of
the road isn't really at rest.

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"They're on the earth
and the earth is moving."

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You're completely correct.

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The person is at rest
with respect to the earth.

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And the earth is the most
common frame of reference

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that we use.

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To an observer in space who is
not rotating with the earth,

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the blue car is going 45 miles per hour,

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plus the speed of Earth's rotation.

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And this is why a frame of
reference is so important.

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We just talked about one blue car

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having three different velocities

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depending what the frame of reference is.

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How would we communicate
this to avoid confusion?

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Well, we state the
reference frame we're using.

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The blue car is moving
at five miles per hour

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with respect to, which I'll
write as WRT, the yellow truck.

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This tells us that the yellow truck

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is our frame of reference.

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Or we could say that the yellow truck

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is moving at 40 miles
per hour and the blue car

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at 45 miles per hour,
with respect to the earth.

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That way everyone is on the same page,

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a page which, to be clear, is
in a book that relative to me

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is at rest.


Units

WEBVTT
Kind: captions
Language: en

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- [Illustrator] Did you
know that communication

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is actually one of the most
important things in science?

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As we discover cool things,

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we need to be able to
share them with others.

00:00:09.130 --> 00:00:11.700
And when we're talking
about data and measurements

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with other scientists,

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we need to make sure
we're on the same page.

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So how do we do that?

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Well, one of the ways is to use units.

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We use units whenever we talk
about things like position,

00:00:25.750 --> 00:00:30.080
where an object is located,
how long it is, it's mass,

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how much matter it's made
up of or it's motion.

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How is that object moving?

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You probably hear units every day.

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For example, you've grown,

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let's say an inch and a
half in the past year,

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or that tree over there is 25 feet tall.

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And maybe you went swimming
in a 25 meter pool.

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And we're just gonna pretend
that the pool is a rectangle

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because as you can tell from my tree,

00:01:01.480 --> 00:01:03.463
my artistic skills are not that great.

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Anyway, this brings up
a super important point

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about why we use units.

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I just used three examples
of length measurements

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with three different units,
inches, feet, and meters.

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Imagine if I didn't attach a unit

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to any of these measurements,

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you grew one and a half, what? Meters?

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Whoa, one and a half hands.

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Well, whose hands?

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Your hands or my hands?

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Woof, well, pretend those are hands.

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Units let us know how much
of a quantity there is.

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So a meter is always
used to measure length

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and we know exactly how long a meter is.

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That way when we say
something is two meters long,

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no one has to guess at how big that is.

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Any measurement or data point
always needs to have a unit

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or else it's just a meaningless number.

00:02:02.170 --> 00:02:04.080
To avoid any confusion,

00:02:04.080 --> 00:02:07.890
in science we use what
are called SI units.

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SI units are the International System.

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Could there be any more
letters in this word system

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used by scientists all over the world.

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We'll use meters to
describe position or length,

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kilograms for mass,

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and if we're talking about
the motion of something,

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meters per second.

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And while this is the agreed
upon scientific unit system,

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you should be aware that
other systems do exist,

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which means things can very
easily get very confusing

00:02:43.060 --> 00:02:44.960
if you forget your units.

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And you might be thinking,

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"Oh, come on, who mixes up units?'

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Well, it happens more
often than you think,

00:02:52.910 --> 00:02:55.500
even rocket scientists have done it.

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I mean, a Mars Orbiter actually crashed

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due to a mix up in units.

00:03:00.830 --> 00:03:03.410
Now seriously, that actually happened,

00:03:03.410 --> 00:03:07.933
look it up and remember to use your units.


Meaning of absolute value

WEBVTT
Kind: captions
Language: en

00:00:00.300 --> 00:00:01.133
- [Instructor] In this video,

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we're going to introduce ourselves

00:00:02.190 --> 00:00:04.230
to the idea of absolute value,

00:00:04.230 --> 00:00:09.100
which you can view as,
how far are you from zero?

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So for example,

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let's say that we have a bunch
of people living on a street.

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And let's say that we say
that the school is at zero,

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and we could think
about other people live.

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So let's say I live three miles

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to the right of the
school, maybe that's east.

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So this is where I live.

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So that's me right over here.

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And that you live three miles
to the left of the school.

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So this is where you would
be, three miles to the left.

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Or maybe we could say that's
to the west of the school.

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Now you could say that your position

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is at negative three miles
relative to the school.

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And my position is at positive three miles

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relative to the school.

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But what we might care about

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is just how far are we from the school?

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And so there, you could say,

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well, we're each exactly
three miles from the school.

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You're three miles from the school,

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and I am three miles from the school.

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And that's what absolute value
is actually trying to get at.

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So for example, your
position is negative three,

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but if we were to take the absolute value,

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which you denote by these
two straight up down bars

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around the number, then we say,

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that's just going to be
your distance from zero,

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which is just going to be three miles.

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Similarly,

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my position is at three
miles, positive three miles.

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The absolute value of that is going to be,

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drum roll, please.

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It is going to be three as well.

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You might already see a pattern.

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If you're taking an absolute
value of a negative number,

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you get the number without the negative.

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And if you take the absolute
value of a positive number,

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it just equals itself again.

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But the reason why that is the case

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is because we're just saying,

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how far is that thing from zero?

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Let me give you another example.

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Let's say that we have
some type of a cruise ship,

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and that's the water right over there.

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This is the cruise ship.

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Let me draw it.

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It's this big cruise
ship, nice and big one,

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has water slides on it, and whatever else,

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whatever you would expect
from a huge cruise ship.

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And let say, we think about the height

00:02:25.970 --> 00:02:28.020
of where the different
floors are in the ship.

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And a natural place to think about

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is based on where the sea level is.

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So we call that height zero.

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Now there's this big waterfall
pool type thing up here.

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Let's just say, it's a pool
for simplicity, on the roof.

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And let's say that that is
at an altitude of 80 feet.

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So we would call that at positive 80 feet.

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And let's say the engine
room is right over here.

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And if you wanted to know its position,

00:02:58.550 --> 00:03:02.040
its height, well, it is
going to be below zero,

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it's below sea level, let's
say it's at negative 20 feet.

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So that would give you its position.

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One is 80 feet above the sea level,

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and then one is 20 feet
below the sea level.

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But if you just wanted
to know how far they are,

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well, you could take the absolute value.

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How far is that roof deck pool?

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Well, you take the absolute value of 80.

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You are going to get 80.

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How far is that engine room from zero?

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How far is it from sea level?

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Well, the absolute value of
negative 20 is going to be 20.


Compare rational numbers using a number line

WEBVTT
Kind: captions
Language: en

00:00:00.300 --> 00:00:01.690
- [Sal] What we're gonna do in this video

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is get some practice comparing numbers,

00:00:04.040 --> 00:00:07.640
especially positive and negative numbers.

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So for each of these pairs of numbers,

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I want you to either
write a less than sign

00:00:13.330 --> 00:00:14.760
or a greater than sign,

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or just think about which of these two

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is greater than the other.

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Pause this video and see if you can work

00:00:20.440 --> 00:00:22.003
through these four pairs.

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All right, now let's do it together.

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So let's first compare -7/4 to -3/4.

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And I'm going to try to do that

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by visualizing them on a number line.

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So let me draw a straighter line.

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There we go.

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Let's see, they're both negative,

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which means both to the left of zero.

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So I'll focus on the left of zero.

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So that's zero.

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And let's see,

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they're both given in fourths

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and we need to go all the way to 7/4,

00:00:51.260 --> 00:00:52.340
less than zero.

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So let me think of each
of these as a fourth.

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So one, two, three, four.

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That would be -1.

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One, two, three, four.

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That would be -2 and that's enough for us,

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but I could keep going if I liked.

00:01:09.170 --> 00:01:13.790
Now, where is -7/4 on this number line?

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Well, I just said each
of these is a fourth,

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so negative 1/4, 2/4, 3/4,

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4/4, 5/4, 6/4, 7/4.

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So this right over here is -7/4.

00:01:28.720 --> 00:01:32.082
And where is negative
-3/4 on the number line?

00:01:32.082 --> 00:01:36.373
- 1/4, -2/4, -3/4.

00:01:37.850 --> 00:01:39.670
So which one is greater?

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Well, we can see that -3/4

00:01:42.240 --> 00:01:46.580
is to the right of -7/4.

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So -3/4 is greater or that
-7/4 is less than -3/4.

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So I'll put a less than right over here.

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Let's do this next example.

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We're going to compare 0.6 to -1.8.

00:02:00.524 --> 00:02:02.270
If you haven't already given it a shot

00:02:02.270 --> 00:02:05.120
or if this previous example
helped inspire something

00:02:05.120 --> 00:02:06.430
and you give it another shot,

00:02:06.430 --> 00:02:08.640
and then we'll do it together.

00:02:08.640 --> 00:02:11.493
So let's draw a number line again.

00:02:12.480 --> 00:02:17.480
And let me put zero right over here.

00:02:18.950 --> 00:02:20.620
That's 1.

00:02:20.620 --> 00:02:22.340
That's 2.

00:02:22.340 --> 00:02:24.700
This is -1.

00:02:24.700 --> 00:02:27.000
This is -2.

00:02:27.000 --> 00:02:29.500
And actually let me make half marks here,

00:02:29.500 --> 00:02:32.140
so we can get a little
bit closer to thinking

00:02:32.140 --> 00:02:35.440
about where these two numbers
sit on the number line.

00:02:35.440 --> 00:02:37.233
I'll start with 0.6.

00:02:38.440 --> 00:02:41.460
0.6 is you could view that as 6/10.

00:02:41.460 --> 00:02:42.990
It's a little bit more than 5/10.

00:02:42.990 --> 00:02:44.520
It's a little bit more than 1/2.

00:02:44.520 --> 00:02:47.220
So 0.6 is gonna be
roughly right around here

00:02:47.220 --> 00:02:49.053
on our number line, 0.6.

00:02:50.230 --> 00:02:51.193
And where is -1.8?

00:02:53.230 --> 00:02:54.100
Well, it's negative.

00:02:54.100 --> 00:02:56.030
So it's going to be to the left of zero,

00:02:56.030 --> 00:02:58.220
and we're gonna go 1.8 to the left.

00:02:58.220 --> 00:02:59.950
So this is -1.

00:02:59.950 --> 00:03:02.090
This is -2, that's too far.

00:03:02.090 --> 00:03:03.660
This is -1.5.

00:03:03.660 --> 00:03:07.230
- 1.8 is going to be roughly,

00:03:07.230 --> 00:03:09.460
let me do this in this
color, right over here.

00:03:09.460 --> 00:03:12.063
It's going to be roughly
right over there, -1.8.

00:03:13.600 --> 00:03:16.173
And so you can see that it is left of 0.6

00:03:17.401 --> 00:03:18.742
on our number line.

00:03:18.742 --> 00:03:21.667
And so -1.8 is less than 0.6,

00:03:21.667 --> 00:03:24.000
or 0.6 is greater than -1.8.

00:03:26.900 --> 00:03:28.280
Let's do more examples here.

00:03:28.280 --> 00:03:30.670
Let's compare these two numbers.

00:03:30.670 --> 00:03:31.503
Well, once again,

00:03:31.503 --> 00:03:33.070
let me put them on a number line.

00:03:33.070 --> 00:03:34.300
And I wanna show you that the number line

00:03:34.300 --> 00:03:35.390
does not have to go left-right.

00:03:35.390 --> 00:03:37.260
It could go up-down.

00:03:37.260 --> 00:03:38.780
So let's try that.

00:03:38.780 --> 00:03:40.700
And I'll do it in a different color.

00:03:40.700 --> 00:03:44.480
So I'll make a line like this.

00:03:44.480 --> 00:03:48.160
And I am going to have,

00:03:48.160 --> 00:03:52.200
let's call this zero right over here.

00:03:52.200 --> 00:03:53.820
And so this is 1.

00:03:53.820 --> 00:03:55.990
This is 2.

00:03:55.990 --> 00:03:58.570
This is -1.

00:03:58.570 --> 00:04:01.600
This is -2.

00:04:01.600 --> 00:04:05.430
Now, where is 2 1/5 on the number line?

00:04:05.430 --> 00:04:08.980
So that is positive 1, positive 2.

00:04:08.980 --> 00:04:11.020
And then we're going to go about a fifth.

00:04:11.020 --> 00:04:14.710
So that'll get us
roughly right over there.

00:04:14.710 --> 00:04:18.790
And then where is -1 1/10?

00:04:18.790 --> 00:04:21.875
Well, we're not gonna
go below zero, so -1.

00:04:21.875 --> 00:04:25.270
And we're gonna go another
1/10 beyond that below zero.

00:04:25.270 --> 00:04:28.030
So it's gonna be roughly around there.

00:04:28.030 --> 00:04:31.070
So that is -1 1/10.

00:04:31.070 --> 00:04:36.070
And so we can see that -1 1/10
is less than positive 2 1/5,

00:04:36.830 --> 00:04:41.830
or positive 2 1/5 is greater than -1 1/10.

00:04:42.880 --> 00:04:46.850
Let's do one last example,
comparing these two numbers here.

00:04:46.850 --> 00:04:51.160
And actually, I can extend this
number line right over here,

00:04:51.160 --> 00:04:54.410
and I should be able to
fit both of these numbers.

00:04:54.410 --> 00:04:56.050
So let me try to do that.

00:04:56.050 --> 00:04:57.920
So I'm going to extend it.

00:04:57.920 --> 00:05:01.490
This is -3 right over here.

00:05:01.490 --> 00:05:03.167
So where would -1.5 sit?

00:05:04.700 --> 00:05:07.554
Well, we're going below
zero so that's a -1.

00:05:07.554 --> 00:05:09.920
- 1.5 would be another half,

00:05:09.920 --> 00:05:11.999
it'd be right in between -1 and -2.

00:05:11.999 --> 00:05:16.600
So -1.5 is right over there.

00:05:16.600 --> 00:05:19.230
And where would -2.5 be?

00:05:19.230 --> 00:05:22.860
Well, we go -1, -2, and then another half.

00:05:22.860 --> 00:05:25.073
So this right over here is -2.5.

00:05:27.650 --> 00:05:29.630
And we could see very clearly that -1.5

00:05:31.210 --> 00:05:32.800
is higher than -2.5,

00:05:34.010 --> 00:05:37.260
so it is also greater.

00:05:37.260 --> 00:05:38.173
And we're done.


Introduction to negative numbers

WEBVTT
Kind: captions
Language: en

00:00:00.860 --> 00:00:03.150
- [Instructor] In this video,
we're gonna introduce ourself

00:00:03.150 --> 00:00:06.560
to the idea of negative numbers.

00:00:06.560 --> 00:00:10.210
Now you're already used to
the idea of positive numbers.

00:00:10.210 --> 00:00:13.280
You just call them numbers, not
positive (chuckles) numbers.

00:00:13.280 --> 00:00:14.810
And just to give you an example,

00:00:14.810 --> 00:00:16.620
I will draw a number line here.

00:00:16.620 --> 00:00:19.550
And this should all be review for you,

00:00:19.550 --> 00:00:23.160
so let me start at zero,

00:00:23.160 --> 00:00:25.760
and then this would be one.

00:00:25.760 --> 00:00:27.510
This would be two.

00:00:27.510 --> 00:00:29.490
This would be three.

00:00:29.490 --> 00:00:32.530
And you can think of these
numbers, which you're used to,

00:00:32.530 --> 00:00:34.650
which we could call positive numbers,

00:00:34.650 --> 00:00:37.460
as how far we are above zero.

00:00:37.460 --> 00:00:41.650
One is one above zero.
Two is two above zero.

00:00:41.650 --> 00:00:43.920
Now what do you think negative
numbers are going to be?

00:00:43.920 --> 00:00:47.970
If positive numbers are
how far we are above zero,

00:00:47.970 --> 00:00:52.250
then a negative number would
be how far are we below zero.

00:00:52.250 --> 00:00:56.460
So for example, if I go one to
the left on this number line,

00:00:56.460 --> 00:00:59.240
that would now get us to negative one.

00:00:59.240 --> 00:01:01.320
Positive one is one to the right.

00:01:01.320 --> 00:01:03.610
Negative one is one to the left.

00:01:03.610 --> 00:01:05.930
If I were to go another one to the left,

00:01:05.930 --> 00:01:09.920
I would get to negative
two, and I could keep going.

00:01:09.920 --> 00:01:12.030
As many positive numbers there are,

00:01:12.030 --> 00:01:14.040
I can have the negative version of it.

00:01:14.040 --> 00:01:15.620
However far I am to the right,

00:01:15.620 --> 00:01:18.770
I could be that far to the left.

00:01:18.770 --> 00:01:19.730
Now some of you,

00:01:19.730 --> 00:01:22.550
especially if you live in
very cold parts of the world,

00:01:22.550 --> 00:01:24.970
might have already
experienced negative numbers

00:01:24.970 --> 00:01:26.420
in some way.

00:01:26.420 --> 00:01:29.930
For example, if you look at a thermometer,

00:01:29.930 --> 00:01:33.400
this has both a Celsius
thermometer, right over here,

00:01:33.400 --> 00:01:34.870
and Fahrenheit.

00:01:34.870 --> 00:01:37.970
We know that you can get temperatures

00:01:37.970 --> 00:01:41.050
below zero degrees Celsius

00:01:41.050 --> 00:01:43.810
and temperatures below
zero degrees Fahrenheit.

00:01:43.810 --> 00:01:46.140
On this thermometer, they just mark

00:01:46.140 --> 00:01:49.340
how far we are below zero
with these red numbers,

00:01:49.340 --> 00:01:51.490
but really these are negative numbers.

00:01:51.490 --> 00:01:53.650
And we specify negative numbers

00:01:53.650 --> 00:01:57.700
by putting that negative
sign right in front of it

00:01:57.700 --> 00:01:59.070
like that.

00:01:59.070 --> 00:02:02.300
So for example, 20 degrees Celsius

00:02:02.300 --> 00:02:04.640
is positive of 20 degrees Celsius

00:02:04.640 --> 00:02:07.640
is actually a pretty
comfortable temperature,

00:02:07.640 --> 00:02:11.890
but negative 20 degrees
Celsius, that is below,

00:02:11.890 --> 00:02:15.350
20 degrees Celsius below
the freezing point of water,

00:02:15.350 --> 00:02:19.430
that is a very, very, very,
very cold temperature.

00:02:19.430 --> 00:02:21.840
One is 20 degrees above zero.

00:02:21.840 --> 00:02:25.650
One is 20 degrees below zero.

00:02:25.650 --> 00:02:28.440
So a big picture, for any given number,

00:02:28.440 --> 00:02:30.030
there's a negative version of it.

00:02:30.030 --> 00:02:33.080
For example, this right over
here would be positive six,

00:02:33.080 --> 00:02:35.700
and then you could have negative six.

00:02:35.700 --> 00:02:38.900
But negative six is six below zero

00:02:38.900 --> 00:02:42.060
or six left of the zero
on the number line,

00:02:42.060 --> 00:02:46.240
while positive six is, of
course, six above zero.

00:02:46.240 --> 00:02:48.540
So I will leave you there.

00:02:48.540 --> 00:02:49.373
You might be thinking,

00:02:49.373 --> 00:02:52.090
"Oh wow, this looks a lot
like a subtraction sign.

00:02:52.090 --> 00:02:54.360
Maybe it is related to
subtraction somehow."

00:02:54.360 --> 00:02:57.200
Or "How can I do addition and subtraction,

00:02:57.200 --> 00:02:59.750
multiplication and division
with negative numbers?"

00:02:59.750 --> 00:03:03.083
And for that we will go to future videos.


Seasons

WEBVTT
Kind: captions
Language: en

00:00:00.260 --> 00:00:01.850
- [Instructor] In this video,
we're gonna think about

00:00:01.850 --> 00:00:04.230
why we have seasons on Earth,

00:00:04.230 --> 00:00:08.340
like summer and fall
and winter and spring.

00:00:08.340 --> 00:00:10.530
Now, one theory that some folks might have

00:00:10.530 --> 00:00:12.150
is maybe it's due to the distance

00:00:12.150 --> 00:00:13.550
between the Earth and the sun.

00:00:13.550 --> 00:00:16.210
We know that the Earth orbits the sun,

00:00:16.210 --> 00:00:19.170
the sun is where the
great majority of the heat

00:00:19.170 --> 00:00:22.100
and the energy on the surface
of the Earth comes from.

00:00:22.100 --> 00:00:23.670
And maybe it's the case

00:00:23.670 --> 00:00:25.630
that there's certain times of year

00:00:25.630 --> 00:00:27.580
when we are further from the sun,

00:00:27.580 --> 00:00:29.320
and there's other times of year

00:00:29.320 --> 00:00:32.490
when we are closer to the sun.

00:00:32.490 --> 00:00:36.050
Well, this doesn't actually
hold up to why we have seasons

00:00:36.050 --> 00:00:38.840
because first of all, when
the Northern Hemisphere

00:00:38.840 --> 00:00:41.060
the top half of Earth has winter,

00:00:41.060 --> 00:00:44.090
the bottom hemisphere has
summer and vice versa.

00:00:44.090 --> 00:00:46.820
So it can't just be due to the
distance of the whole planet,

00:00:46.820 --> 00:00:48.270
it also turns out

00:00:48.270 --> 00:00:53.200
that when Earth is furthest
from the sun is in July,

00:00:53.200 --> 00:00:55.710
which is in the middle of summer

00:00:55.710 --> 00:00:57.600
in the Northern Hemisphere,

00:00:57.600 --> 00:00:59.580
and when we are closest to the sun

00:00:59.580 --> 00:01:01.660
is actually in January

00:01:01.660 --> 00:01:04.540
which we know tends to
be our colder season

00:01:04.540 --> 00:01:06.040
in the Northern Hemisphere.

00:01:06.040 --> 00:01:08.780
So distance to the sun does not hold up

00:01:08.780 --> 00:01:11.200
as to why we have seasons.

00:01:11.200 --> 00:01:14.030
The real reason why we have seasons

00:01:14.030 --> 00:01:16.840
is because of Earth's axial tilt,

00:01:16.840 --> 00:01:19.500
I guess you could say that
or it's rotational tilt.

00:01:19.500 --> 00:01:21.630
Now this picture shows that tilt

00:01:21.630 --> 00:01:23.940
but before we go into it,
I'd like to remind folks

00:01:23.940 --> 00:01:27.030
that this is nowhere near drawn at scale.

00:01:27.030 --> 00:01:30.800
The actual sun has a diameter
over 100 times out of Earth,

00:01:30.800 --> 00:01:32.950
a million Earths can fit in the sun

00:01:32.950 --> 00:01:36.210
and the actual distance
between the Earth and the sun

00:01:36.210 --> 00:01:40.160
is over 100 times the diameter
between the sun and Earth.

00:01:40.160 --> 00:01:41.700
But going back to tilt

00:01:41.700 --> 00:01:44.680
and you could see that
here in this picture,

00:01:44.680 --> 00:01:48.430
Earth's north pole does
not point straight up

00:01:48.430 --> 00:01:52.340
from the plane of Earth's
orbit around the sun.

00:01:52.340 --> 00:01:55.560
What do I mean by the plane of
Earth's orbit around the sun?

00:01:55.560 --> 00:01:58.160
This red circle that you see,

00:01:58.160 --> 00:01:59.920
or this ellipse that you see,

00:01:59.920 --> 00:02:02.440
if you imagine that being on a surface

00:02:02.440 --> 00:02:04.330
of a table or a plane,

00:02:04.330 --> 00:02:06.010
that would be our orbital plane.

00:02:06.010 --> 00:02:07.810
And we can see that the north pole

00:02:07.810 --> 00:02:09.530
does not go straight up from that

00:02:09.530 --> 00:02:11.720
and the south pole does
not go straight down,

00:02:11.720 --> 00:02:13.370
that actually we're looking

00:02:13.370 --> 00:02:17.620
at an angle of about 23.5 degrees.

00:02:17.620 --> 00:02:21.120
And that's the reason
why we have the seasons.

00:02:21.120 --> 00:02:23.290
To understand why that is the case,

00:02:23.290 --> 00:02:25.510
let's imagine Earth when
the Northern Hemisphere

00:02:25.510 --> 00:02:27.330
is most pointed towards the sun,

00:02:27.330 --> 00:02:29.310
which happens in late June.

00:02:29.310 --> 00:02:30.490
And so let me draw the equator

00:02:30.490 --> 00:02:32.630
to help us visualize this a little bit

00:02:32.630 --> 00:02:34.210
and let's compare that

00:02:34.210 --> 00:02:35.800
to when the Northern Hemisphere

00:02:35.800 --> 00:02:37.630
is most pointed away from the sun,

00:02:37.630 --> 00:02:39.650
which happens in late December.

00:02:39.650 --> 00:02:42.340
And so I will draw the equator again

00:02:42.340 --> 00:02:46.400
to help us visualize this.

00:02:46.400 --> 00:02:50.250
And let's pick a similar point
in the Northern Hemisphere.

00:02:50.250 --> 00:02:53.550
So let's pick a point that's a
little bit above the equator.

00:02:53.550 --> 00:02:54.920
So let's say that point

00:02:54.920 --> 00:02:58.410
and a comparable point in this scenario

00:02:58.410 --> 00:03:01.060
is going to be right over here.

00:03:01.060 --> 00:03:04.480
It's about that same
distance above the equator.

00:03:04.480 --> 00:03:08.240
Notice, in late June in
the Northern Hemisphere

00:03:08.240 --> 00:03:10.700
the sun is almost directly above

00:03:10.700 --> 00:03:12.910
this white point that we're seeing here.

00:03:12.910 --> 00:03:16.300
While in this scenario,
the sun is at an angle.

00:03:16.300 --> 00:03:18.700
The surface of the
Earth is more like this,

00:03:18.700 --> 00:03:22.420
so the sun's rays are coming at an angle.

00:03:22.420 --> 00:03:24.050
And if you think about it,

00:03:24.050 --> 00:03:25.050
think about the scenario,

00:03:25.050 --> 00:03:26.580
the difference between when the sun

00:03:26.580 --> 00:03:28.870
is directly bearing down on something,

00:03:28.870 --> 00:03:30.650
versus when it is coming at an angle.

00:03:30.650 --> 00:03:33.700
Let's say this is a side
view of two surfaces.

00:03:33.700 --> 00:03:36.870
And the surface on the right
has twice the surface area.

00:03:36.870 --> 00:03:38.900
You can see the side view
has twice the length,

00:03:38.900 --> 00:03:41.820
so the surface area if
you were to see it in 3D

00:03:41.820 --> 00:03:43.380
would be twice the surface area

00:03:43.380 --> 00:03:46.470
of what we have on the left here.

00:03:46.470 --> 00:03:48.400
But if you have the same amount of sun

00:03:48.400 --> 00:03:50.460
coming from the same direction,

00:03:50.460 --> 00:03:54.330
so here, let me just
draw three sun rays here,

00:03:54.330 --> 00:03:55.300
this is just indicative

00:03:55.300 --> 00:03:58.810
and let me draw three sun rays here.

00:03:58.810 --> 00:04:01.280
Notice you have this same amount of energy

00:04:01.280 --> 00:04:03.760
but here you're hitting
twice the surface area.

00:04:03.760 --> 00:04:06.360
So, the amount of energy
per unit surface area

00:04:06.360 --> 00:04:09.660
is gonna be half as much in this scenario

00:04:09.660 --> 00:04:11.840
where the sun is coming at an angle

00:04:11.840 --> 00:04:14.130
versus this scenario where the sunlight

00:04:14.130 --> 00:04:17.870
is coming more directly
on top of that point.

00:04:17.870 --> 00:04:19.970
And wherever you go in
the Northern Hemisphere

00:04:19.970 --> 00:04:22.590
the angle is less direct in the winter

00:04:22.590 --> 00:04:24.260
than it is in the summer.

00:04:24.260 --> 00:04:25.640
Now there's also some effects

00:04:25.640 --> 00:04:27.700
on the amount of daylight you get.

00:04:27.700 --> 00:04:29.610
For example, in the summer,

00:04:29.610 --> 00:04:30.810
when the Northern Hemisphere

00:04:30.810 --> 00:04:33.220
is most tilted towards the Earth,

00:04:33.220 --> 00:04:35.500
in the north pole, you're
gonna have constant daylight

00:04:35.500 --> 00:04:37.640
and the south pole you're
gonna have constant nighttime.

00:04:37.640 --> 00:04:38.940
And then the opposite happens

00:04:38.940 --> 00:04:41.370
when the Northern
Hemisphere is pointed away.

00:04:41.370 --> 00:04:43.530
And then when we think
about spring and autumn

00:04:43.530 --> 00:04:45.030
in either hemisphere,

00:04:45.030 --> 00:04:46.890
you can see that the
angle of Earth's rotation

00:04:46.890 --> 00:04:49.920
does not change from that 23.5 degrees,

00:04:49.920 --> 00:04:51.610
but in spring and autumn

00:04:51.610 --> 00:04:53.660
the Northern Hemisphere is not pointed

00:04:53.660 --> 00:04:55.360
to or away from the sun,

00:04:55.360 --> 00:04:57.500
it's kind of just pointed to the side.

00:04:57.500 --> 00:04:59.030
So in these two points,

00:04:59.030 --> 00:05:01.760
comparable points on the
Northern or Southern hemisphere

00:05:01.760 --> 00:05:05.723
are seeing similar angles
of the actual sunlight.


Comparing animal and plant cells

WEBVTT
Kind: captions
Language: en

00:00:00.190 --> 00:00:02.890
- [Instructor] So let's play
a game of Spot the Difference.

00:00:02.890 --> 00:00:04.700
Now, if you were asked
to spot the difference

00:00:04.700 --> 00:00:06.380
between these two pictures,

00:00:06.380 --> 00:00:09.060
you'd probably laugh and
say, "That's too easy."

00:00:09.060 --> 00:00:11.720
Because it's obvious that this
picture of a lion on the left

00:00:11.720 --> 00:00:14.020
is nowhere close to
looking like the picture

00:00:14.020 --> 00:00:16.090
of a green fern plant on the right.

00:00:16.090 --> 00:00:17.860
What's more, a lion and a fern

00:00:17.860 --> 00:00:19.680
not only look completely different,

00:00:19.680 --> 00:00:21.930
they also function differently.

00:00:21.930 --> 00:00:24.920
But what if I told you that
if we zoomed in really close

00:00:24.920 --> 00:00:27.610
and compared the lion's
cells with the fern's cells,

00:00:27.610 --> 00:00:30.240
they'd actually share many similarities?

00:00:30.240 --> 00:00:33.620
An animal cell and a plant cell
have several common features

00:00:33.620 --> 00:00:36.030
as well as a few key differences.

00:00:36.030 --> 00:00:39.000
In this video, we're going
to spot the similarities

00:00:39.000 --> 00:00:41.540
and the differences between
the two types of cells,

00:00:41.540 --> 00:00:44.440
and talk about their
functions inside the cells.

00:00:44.440 --> 00:00:47.290
So, first off, let's take
a look at some cell models.

00:00:47.290 --> 00:00:49.500
Here on the left is an animal cell,

00:00:49.500 --> 00:00:51.880
and on the right is a plant cell.

00:00:51.880 --> 00:00:53.970
First, let's try and identify the things

00:00:53.970 --> 00:00:57.110
that both animal and plant
cells share in common.

00:00:57.110 --> 00:00:59.530
If you recall, both animal and plant cells

00:00:59.530 --> 00:01:00.750
have a cell membrane,

00:01:00.750 --> 00:01:03.000
which acts like a gate
to control what enters

00:01:03.000 --> 00:01:04.420
and leaves the cell.

00:01:04.420 --> 00:01:05.870
Animal cells and plant cells

00:01:05.870 --> 00:01:09.320
also have this jelly-like
substance called the cytosol,

00:01:09.320 --> 00:01:11.720
which contains organelles
or small compartments

00:01:11.720 --> 00:01:14.410
with specific functions inside the cell.

00:01:14.410 --> 00:01:17.630
Animal and plant cells share
several common organelles,

00:01:17.630 --> 00:01:22.470
two of which include the
nucleus and the mitochondria.

00:01:22.470 --> 00:01:24.180
The nucleus within each cell type

00:01:24.180 --> 00:01:27.960
serves as an information database
to store the cell's genes,

00:01:27.960 --> 00:01:32.010
while the mitochondria act as
factories to break down sugars

00:01:32.010 --> 00:01:34.860
and release energy that the cells can use.

00:01:34.860 --> 00:01:37.030
So now that we've identified some features

00:01:37.030 --> 00:01:38.840
found in both kinds of cells,

00:01:38.840 --> 00:01:41.750
let's look closer to spot
the fundamental differences

00:01:41.750 --> 00:01:44.030
between animal and plant cells.

00:01:44.030 --> 00:01:45.610
As you can see in this diagram,

00:01:45.610 --> 00:01:48.070
plant cells have an
additional layer of material

00:01:48.070 --> 00:01:49.890
that surrounds the cell membrane.

00:01:49.890 --> 00:01:52.180
This is called a cell wall,

00:01:52.180 --> 00:01:55.390
which makes the plant cell
more structured and stiff.

00:01:55.390 --> 00:01:56.930
Think of a celery stalk

00:01:56.930 --> 00:02:00.020
compared to a raw piece
of chicken or fish.

00:02:00.020 --> 00:02:02.200
The animal muscle tissue is floppy

00:02:02.200 --> 00:02:04.300
while the celery stalk is firm.

00:02:04.300 --> 00:02:06.530
That's cell walls in action.

00:02:06.530 --> 00:02:08.810
Also, plant cells have
these special organelles

00:02:08.810 --> 00:02:11.380
called chloroplasts, which
are what give plants,

00:02:11.380 --> 00:02:14.150
like the fern we saw, their green color.

00:02:14.150 --> 00:02:16.380
Chloroplasts are the
site of photosynthesis,

00:02:16.380 --> 00:02:18.100
which is how plants make their own food

00:02:18.100 --> 00:02:19.680
in the form of sugars.

00:02:19.680 --> 00:02:22.670
If the word sugar rings a
bell, you're on the right track

00:02:22.670 --> 00:02:24.930
because I mentioned
earlier that mitochondria

00:02:24.930 --> 00:02:27.910
are responsible for breaking down sugars.

00:02:27.910 --> 00:02:30.550
In plant cells, chloroplasts
and mitochondria

00:02:30.550 --> 00:02:32.590
are like good buddies that help each other

00:02:32.590 --> 00:02:33.900
and work together.

00:02:33.900 --> 00:02:36.750
Chloroplasts make sugars
through photosynthesis

00:02:36.750 --> 00:02:39.380
and mitochondria convert
the sugars into energy

00:02:39.380 --> 00:02:42.110
that, ultimately, the plant can use.

00:02:42.110 --> 00:02:45.520
Both cell walls and chloroplasts
are found in plant cells

00:02:45.520 --> 00:02:48.760
but not animal cells, such
as the ones in you and me.

00:02:48.760 --> 00:02:52.570
And luckily for you and me,
this means we aren't green.

00:02:52.570 --> 00:02:55.720
In summary, we just identified
several similarities

00:02:55.720 --> 00:02:59.560
and differences in our comparison
of animal and plant cells.

00:02:59.560 --> 00:03:02.430
While both cell types
have a cell membrane,

00:03:02.430 --> 00:03:06.400
cytosol, a nucleus, and mitochondria,

00:03:06.400 --> 00:03:07.680
plant cells have a cell wall

00:03:07.680 --> 00:03:11.720
that makes them stiff and rigid,
think about celery stalks,

00:03:11.720 --> 00:03:13.240
and they have chloroplasts,

00:03:13.240 --> 00:03:16.750
which makes sugars and give
plants their green color.

00:03:16.750 --> 00:03:18.560
All of these are just a handful

00:03:18.560 --> 00:03:20.570
of the similarities and differences

00:03:20.570 --> 00:03:22.950
between plant and animal cells.

00:03:22.950 --> 00:03:25.080
As you go forward in your biology journey,

00:03:25.080 --> 00:03:27.910
you'll probably learn about a lot more.

00:03:27.910 --> 00:03:29.540
But the differences that we've covered

00:03:29.540 --> 00:03:32.560
are a big part of what
makes plant and animal cells

00:03:32.560 --> 00:03:35.320
so distinct and unique from each other.

00:03:35.320 --> 00:03:38.430
These differences are why
we don't see green lions

00:03:38.430 --> 00:03:41.270
that photosynthesize using chloroplasts

00:03:41.270 --> 00:03:45.980
or floppy raw veggies with cell
membranes but no cell walls.

00:03:45.980 --> 00:03:48.330
- Now I hope that you
have a clear understanding

00:03:48.330 --> 00:03:51.670
of the different cell parts in
both animal and plant cells,

00:03:51.670 --> 00:03:53.890
and that spotting the
differences between the two

00:03:53.890 --> 00:03:55.793
will be easy breezy.


Khan Academy Ed Talks with Ted Coe, PhD - Tuesday, March 15

WEBVTT
Kind: captions
Language: en

00:00:00.330 --> 00:00:04.010
- Hello and welcome to Ed
Talks with Khan Academy.

00:00:04.010 --> 00:00:04.990
I'm Kristen DiCerbo,

00:00:04.990 --> 00:00:06.880
the Chief Learning
Officer at Khan Academy.

00:00:06.880 --> 00:00:11.140
And today, I am looking forward
to talking to Dr. Ted Coe,

00:00:11.140 --> 00:00:15.270
who is with NWEA, one of
our key partners here.

00:00:15.270 --> 00:00:18.340
He is the Director of
Content, Advocacy and Design.

00:00:18.340 --> 00:00:20.270
We're looking forward
to talking about math

00:00:20.270 --> 00:00:22.330
and math learning today.

00:00:22.330 --> 00:00:25.250
Before we get started, I wanna
remind you that Khan Academy

00:00:25.250 --> 00:00:29.180
is a nonprofit organization
and relies on donations

00:00:29.180 --> 00:00:31.920
from folks like you to help us continue

00:00:31.920 --> 00:00:32.930
to be able to do our work.

00:00:32.930 --> 00:00:36.230
So if you go to khanacademy.org/donate,

00:00:36.230 --> 00:00:39.500
you'll find a place where you
can help keep us supported

00:00:39.500 --> 00:00:43.250
and work in continuing our
work, so thank you for that.

00:00:43.250 --> 00:00:47.710
I also want to acknowledge
our corporate supporters

00:00:47.710 --> 00:00:49.980
who have come and helped us work

00:00:49.980 --> 00:00:53.580
through the COVID-19
crisis, including AT&T,

00:00:53.580 --> 00:00:56.290
General Motors, and Fastly.

00:00:56.290 --> 00:01:01.290
If you would like to
listen to this conversation

00:01:02.310 --> 00:01:04.860
or any of our previous conversations,

00:01:04.860 --> 00:01:07.230
you can, wherever you get your podcasts,

00:01:07.230 --> 00:01:09.950
find Homeroom with Sal, The Podcast

00:01:09.950 --> 00:01:13.170
and you'll be able to
listen wherever you prefer,

00:01:13.170 --> 00:01:17.580
at the gym, on your
walks, doing the dishes.

00:01:17.580 --> 00:01:18.683
We hope you enjoy it.

00:01:19.780 --> 00:01:24.780
So without further ado, let
me introduce Dr. Ted Coe.

00:01:25.080 --> 00:01:28.930
So he has over 25 years of
experience as a teacher,

00:01:28.930 --> 00:01:31.690
professor, department
chair, administrator,

00:01:31.690 --> 00:01:34.570
and a nonprofit director,
basically weaving together

00:01:34.570 --> 00:01:37.510
perspectives about mathematics education.

00:01:37.510 --> 00:01:39.400
He has experience as a full-time

00:01:39.400 --> 00:01:40.980
high school mathematics teacher,

00:01:40.980 --> 00:01:43.120
community college faculty member,

00:01:43.120 --> 00:01:45.550
a mathematics chair at
two community colleges,

00:01:45.550 --> 00:01:48.330
and an assistant dean
at the university level.

00:01:48.330 --> 00:01:52.410
And I will say, as
someone who is a graduate

00:01:52.410 --> 00:01:53.660
of Arizona State University,

00:01:53.660 --> 00:01:57.093
he is a fellow Sun Devil as well, welcome.

00:01:58.250 --> 00:02:00.773
- Thank you, thank you, glad to be here.

00:02:01.810 --> 00:02:03.150
- We are glad to have you.

00:02:03.150 --> 00:02:07.490
So first of all, tell us what
your role is specifically.

00:02:07.490 --> 00:02:09.053
What do you do at NWEA?

00:02:10.155 --> 00:02:12.955
- This is an interesting question, right?

00:02:12.955 --> 00:02:16.910
The answer is, the title
is Director of Content,

00:02:16.910 --> 00:02:19.550
Advocacy and Design for mathematics.

00:02:19.550 --> 00:02:21.660
And the interesting side to it is,

00:02:21.660 --> 00:02:23.740
well, I get to advocate for content.

00:02:23.740 --> 00:02:26.260
And so for many ways for me

00:02:26.260 --> 00:02:27.760
it's like this dream world to be in,

00:02:27.760 --> 00:02:30.710
where I get to kind of
imagine the kinds of things

00:02:30.710 --> 00:02:32.570
that we wanna work on,
how do we wanna grow,

00:02:32.570 --> 00:02:36.380
how do we want to move
beyond a focus on assessment

00:02:36.380 --> 00:02:40.140
to teaching and learning and
getting into the classroom

00:02:40.140 --> 00:02:43.410
and getting it, so it's
envisioning these kinds of things.

00:02:43.410 --> 00:02:46.050
It's being able to work with
different state and districts

00:02:46.050 --> 00:02:47.670
and get in there and roll up our sleeves

00:02:47.670 --> 00:02:49.890
and get our hands dirty trying to solve

00:02:49.890 --> 00:02:52.300
some pretty messy problems.

00:02:52.300 --> 00:02:55.090
So that's a lot of what I get to do.

00:02:55.090 --> 00:02:57.633
And so to me, it's great fun.

00:02:58.870 --> 00:03:01.550
- That's fantastic, how did
you come to be in this role?

00:03:01.550 --> 00:03:04.773
What was your path that
you took to end up here?

00:03:05.691 --> 00:03:10.543
- It was so bizarre, it's
a crazy path, career path,

00:03:12.350 --> 00:03:14.430
started out as a high school teacher,

00:03:14.430 --> 00:03:17.310
things were going well, I
loved high school teaching,

00:03:17.310 --> 00:03:19.380
highlight of the career, right?

00:03:19.380 --> 00:03:23.040
Then I ended up getting pulled over

00:03:23.040 --> 00:03:24.840
to one of the community colleges

00:03:24.840 --> 00:03:26.660
and I actually walked
right in my first job

00:03:26.660 --> 00:03:29.600
in the community college
system was as a chair

00:03:29.600 --> 00:03:30.900
at Rio Salado College

00:03:30.900 --> 00:03:32.530
in the Maricopa Community
College District.

00:03:32.530 --> 00:03:36.100
So it was like this big sort of leap.

00:03:36.100 --> 00:03:38.890
I ended up switching over
to another community college

00:03:38.890 --> 00:03:42.270
in the district, Scotts
Dale and while I was there,

00:03:42.270 --> 00:03:46.810
I ended up being involved
deeply in the mathematics

00:03:46.810 --> 00:03:48.790
around the whole community college system

00:03:48.790 --> 00:03:51.690
and kind of involved in the
articulation conversations

00:03:51.690 --> 00:03:53.000
around the state and everything.

00:03:53.000 --> 00:03:57.580
And somewhere along that time
the Park Consortium came along

00:03:57.580 --> 00:03:58.413
and you might remember this,

00:03:58.413 --> 00:03:59.960
this was in the early
years of the common core

00:03:59.960 --> 00:04:01.860
and there were the two major consortium,

00:04:01.860 --> 00:04:03.660
Park and Smarter Balanced.

00:04:03.660 --> 00:04:07.790
And I was brought on to the
Park side of the conversation.

00:04:07.790 --> 00:04:10.910
Arizona was one of the
governing states at the time.

00:04:10.910 --> 00:04:11.743
And I was brought in

00:04:11.743 --> 00:04:14.090
as one of the higher ed content experts.

00:04:14.090 --> 00:04:16.080
And so I was dropped into
this space all of a sudden,

00:04:16.080 --> 00:04:18.940
where I had been a college professor

00:04:18.940 --> 00:04:21.780
and high school teacher and
now I was in this space,

00:04:21.780 --> 00:04:23.020
where it's like, we want your input

00:04:23.020 --> 00:04:25.300
on this multi-state assessment

00:04:25.300 --> 00:04:26.700
that's on these new standards.

00:04:26.700 --> 00:04:28.000
And so I'm like, "Well,
let's read the standards,

00:04:28.000 --> 00:04:29.700
let's see what this is about."

00:04:29.700 --> 00:04:32.920
And I got really involved
in it and so much, in fact

00:04:32.920 --> 00:04:36.250
that eventually Park
split off of the group

00:04:36.250 --> 00:04:38.060
that was running it,
which was called Achieve.

00:04:38.060 --> 00:04:41.150
And Achieve was the ones for
the American Diploma Product,

00:04:41.150 --> 00:04:42.730
helped lead the common core and all that,

00:04:42.730 --> 00:04:44.800
and the next generation science standards.

00:04:44.800 --> 00:04:47.380
And so they only hired me
to be their math director.

00:04:47.380 --> 00:04:52.290
And so for the years prior
to coming into this space

00:04:52.290 --> 00:04:54.570
at NWEA where I've been for two years,

00:04:54.570 --> 00:04:56.990
I was the director of mathematics
there and got to work all

00:04:56.990 --> 00:04:59.740
around the country with
great folks everywhere.

00:04:59.740 --> 00:05:03.797
And really get to see how
the policies worked out

00:05:03.797 --> 00:05:05.880
and the difficulties that
people were encountering

00:05:05.880 --> 00:05:07.607
and trying to talk through
some of those things

00:05:07.607 --> 00:05:09.497
and getting the chance to
speak all over the country.

00:05:09.497 --> 00:05:11.507
It was great fun, it's been great fun

00:05:11.507 --> 00:05:15.760
and it's been it one
surprise after the other.

00:05:15.760 --> 00:05:17.083
And here I am today.

00:05:18.160 --> 00:05:19.950
- Fantastic, that sounds great.

00:05:19.950 --> 00:05:23.373
So let's talk a little bit
about teaching and leaning math.

00:05:24.320 --> 00:05:28.260
Historically, there's been
all this discussion about,

00:05:28.260 --> 00:05:30.850
should we teach procedural skills?

00:05:30.850 --> 00:05:33.440
Should we teach conceptual understanding?

00:05:33.440 --> 00:05:37.260
And these wars about which
one is more important

00:05:37.260 --> 00:05:38.140
and where these is,

00:05:38.140 --> 00:05:40.340
is that the right
conversation to be having?

00:05:41.732 --> 00:05:44.270
- It's a tale as old as time,

00:05:44.270 --> 00:05:46.310
at least as old as my
career has been, right?

00:05:46.310 --> 00:05:49.290
But there's always this tension in there.

00:05:49.290 --> 00:05:53.118
And so I've had to sit
back and think to myself

00:05:53.118 --> 00:05:56.920
how would I describe teaching
and learning mathematics

00:05:56.920 --> 00:05:58.950
after my 20 years of teaching?

00:05:58.950 --> 00:06:02.420
And I was like, "Well,
how do I sum this up?"

00:06:02.420 --> 00:06:04.230
And it was somehow
developed along the way,

00:06:04.230 --> 00:06:07.630
but it was this idea that
look, part of what we do

00:06:07.630 --> 00:06:11.030
in mathematics is we
teach these ways of doing

00:06:12.290 --> 00:06:13.780
and we want you to be able to do those

00:06:13.780 --> 00:06:16.190
but we also wanna make
sure that you're picking up

00:06:16.190 --> 00:06:18.710
ways of thinking, and I'll
give you an example of that

00:06:18.710 --> 00:06:22.440
in just a moment, that go
alongside habits of thinking.

00:06:22.440 --> 00:06:25.260
So you have these ways of
thinking sort of at a core

00:06:25.260 --> 00:06:28.620
that are bolstered by
these habits of thinking

00:06:28.620 --> 00:06:32.710
that are then in turn
really sort of brought,

00:06:32.710 --> 00:06:34.220
they come to the table in certain ways,

00:06:34.220 --> 00:06:36.500
through the ways of doing
that allow you to go on

00:06:36.500 --> 00:06:39.580
and do something bigger
with the mathematics.

00:06:39.580 --> 00:06:41.910
An example I use quite frequently

00:06:41.910 --> 00:06:43.970
is with this idea of ways of thinking.

00:06:43.970 --> 00:06:46.390
And I can ask a room full
of adults this question

00:06:46.390 --> 00:06:47.837
and basically I say something like,

00:06:47.837 --> 00:06:52.210
"Hey, how many years was
it from December 7th, 1941

00:06:53.730 --> 00:06:54.887
to December 7th, 2014?"

00:06:56.220 --> 00:06:57.790
That's how long I've
been using this question.

00:06:57.790 --> 00:07:02.790
Okay, so December 7th
2014 and by and large

00:07:04.950 --> 00:07:08.010
you ask this to a room
full of even adults, right?

00:07:08.010 --> 00:07:10.830
And people will sit there
and they start chewing on

00:07:10.830 --> 00:07:12.782
an answer and they start,
"Oh, what can I do?

00:07:12.782 --> 00:07:13.615
What can I do?"

00:07:13.615 --> 00:07:15.060
And they go through some
mechanizations in their head

00:07:15.060 --> 00:07:15.977
and they might think,

00:07:15.977 --> 00:07:19.050
"Well, that's actually kind
of a subtraction problem

00:07:19.050 --> 00:07:22.370
but I don't really need to
use subtraction to get it,"

00:07:22.370 --> 00:07:23.890
because in this case, I'm just trying

00:07:23.890 --> 00:07:26.660
to find this additive comparison
and this gap, if you will,

00:07:26.660 --> 00:07:28.160
between the two numbers

00:07:28.160 --> 00:07:29.320
and there are different ways to do it.

00:07:29.320 --> 00:07:32.220
Maybe I wanna go from
1941 to 2000, cut it off,

00:07:32.220 --> 00:07:33.850
and then go from 2000 to 2014,

00:07:33.850 --> 00:07:35.910
or maybe I wanna take the whole thing.

00:07:35.910 --> 00:07:37.280
So starting in 1941,

00:07:37.280 --> 00:07:42.280
I wanna slide the whole thing
back a year and start at 1940.

00:07:42.460 --> 00:07:44.760
Either way, all of these things are fair

00:07:44.760 --> 00:07:48.730
but the majority of the
folks I asked that question,

00:07:48.730 --> 00:07:51.050
they don't answer it
with the way of doing,

00:07:51.050 --> 00:07:53.790
they don't do the 15 steps
of setting up the algorithm,

00:07:53.790 --> 00:07:55.940
borrowing, not giving back all that thing,

00:07:55.940 --> 00:07:58.699
putting the one, they don't do that,

00:07:58.699 --> 00:08:02.740
they bring ways of
thinking to bear, right?

00:08:02.740 --> 00:08:03.580
- Yeah.

00:08:03.580 --> 00:08:07.300
- And I think maybe part of
why we get into this mess

00:08:07.300 --> 00:08:11.020
is in the standards, we have
the learning progressions

00:08:11.020 --> 00:08:15.030
and the learning progressions
and with the ways of doing.

00:08:15.030 --> 00:08:17.660
And so it looks like the
way of doing is the goal,

00:08:17.660 --> 00:08:20.230
but the way of doing
is just one more thing,

00:08:20.230 --> 00:08:22.830
it's just one more piece, right?

00:08:22.830 --> 00:08:25.620
Yeah, so I really like to emphasize

00:08:25.620 --> 00:08:29.340
this idea of ways of
thinking with regards to

00:08:29.340 --> 00:08:31.210
ways of thinking, ways of
doing, habits of thinking,

00:08:31.210 --> 00:08:33.640
all of those things working together.

00:08:33.640 --> 00:08:36.130
'Cause if you have just
one, the ways of doing,

00:08:36.130 --> 00:08:38.870
all you've got is a box of puzzle pieces

00:08:38.870 --> 00:08:40.723
when you're done with it, yeah.

00:08:41.606 --> 00:08:44.650
- Right, so I'm gonna keep
going with the year example here

00:08:44.650 --> 00:08:48.240
to push on this, so my
sister got married in 1997

00:08:48.240 --> 00:08:52.050
and I have to say, somehow
never made this connection,

00:08:52.050 --> 00:08:53.667
but she said to me one day,

00:08:53.667 --> 00:08:55.190
"If you wanna know how
long we've been married,

00:08:55.190 --> 00:08:57.360
you just take what current
year it is in add three,

00:08:57.360 --> 00:08:58.713
because 1997 to 2003."

00:09:00.660 --> 00:09:03.757
Then I was like, "Oh yeah,
why did I not think of that?"

00:09:03.757 --> 00:09:04.670
(Kristen laughing)

00:09:04.670 --> 00:09:09.140
So that's a way of doing
it, so then that's one way,

00:09:09.140 --> 00:09:11.780
or is that how does that relate
then to ways of thinking?

00:09:11.780 --> 00:09:15.680
And so are there many
different ways you can do it

00:09:15.680 --> 00:09:17.320
and the ways of thinking around it?

00:09:17.320 --> 00:09:20.350
- Yes, the idea is that
when I ask that question,

00:09:20.350 --> 00:09:23.030
there are so many different
ways you could approach it.

00:09:23.030 --> 00:09:25.320
You could approach it with a way of doing

00:09:25.320 --> 00:09:26.530
and no harm, no foul.

00:09:26.530 --> 00:09:28.240
You could approach it
with ways of thinking,

00:09:28.240 --> 00:09:30.170
but if all you have is the way of doing

00:09:30.170 --> 00:09:32.160
and you don't have those ways of thinking,

00:09:32.160 --> 00:09:34.830
then when you get to
somewhere in real life,

00:09:34.830 --> 00:09:36.500
it doesn't illuminate.

00:09:36.500 --> 00:09:40.586
And a place where this
happens is you can ask

00:09:40.586 --> 00:09:43.280
like where in real life,
ask this to an adult,

00:09:43.280 --> 00:09:45.560
where in real life have
you ever actually used

00:09:45.560 --> 00:09:47.013
division of fractions?

00:09:47.880 --> 00:09:49.820
And I'll be surprised if you actually get

00:09:49.820 --> 00:09:54.740
any valid answer back from
anybody and why is that?

00:09:54.740 --> 00:09:57.130
Because if we reflect back to it,

00:09:57.130 --> 00:10:00.100
when we were taught the
division of fractions,

00:10:00.100 --> 00:10:02.630
those of us who were of
a certain age, right?

00:10:02.630 --> 00:10:04.780
We were caught a way of doing

00:10:04.780 --> 00:10:08.790
and it was totally disconnected
from ways of thinking

00:10:08.790 --> 00:10:12.280
grounded in what does it
mean to divide so that-

00:10:12.280 --> 00:10:16.180
- Yes, you were just
taught the procedure, yeah.

00:10:16.180 --> 00:10:18.450
- Yeah and so you've got the procedure

00:10:18.450 --> 00:10:20.170
but you have no place to hang it,

00:10:20.170 --> 00:10:22.380
when it comes and shows up in real life.

00:10:22.380 --> 00:10:26.650
- Right, that totally makes
sense, so if I'm a teacher

00:10:26.650 --> 00:10:29.710
how do I start thinking about encouraging

00:10:29.710 --> 00:10:31.103
these ways of thinking?

00:10:32.500 --> 00:10:34.513
- See, that's the tricky part, right?

00:10:35.526 --> 00:10:36.359
- Right?

00:10:36.359 --> 00:10:41.120
- Yeah, and so one really
cool thing that happened

00:10:42.180 --> 00:10:43.980
in the last couple years, Peter Liljedahl

00:10:43.980 --> 00:10:47.050
came out with a book called
"Building Thinking Classrooms."

00:10:47.050 --> 00:10:49.420
And I'm like, yes, yes, we're seeing

00:10:49.420 --> 00:10:52.460
this emphasis shifting
to thinking, fantastic.

00:10:52.460 --> 00:10:56.623
Because at the same time
my colleagues and I at NWEA

00:10:56.623 --> 00:11:00.030
have been trying to work on this idea

00:11:00.030 --> 00:11:02.850
of how can we get ways of thinking moving

00:11:02.850 --> 00:11:04.450
and talked about in classrooms

00:11:04.450 --> 00:11:06.810
in ways that are non-threatening, right?

00:11:06.810 --> 00:11:09.640
That feel safe to both
teachers and students

00:11:09.640 --> 00:11:13.790
because there's awkwardness
when we ask ourselves

00:11:13.790 --> 00:11:16.890
thinking questions, all of
us have to stop and think,

00:11:16.890 --> 00:11:20.300
and with thinking comes
vulnerability, right?

00:11:20.300 --> 00:11:24.170
So we actually built out some things

00:11:24.170 --> 00:11:26.860
called these formative
conversation starters.

00:11:26.860 --> 00:11:29.300
And the role of the formative
conversation starters

00:11:29.300 --> 00:11:33.250
is to basically help shape
how you might enter into

00:11:33.250 --> 00:11:34.930
some of these kinds of conversations

00:11:34.930 --> 00:11:37.910
that are designed to
focus on ways of thinking

00:11:39.420 --> 00:11:42.830
and then to do it in such
a way that you also know

00:11:42.830 --> 00:11:46.760
what it is you're trying to
listen for at the same time.

00:11:46.760 --> 00:11:48.470
So we've got these bins,

00:11:48.470 --> 00:11:50.920
these big ideas to nurture sense making

00:11:50.920 --> 00:11:54.300
and then we've got clusters of questions

00:11:54.300 --> 00:11:57.623
that unfold as you ask them and might lead

00:11:57.623 --> 00:12:01.010
to moments of cognitive
dissonance or might lead to ahas

00:12:01.010 --> 00:12:04.217
or might lead to places
where you step back and go,

00:12:04.217 --> 00:12:07.077
"I really do need to think
more deeply about that."

00:12:08.115 --> 00:12:10.250
So there are different options to do it.

00:12:10.250 --> 00:12:14.302
You can put in classroom
routines, you can build tools,

00:12:14.302 --> 00:12:16.213
like we're trying to build out.

00:12:17.830 --> 00:12:21.507
But the idea is what can we do to do that?

00:12:21.507 --> 00:12:24.590
All kinds of things, like
Peter's got in his book,

00:12:24.590 --> 00:12:26.420
all kinds of options,

00:12:26.420 --> 00:12:29.670
as well as what I'm offering here today.

00:12:29.670 --> 00:12:32.100
- Yeah, so I like this idea
of conversation starters.

00:12:32.100 --> 00:12:36.170
I think we're putting a
link to them in the chat

00:12:36.170 --> 00:12:38.940
for folks that are following along.

00:12:38.940 --> 00:12:41.700
Can you give us some examples,
what are some examples

00:12:41.700 --> 00:12:43.840
of what these are and how do they work?

00:12:43.840 --> 00:12:48.840
- Yeah, so, and sometimes
the idea like with fractions,

00:12:51.410 --> 00:12:54.346
I might come out and we might
start with a question like,

00:12:54.346 --> 00:12:56.280
well, what's a fraction?

00:12:56.280 --> 00:12:58.120
And then, well, the
next question might be,

00:12:58.120 --> 00:13:01.470
well, is a fraction one
number or two numbers?

00:13:01.470 --> 00:13:03.700
And just sit back and talk about it.

00:13:03.700 --> 00:13:06.350
Talk about what you
think on that, all right?

00:13:06.350 --> 00:13:08.420
And then, well, what do you think of

00:13:08.420 --> 00:13:10.193
when you think of three eighths?

00:13:11.140 --> 00:13:14.170
Okay, what do you think of
when you see eight thirds?

00:13:14.170 --> 00:13:16.840
'Cause if you're of three
eighths as three out of eight,

00:13:16.840 --> 00:13:18.360
then eight thirds becomes something

00:13:18.360 --> 00:13:21.230
that's maybe a little
tougher to think about.

00:13:21.230 --> 00:13:23.560
Another example would be
a question that starts off

00:13:23.560 --> 00:13:27.840
with like, well, what
does division do for us?

00:13:27.840 --> 00:13:29.210
And so you wanna sit
back and you think about,

00:13:29.210 --> 00:13:31.110
well, what does division do for us?

00:13:31.110 --> 00:13:32.640
And then the next question would be

00:13:32.640 --> 00:13:36.280
not to do a division problem,
but to ask a question like,

00:13:39.628 --> 00:13:42.620
without computing how can you
think about a problem like

00:13:42.620 --> 00:13:44.090
10 divided by one half

00:13:45.250 --> 00:13:48.660
and to be able to go on to the next one.

00:13:48.660 --> 00:13:51.090
Well, then how would you
think about negative 10

00:13:51.090 --> 00:13:53.060
divided by one half, right?

00:13:53.060 --> 00:13:56.720
And if your ways of thinking
are consistent and robust,

00:13:56.720 --> 00:13:59.130
then your answers were
sort of gel together

00:13:59.130 --> 00:14:02.610
but if you have fractures
and if they're disjoint,

00:14:02.610 --> 00:14:04.220
then you kind of have to go back

00:14:04.220 --> 00:14:06.150
and kind of try to figure
out, well, how do I get the,

00:14:06.150 --> 00:14:09.340
I know that my thinking should
gel together with my answers

00:14:09.340 --> 00:14:12.110
to all of these things,
what do I need to do?

00:14:12.110 --> 00:14:13.920
How do I need to accommodate
the way I'm thinking

00:14:13.920 --> 00:14:16.390
in order to make these things work?

00:14:16.390 --> 00:14:18.050
From the teacher's perspective,

00:14:18.050 --> 00:14:21.470
we help provide what you might
be listening for in these-

00:14:21.470 --> 00:14:23.087
- I was just gonna ask that.

00:14:23.087 --> 00:14:24.686
(Kristen laughing)

00:14:24.686 --> 00:14:26.620
Yeah, what are the things
that you're looking for

00:14:26.620 --> 00:14:28.335
from the teacher's perspective?

00:14:28.335 --> 00:14:31.557
- Yeah, so like we know
that we want fraction

00:14:31.557 --> 00:14:34.330
and we want students to be
able to think of a fraction

00:14:34.330 --> 00:14:39.330
as a single number, as a point
on the number line, right?

00:14:39.870 --> 00:14:43.940
But if I ask my students about fractions

00:14:43.940 --> 00:14:44.773
and they're saying,

00:14:44.773 --> 00:14:48.130
"Well, we're only thinking
of it as two numbers."

00:14:48.130 --> 00:14:50.870
Then I'm talking about
something as the teacher

00:14:50.870 --> 00:14:53.860
that's completely different
from what they're hearing.

00:14:53.860 --> 00:14:56.420
And so it's this idea of
getting these meanings

00:14:56.420 --> 00:14:58.960
out in the open so that we all know

00:14:58.960 --> 00:15:00.920
that we're talking about the same thing,

00:15:00.920 --> 00:15:03.660
so when I say fraction, you're
thinking the same thing.

00:15:03.660 --> 00:15:05.540
Or when I talk about division,

00:15:05.540 --> 00:15:07.570
you've got a notion of thinking of it

00:15:07.570 --> 00:15:09.750
as a multiplicative comparison.

00:15:09.750 --> 00:15:11.930
Or you've got way of
thinking about it in terms of

00:15:11.930 --> 00:15:14.210
how many copies of run
thing are in another,

00:15:14.210 --> 00:15:17.690
or this time's as large
as this thing, right?

00:15:17.690 --> 00:15:19.030
Which when you have those ways of thinking

00:15:19.030 --> 00:15:19.863
that a question like,

00:15:19.863 --> 00:15:21.530
how can you think of
10 divided by one half,

00:15:21.530 --> 00:15:24.610
doesn't become something
that's out of bounds at all.

00:15:24.610 --> 00:15:26.320
It becomes something that
you can already hang onto

00:15:26.320 --> 00:15:28.888
one of those previous
existing meanings of division,

00:15:28.888 --> 00:15:32.370
if they're there, if you've
got those ways of thinking.

00:15:32.370 --> 00:15:35.020
- Right, right, yeah, that makes sense.

00:15:35.020 --> 00:15:39.855
So do these starters work
across ages and grade levels?

00:15:39.855 --> 00:15:42.190
Are there things that we need to be,

00:15:42.190 --> 00:15:43.957
what kinds of things can younger kids do

00:15:43.957 --> 00:15:47.460
and what kinds of things
can older kids start to get?

00:15:47.460 --> 00:15:50.850
- So the interesting thing
about them is the way,

00:15:50.850 --> 00:15:52.810
if you go download, maybe
some people have already gone

00:15:52.810 --> 00:15:54.830
to download the documents
just while we're sitting here.

00:15:54.830 --> 00:15:59.230
But you'll see the entry point
into this is through an item,

00:15:59.230 --> 00:16:02.040
it's through a standard, but the idea is

00:16:02.040 --> 00:16:06.500
we've spent so many years
unpacking standards,

00:16:06.500 --> 00:16:08.990
digging in and saying, let's
look at this one standard.

00:16:08.990 --> 00:16:09.970
What we wanna do is say,

00:16:09.970 --> 00:16:12.630
we're only using this as the entry point,

00:16:12.630 --> 00:16:14.370
because what we wanna
do is we wanna find out,

00:16:14.370 --> 00:16:17.270
what is all of the other
mathematics that has to come in

00:16:17.270 --> 00:16:20.480
alongside it to help get through this.

00:16:20.480 --> 00:16:23.080
We tend to look at an item
go, this is the standard.

00:16:23.080 --> 00:16:24.360
And then we say, well,
if they get it wrong,

00:16:24.360 --> 00:16:25.193
then we wanna go back

00:16:25.193 --> 00:16:27.020
and go to that nearest
connecting standard.

00:16:27.020 --> 00:16:29.130
What we're saying here is
actually maybe you wanna go

00:16:29.130 --> 00:16:31.903
ask them about what's a fraction, right?

00:16:31.903 --> 00:16:32.951
- Right.

00:16:32.951 --> 00:16:35.090
- So let's go talk about
what a fraction is.

00:16:35.090 --> 00:16:37.270
It might not be the
nearest neighbor standard

00:16:37.270 --> 00:16:39.500
that's the issue, it could
be some ways of thinking

00:16:39.500 --> 00:16:41.890
that endure and that goes
back to your question

00:16:41.890 --> 00:16:43.570
about who are these for?

00:16:43.570 --> 00:16:47.390
Well, you can take the ones
that we've got packaged

00:16:47.390 --> 00:16:48.770
in the third grade and ask them*8

00:16:48.770 --> 00:16:50.100
to seventh and eighth graders,

00:16:50.100 --> 00:16:53.450
because the ways of thinking
are enduring, right?

00:16:53.450 --> 00:16:56.100
And so the ideas are, yes,
they grow a little bit,

00:16:56.100 --> 00:16:58.230
but they endure and they
grew out of these things,

00:16:58.230 --> 00:17:02.460
actually grew out of, are
thinking about what could we help

00:17:02.460 --> 00:17:07.060
to provide teachers with as
we move into this phase now,

00:17:07.060 --> 00:17:08.070
where students are coming with

00:17:08.070 --> 00:17:11.130
such uneven opportunities to learn.

00:17:11.130 --> 00:17:12.790
And philosophically I'd say,

00:17:12.790 --> 00:17:15.020
well, I can't just be
focus on ways of doing.

00:17:15.020 --> 00:17:17.107
I have to be focusing some
way on the ways of thinking

00:17:17.107 --> 00:17:20.320
and these habits of thinking
that come alongside it.

00:17:20.320 --> 00:17:21.940
And so what could we do?

00:17:21.940 --> 00:17:23.540
That's where we ended up with this.

00:17:23.540 --> 00:17:26.970
So if you are a third grade teacher,

00:17:26.970 --> 00:17:28.140
you could probably pull stuff

00:17:28.140 --> 00:17:29.610
from the fourth and fifth grade.

00:17:29.610 --> 00:17:30.870
If you are a high school teacher,

00:17:30.870 --> 00:17:32.940
you can pull things
from any grades, right?

00:17:32.940 --> 00:17:34.890
And they'll still be fair game

00:17:34.890 --> 00:17:36.480
because there're things to talk about,

00:17:36.480 --> 00:17:39.450
ideas that endure that go on and on.

00:17:39.450 --> 00:17:40.790
So if you're in high school,

00:17:40.790 --> 00:17:42.130
you might dig into the functions,

00:17:42.130 --> 00:17:43.330
you might dig into comparison,

00:17:43.330 --> 00:17:45.030
you might dig into operations.

00:17:45.030 --> 00:17:48.300
I hope you dig into
proportional relationships.

00:17:48.300 --> 00:17:52.629
- Yes, so this whole conversation
is making me think about

00:17:52.629 --> 00:17:55.580
something that we talk a lot
about at Khan Academy which is,

00:17:55.580 --> 00:17:57.970
what Sal used to call Swiss cheese gaps

00:17:57.970 --> 00:18:00.520
but now everyone calls
unfinished learning.

00:18:00.520 --> 00:18:04.370
Which is the idea that lots of folks

00:18:04.370 --> 00:18:07.870
didn't get some of those
foundational concepts

00:18:07.870 --> 00:18:12.250
and when they were first
presented and so try to then build

00:18:12.250 --> 00:18:14.490
the next level without those concepts,

00:18:14.490 --> 00:18:18.093
which is kinda the shaky
foundation and it just keeps going.

00:18:19.010 --> 00:18:23.300
So it sounds like these
conversation starters

00:18:23.300 --> 00:18:27.390
are starting to think about
almost diagnosing in some ways,

00:18:27.390 --> 00:18:29.303
like do you have those-

00:18:30.140 --> 00:18:32.750
- Do you have the ways of thinking, right?

00:18:32.750 --> 00:18:37.140
The foundational ways
of thinking which are,

00:18:37.140 --> 00:18:39.340
when you look at your state standards,

00:18:39.340 --> 00:18:41.990
you're going to see them kind of in there,

00:18:41.990 --> 00:18:43.620
but you might not see them as explicit

00:18:43.620 --> 00:18:45.470
as we're trying to call them out here.

00:18:45.470 --> 00:18:46.990
Like these are some core ones

00:18:46.990 --> 00:18:48.420
that you wanna keep coming back to.

00:18:48.420 --> 00:18:52.810
You wanna keep revisiting
these and keep listening.

00:18:52.810 --> 00:18:55.870
And so the kinds of questions
that we're putting out here,

00:18:55.870 --> 00:18:58.720
use them however you wanna
use them, use them full class,

00:18:58.720 --> 00:19:00.990
use them one on one, use
them in small groups,

00:19:00.990 --> 00:19:02.340
use them for turning talks,

00:19:04.340 --> 00:19:06.973
the idea is to sit back and listen.

00:19:08.791 --> 00:19:11.503
What we would point out
is it's also not intended,

00:19:14.370 --> 00:19:17.680
there will be a teachable
moment, it's not during this time

00:19:17.680 --> 00:19:19.910
because we wanna set up the
culture in such a way that

00:19:19.910 --> 00:19:24.200
this is free, open up, tell
me what you're thinking

00:19:24.200 --> 00:19:26.530
and it's not to correct, it's to listen.

00:19:26.530 --> 00:19:27.790
And what's interesting about that, right?

00:19:27.790 --> 00:19:29.760
Is if you keep asking more questions,

00:19:29.760 --> 00:19:31.950
you might realize that your first thoughts

00:19:31.950 --> 00:19:35.160
about what people like
to call misconceptions

00:19:35.160 --> 00:19:36.630
could be completely wrong.

00:19:36.630 --> 00:19:40.088
That you've misconceived
their misconceptions.

00:19:40.088 --> 00:19:41.160
(both laughing)

00:19:41.160 --> 00:19:42.690
I don't like using the word misconceptions

00:19:42.690 --> 00:19:45.560
'cause the students have the conceptions

00:19:45.560 --> 00:19:46.860
and this is all about,

00:19:46.860 --> 00:19:49.740
what conceptions might they have, right?

00:19:49.740 --> 00:19:51.930
Not what don't they have, what
conceptions might they have?

00:19:51.930 --> 00:19:54.320
How are they thinking about these things?

00:19:54.320 --> 00:19:57.300
And let's build from that,
that connects back very closely

00:19:57.300 --> 00:20:01.330
to Sal's house building analogy, right?

00:20:01.330 --> 00:20:02.647
- Yeah, right.

00:20:02.647 --> 00:20:04.870
- These are these foundational,

00:20:04.870 --> 00:20:06.500
it's more like these foundational threads

00:20:06.500 --> 00:20:08.550
that wind their way all the way through,

00:20:08.550 --> 00:20:12.910
not just on the bottom floor
but you just keep continuing

00:20:12.910 --> 00:20:15.290
to strengthen them like
the trunk of a tree, right?

00:20:15.290 --> 00:20:17.940
It just keeps getting
stronger and stronger.

00:20:17.940 --> 00:20:20.810
- Yeah, absolutely, that
totally makes sense.

00:20:20.810 --> 00:20:25.280
How do you think about the
idea of mastery in this world?

00:20:25.280 --> 00:20:28.080
We talk a lot about mastery learning here

00:20:28.080 --> 00:20:31.370
and thinking it's easy when
you're talking about skills

00:20:31.370 --> 00:20:33.500
and having mastery of skills,

00:20:33.500 --> 00:20:37.370
but mastery of some of these
things is somewhat different.

00:20:37.370 --> 00:20:39.040
Is that even a valid concept?

00:20:39.040 --> 00:20:39.890
I don't know.

00:20:39.890 --> 00:20:43.256
- Yeah, it's so hard
to say what is mastery.

00:20:43.256 --> 00:20:46.510
I mean, we always wanna draw a line

00:20:46.510 --> 00:20:48.521
for proficiency somewhere, right?

00:20:48.521 --> 00:20:49.354
- Right.

00:20:49.354 --> 00:20:50.820
- What it means to have learned something

00:20:50.820 --> 00:20:53.690
but in this mindset on
the ways of thinking,

00:20:53.690 --> 00:20:55.690
it's like these are things
that continue to grow

00:20:55.690 --> 00:20:57.963
and morph and evolve.

00:20:58.808 --> 00:21:03.410
And as I think about, well,
how do we ever establish

00:21:03.410 --> 00:21:04.750
whether students have mastered this?

00:21:04.750 --> 00:21:07.570
I'm not sure that that's even
the right type of question.

00:21:07.570 --> 00:21:09.760
But rather to just likely,
it's just to keep on

00:21:09.760 --> 00:21:13.040
how is that scheme of
building up in their minds

00:21:13.040 --> 00:21:17.110
as they continue to go and
how can I leverage that

00:21:17.110 --> 00:21:19.290
to go on to that next place?

00:21:19.290 --> 00:21:21.810
- Right and you can think
about how you would expect

00:21:21.810 --> 00:21:25.210
some of these answers to
change as you learn new things,

00:21:25.210 --> 00:21:27.790
you're changing your
ideas about what these are

00:21:27.790 --> 00:21:29.750
as you kind of move up through new skills

00:21:29.750 --> 00:21:32.670
and things you're developing, interesting.

00:21:32.670 --> 00:21:35.820
So we obviously do a lot with technology

00:21:35.820 --> 00:21:37.630
but we also wanna think about

00:21:37.630 --> 00:21:41.010
how teachers and technology work together.

00:21:41.010 --> 00:21:44.904
And so I'm interested
in your thoughts about,

00:21:44.904 --> 00:21:47.680
the interplay between
the two is I think about

00:21:47.680 --> 00:21:48.890
what you're talking about,

00:21:48.890 --> 00:21:50.570
things technology's never gonna be good

00:21:50.570 --> 00:21:53.160
at doing what you're talking
about, that's like the thing

00:21:53.160 --> 00:21:55.130
that teachers need to be in classrooms.

00:21:55.130 --> 00:21:58.497
So I'm interested in your
thoughts about how teachers

00:21:58.497 --> 00:22:00.747
and technology can work
together to build on.

00:22:02.880 --> 00:22:06.730
- Yeah, so I'm happy to
hear you see it that way

00:22:06.730 --> 00:22:08.516
'cause that's how I see it.

00:22:08.516 --> 00:22:12.993
It's that idea that
computers, they're really good

00:22:16.070 --> 00:22:18.347
at helping with that way
of doing things, right?

00:22:18.347 --> 00:22:19.480
- Right.

00:22:19.480 --> 00:22:22.110
- But to sort of put these complex

00:22:22.110 --> 00:22:23.460
ways of thinking together,

00:22:23.460 --> 00:22:26.436
I mean, that takes some time
and working and developing

00:22:26.436 --> 00:22:31.436
and to me I see a very human side to that

00:22:31.818 --> 00:22:36.818
that would be very hard to
capture with a computer system.

00:22:37.090 --> 00:22:41.695
So each can play a very
important role, right?

00:22:41.695 --> 00:22:46.695
So the computers provide
an here to foreseen access

00:22:51.840 --> 00:22:55.667
to content in ways that we've
never seen before, right?

00:22:55.667 --> 00:22:58.200
And so building that up,
but that next task is,

00:22:58.200 --> 00:23:02.130
well, how do we take that
access that we've now shared,

00:23:02.130 --> 00:23:04.630
but how do we build in
these kinds of things?

00:23:04.630 --> 00:23:07.960
What can we have the computers
help to support us with

00:23:07.960 --> 00:23:10.850
when it comes to engaging in
these kinds of conversations

00:23:10.850 --> 00:23:13.280
that will be able to help
sort of listen to students

00:23:13.280 --> 00:23:16.620
and figure out exactly sort
of what might the next move be

00:23:16.620 --> 00:23:19.570
based on ways of thinking,
not necessarily just the ways

00:23:19.570 --> 00:23:21.850
of doing as you might see
pointed out in standards

00:23:21.850 --> 00:23:24.043
and standards mappings, that kinda thing.

00:23:25.060 --> 00:23:26.900
- Yeah, absolutely.

00:23:26.900 --> 00:23:31.060
So another piece that we try to encourage

00:23:31.060 --> 00:23:33.700
is helping students become
owners of their own learning

00:23:33.700 --> 00:23:37.130
and thinking about developing
those metacognitive skills.

00:23:37.130 --> 00:23:39.170
Being able to understand what they know

00:23:39.170 --> 00:23:41.240
and evaluate and what they understand

00:23:41.240 --> 00:23:43.823
and need to learn and how those fit in.

00:23:44.660 --> 00:23:46.210
I'm interested in how you think about that

00:23:46.210 --> 00:23:48.930
and some of this framework too.

00:23:48.930 --> 00:23:52.220
- Yeah, well that might land
in that habits space, right?

00:23:52.220 --> 00:23:54.870
Being able to reflect on and
being honest with myself,

00:23:54.870 --> 00:23:56.630
am I making sense?

00:23:56.630 --> 00:24:00.243
In my own mind can I
justify what I'm saying?

00:24:01.370 --> 00:24:04.573
Or am I just spouting things off?

00:24:05.910 --> 00:24:08.900
So maybe part of that is that you can

00:24:08.900 --> 00:24:13.560
with this type of approach you
really do get the opportunity

00:24:13.560 --> 00:24:17.710
for the student to reflect
by not correcting right away,

00:24:17.710 --> 00:24:20.080
by continuing to ask questions.

00:24:20.080 --> 00:24:22.530
You're providing the student
opportunities to reflect

00:24:22.530 --> 00:24:27.150
and then maybe when it's
done and then you sit down

00:24:27.150 --> 00:24:29.290
with the student and
then you help them have

00:24:29.290 --> 00:24:31.320
some metacognitive reflection on it.

00:24:31.320 --> 00:24:33.620
What would you like to work on it?

00:24:33.620 --> 00:24:36.040
What questions did you
answer that you felt like

00:24:36.040 --> 00:24:38.800
you wanted to take back
or think through again,

00:24:38.800 --> 00:24:41.250
or think more about or
learn more about, right?

00:24:41.250 --> 00:24:45.250
To help them spot where they need ways

00:24:45.250 --> 00:24:48.120
they wanted to strengthen
their ways of thinking.

00:24:48.120 --> 00:24:49.120
- Yeah, that makes sense.

00:24:49.120 --> 00:24:53.450
I think that idea of
helping of thinking about

00:24:54.930 --> 00:24:57.000
your confidence in your answers

00:24:57.000 --> 00:24:58.730
is something that we talk about too,

00:24:58.730 --> 00:25:01.710
like after students give
answers having them think about,

00:25:01.710 --> 00:25:03.540
so how sure of you were with that answer

00:25:03.540 --> 00:25:04.520
and what did you know

00:25:04.520 --> 00:25:07.320
and didn't you know and
I could see them doing it

00:25:07.320 --> 00:25:09.170
with this too, so asking students,

00:25:09.170 --> 00:25:12.178
what do you think a fraction is?

00:25:12.178 --> 00:25:15.310
And then how confident
are you in that answer

00:25:15.310 --> 00:25:18.980
and where that fits in would
be interesting to think about,

00:25:18.980 --> 00:25:20.730
yeah, definitely.

00:25:20.730 --> 00:25:25.700
So as you think about advising
teachers on next steps,

00:25:25.700 --> 00:25:28.350
so they've had this conversation,

00:25:28.350 --> 00:25:30.610
what is the next thing they should do

00:25:30.610 --> 00:25:33.053
based on the information that they get?

00:25:34.210 --> 00:25:35.730
- Well, I think as you're listening,

00:25:35.730 --> 00:25:39.000
you're trying to interpret, right?

00:25:39.000 --> 00:25:40.500
What are you noticing?

00:25:40.500 --> 00:25:42.750
Work on those, what do you wanna notice

00:25:42.750 --> 00:25:45.150
with what the student's saying.

00:25:45.150 --> 00:25:50.150
Reflect back on it, the things
that we're putting together

00:25:50.730 --> 00:25:52.080
around these, we've got some videos

00:25:52.080 --> 00:25:56.850
and it's very fun to sit and
watch because you get to,

00:25:56.850 --> 00:25:58.420
if you watch it two or
three times sometimes

00:25:58.420 --> 00:26:01.090
you'll get even more and more out of it.

00:26:01.090 --> 00:26:06.090
So it's, yeah, teachers,
what could you do with these?

00:26:06.825 --> 00:26:09.733
(both laughing)

00:26:09.733 --> 00:26:12.300
I don't know, did I answer that okay or?

00:26:12.300 --> 00:26:14.760
- Yeah, so the idea, it's going to have,

00:26:14.760 --> 00:26:16.220
the teachers are gonna have to do

00:26:16.220 --> 00:26:21.220
some pretty good interpretation
of what they're hearing

00:26:21.360 --> 00:26:24.130
and then think about based on that

00:26:24.130 --> 00:26:29.130
what are the understandings
that they need to either fill in

00:26:29.480 --> 00:26:32.873
or move forward or what that looks like.

00:26:32.873 --> 00:26:37.050
- And it's also self-reflective.

00:26:37.050 --> 00:26:40.460
I mean, when we were putting
these, they made all of us

00:26:40.460 --> 00:26:43.327
stop and think, we had
to sit there and think,

00:26:43.327 --> 00:26:45.467
"Oh, how would we answer this?"

00:26:46.391 --> 00:26:50.000
'Cause basically we weren't
putting questions down

00:26:50.000 --> 00:26:51.330
to get right or wrong answers.

00:26:51.330 --> 00:26:54.590
It's coming up with questions
that uncover thinking

00:26:54.590 --> 00:26:56.490
and you don't have to ask
right or wrong questions

00:26:56.490 --> 00:26:58.240
to uncover thinking.

00:26:58.240 --> 00:27:02.410
- Right, yeah, I think
that's another piece

00:27:02.410 --> 00:27:07.410
in math education that we're
coming to better understandings

00:27:08.330 --> 00:27:11.894
that math education isn't just
about right and wrong answers

00:27:11.894 --> 00:27:12.820
and where things are.

00:27:12.820 --> 00:27:16.263
Math does have right and wrong
answers to some things, but.

00:27:17.655 --> 00:27:21.070
- I'm not minimizing the need
for right or wrong answers.

00:27:21.070 --> 00:27:22.310
But there's a time for that

00:27:22.310 --> 00:27:25.570
and there's a time for
listening to thinking.

00:27:25.570 --> 00:27:29.370
- Yeah, that totally
makes sense, excellent.

00:27:29.370 --> 00:27:31.550
So anything that you're excited about,

00:27:31.550 --> 00:27:32.670
I'll close on this question.

00:27:32.670 --> 00:27:35.210
Anything you're excited about
in the coming couple of months

00:27:35.210 --> 00:27:36.963
that your team work is working on.

00:27:38.011 --> 00:27:43.011
- Oh yeah, so one of the
things I'm working on,

00:27:46.150 --> 00:27:50.270
I just did a talk on this at
South by Southwest last week

00:27:50.270 --> 00:27:53.260
and I called it mathematical rigor mortis,

00:27:53.260 --> 00:27:54.493
the quest for a cure.

00:27:56.146 --> 00:27:59.900
And it's this idea where when we sit back

00:27:59.900 --> 00:28:02.180
and we think about our
field math teachers,

00:28:02.180 --> 00:28:07.000
we think about how many ways
does math kill things, right?

00:28:07.000 --> 00:28:11.073
Math kills dreams, it kills
joy, it kills progress.

00:28:12.762 --> 00:28:15.660
And also it also kills moving policy

00:28:15.660 --> 00:28:16.773
in the right directions

00:28:16.773 --> 00:28:19.980
and making changes at systemic levels.

00:28:19.980 --> 00:28:22.930
This things are so entrenched
in the way that we do things,

00:28:22.930 --> 00:28:24.780
but I'm encouraged and I'm encouraged

00:28:24.780 --> 00:28:27.110
and I hope that the folks
out there are encouraged

00:28:27.110 --> 00:28:29.980
that I think we're moving
in the right direction

00:28:29.980 --> 00:28:32.530
to cure mathematical rigor mortis.

00:28:32.530 --> 00:28:35.780
And if you ever wanna reach
out and talk to me about it,

00:28:35.780 --> 00:28:38.570
I'd love to go into that as well.

00:28:38.570 --> 00:28:40.550
But that's something I'm encouraged about

00:28:40.550 --> 00:28:42.850
is the sort of spaces and the things

00:28:42.850 --> 00:28:45.460
I'm seeing across the
country to help address that.

00:28:45.460 --> 00:28:48.190
- And we had a question
from Angel on YouTube,

00:28:48.190 --> 00:28:51.900
who's a student and wants
to know how they can stay

00:28:51.900 --> 00:28:53.650
motivated when they're doing work.

00:28:53.650 --> 00:28:56.650
We hear this question a lot from folks

00:28:56.650 --> 00:28:58.800
who are needing to stay
motivated to do their work.

00:28:58.800 --> 00:29:00.725
What do you think?

00:29:00.725 --> 00:29:05.725
- Oh, so maybe Angel and
I hope this is helpful

00:29:08.240 --> 00:29:11.820
but if math is being presented to you

00:29:11.820 --> 00:29:14.720
as though it's the
collection of puzzle pieces.

00:29:14.720 --> 00:29:16.100
That you're just shaking the box

00:29:16.100 --> 00:29:17.950
and you can kinda hear them rattling,

00:29:19.643 --> 00:29:20.980
the challenge would be to know that

00:29:20.980 --> 00:29:23.560
it does make a big, beautiful picture,

00:29:23.560 --> 00:29:25.280
that all of the pieces fit together,

00:29:25.280 --> 00:29:27.400
that no piece stands alone.

00:29:27.400 --> 00:29:30.860
And that if you find that encouraging

00:29:30.860 --> 00:29:34.190
then you can figure out how
these pieces fit together,

00:29:34.190 --> 00:29:36.390
what's the story that's being told here.

00:29:36.390 --> 00:29:40.110
It's a great one and
there are lots of places

00:29:40.110 --> 00:29:42.950
where you could go to help get
some support on that as well.

00:29:42.950 --> 00:29:47.950
But don't let the current
situations that you might be in,

00:29:49.170 --> 00:29:53.450
or these things that are
happening all around us right now,

00:29:53.450 --> 00:29:57.490
don't let them destroy the joy
that mathematics has for you.

00:29:57.490 --> 00:29:59.380
That would be my take.

00:29:59.380 --> 00:30:02.010
- I like it and putting
together that puzzle

00:30:02.010 --> 00:30:04.700
could be a challenge, a
fun challenge to undertake

00:30:04.700 --> 00:30:06.470
and to think through, excellent.

00:30:06.470 --> 00:30:09.040
- Yeah, but it's there, it's
ready to be put together,

00:30:09.040 --> 00:30:11.203
but it gets put together in your own head.

00:30:12.370 --> 00:30:15.410
- Fantastic, well thank you
so much for joining us today.

00:30:15.410 --> 00:30:16.950
It was a pleasure to talk to you

00:30:16.950 --> 00:30:19.550
and I hope some of our folks out there

00:30:19.550 --> 00:30:22.260
dive into those conversation starters.

00:30:22.260 --> 00:30:23.960
- Well, thank you, this was great.


Sexual and asexual reproduction

WEBVTT
Kind: captions
Language: en

00:00:00.170 --> 00:00:02.100
- [Narrator] The planet we live on is full

00:00:02.100 --> 00:00:05.150
of life and has been
for billions of years.

00:00:05.150 --> 00:00:07.470
Living things on earth
have existed for as long

00:00:07.470 --> 00:00:11.090
as they have, because life
found a way to create life.

00:00:11.090 --> 00:00:12.520
Sounds crazy, right?

00:00:12.520 --> 00:00:13.840
To put it another way,

00:00:13.840 --> 00:00:16.240
living things found ways to reproduce,

00:00:16.240 --> 00:00:18.220
creating offspring that can then go on

00:00:18.220 --> 00:00:19.910
to reproduce themselves,

00:00:19.910 --> 00:00:22.410
but what exactly is reproduction?

00:00:22.410 --> 00:00:26.160
Well, reproduction is the
process of making new organisms.

00:00:26.160 --> 00:00:28.730
This happens when parent
organisms reproduce

00:00:28.730 --> 00:00:30.330
to form offspring.

00:00:30.330 --> 00:00:31.410
During reproduction,

00:00:31.410 --> 00:00:34.080
organisms pass their genetic information

00:00:34.080 --> 00:00:35.640
on to their offspring.

00:00:35.640 --> 00:00:38.040
This genetic information
provides blueprints

00:00:38.040 --> 00:00:40.760
for how the offspring
will grow and develop

00:00:40.760 --> 00:00:43.800
and it's how traits get
passed on from one generation

00:00:43.800 --> 00:00:44.940
to the next.

00:00:44.940 --> 00:00:48.540
There are two main ways
organisms on earth reproduce.

00:00:48.540 --> 00:00:52.960
This is through asexual
reproduction or sexual reproduction.

00:00:52.960 --> 00:00:56.480
Let's start off by breaking
down asexual reproduction first.

00:00:56.480 --> 00:00:59.870
In asexual reproduction,
only one parent is involved

00:00:59.870 --> 00:01:01.670
in producing offspring.

00:01:01.670 --> 00:01:04.270
Due to this, the
offspring will inherit all

00:01:04.270 --> 00:01:06.930
of their genes from that single parent.

00:01:06.930 --> 00:01:10.420
This means that asexual
reproduction produces offspring

00:01:10.420 --> 00:01:13.240
that are genetically
identical to their parent,

00:01:13.240 --> 00:01:17.200
or in other words, they have
the same collection of genes.

00:01:17.200 --> 00:01:20.190
Various kinds of microorganisms, plants,

00:01:20.190 --> 00:01:23.540
and even animals are able
to reproduce asexually.

00:01:23.540 --> 00:01:25.400
An example of asexual reproduction

00:01:25.400 --> 00:01:28.650
in microorganisms can be seen in bacteria.

00:01:28.650 --> 00:01:31.080
This is due to their
use of a specific type

00:01:31.080 --> 00:01:34.270
of asexual reproduction
called binary fission.

00:01:34.270 --> 00:01:35.450
During this process,

00:01:35.450 --> 00:01:38.800
a single bacteria cell
grows, copies its genes,

00:01:38.800 --> 00:01:41.460
and divides into two identical cells,

00:01:41.460 --> 00:01:43.330
kind of like a copy machine.

00:01:43.330 --> 00:01:45.940
Plants are able to
reproduce asexually too.

00:01:45.940 --> 00:01:48.580
For example, some plants
grow their offspring off

00:01:48.580 --> 00:01:49.870
of themselves.

00:01:49.870 --> 00:01:51.820
In fact, in many succulents,

00:01:51.820 --> 00:01:55.370
you can see baby plants growing
off of their parent plant.

00:01:55.370 --> 00:01:58.430
These babies have the same
genes as their parent plant

00:01:58.430 --> 00:01:59.560
and can grow on their own

00:01:59.560 --> 00:02:01.980
if you remove them and plant them in soil.

00:02:01.980 --> 00:02:03.870
Finally, and interestingly,

00:02:03.870 --> 00:02:06.800
there are various animals
that can reproduce asexually.

00:02:06.800 --> 00:02:10.720
One example is seen in
starfish or sea stars.

00:02:10.720 --> 00:02:12.710
Some species of starfish can split

00:02:12.710 --> 00:02:16.610
into multiple parts that
then grow into new starfish

00:02:16.610 --> 00:02:19.170
and, since they have the same genes,

00:02:19.170 --> 00:02:22.620
each new starfish is a
clone of its original.

00:02:22.620 --> 00:02:25.160
Now that we've covered
asexual reproduction,

00:02:25.160 --> 00:02:27.900
let's move on to sexual reproduction.

00:02:27.900 --> 00:02:30.640
Unlike asexual reproduction,
sexual reproduction

00:02:30.640 --> 00:02:33.530
involves two parents producing
an offspring together

00:02:33.530 --> 00:02:35.070
instead of one.

00:02:35.070 --> 00:02:36.010
This is important

00:02:36.010 --> 00:02:38.510
because it means that the
offspring will inherit half

00:02:38.510 --> 00:02:40.160
of their genes from one parent

00:02:40.160 --> 00:02:42.820
and half of their genes from the other.

00:02:42.820 --> 00:02:46.230
Because of this, a sexual
reproduction produces offspring

00:02:46.230 --> 00:02:47.980
that are genetically distinct

00:02:47.980 --> 00:02:49.250
or have a different combination

00:02:49.250 --> 00:02:51.830
of genes compared to either parent.

00:02:51.830 --> 00:02:54.740
With this, because of the
way the genes are passed on,

00:02:54.740 --> 00:02:56.690
there are tons of different combinations

00:02:56.690 --> 00:02:59.960
of genes that can be received
from the two parents.

00:02:59.960 --> 00:03:01.560
In other words, this means

00:03:01.560 --> 00:03:05.210
that sexual reproduction creates
offspring that show a lot

00:03:05.210 --> 00:03:08.450
of genetic variation
between their siblings.

00:03:08.450 --> 00:03:09.880
To better understand this,

00:03:09.880 --> 00:03:11.640
let's take a look at my own dogs.

00:03:11.640 --> 00:03:12.720
They're brother and sister,

00:03:12.720 --> 00:03:15.660
so they share the same
parents, which I've drawn here.

00:03:15.660 --> 00:03:18.560
As you've probably noticed,
my dogs look pretty different

00:03:18.560 --> 00:03:19.490
from each other.

00:03:19.490 --> 00:03:22.410
One of the most notable
differences though is how one

00:03:22.410 --> 00:03:24.910
of them received genes from this parent

00:03:24.910 --> 00:03:26.780
that gave them markings above their eyes

00:03:26.780 --> 00:03:30.250
that kind of looked like
eyebrows while the other did not.

00:03:30.250 --> 00:03:32.480
And while it's easy to
spot genetic differences,

00:03:32.480 --> 00:03:34.100
like my dog's eyebrows,

00:03:34.100 --> 00:03:38.030
genetic variation goes
way deeper than dog's fur.

00:03:38.030 --> 00:03:40.700
It's what makes sexual
reproduced organisms

00:03:40.700 --> 00:03:43.020
genetically distinct from each other

00:03:43.020 --> 00:03:46.160
and gives the building
blocks to who they are.

00:03:46.160 --> 00:03:48.340
And with that, you now know the difference

00:03:48.340 --> 00:03:51.390
between asexual and sexual reproduction.

00:03:51.390 --> 00:03:54.310
Let's do a quick overview of
what you've learned today.

00:03:54.310 --> 00:03:57.230
Living organisms reproduce
to create offspring

00:03:57.230 --> 00:04:00.770
through either asexual
or sexual reproduction.

00:04:00.770 --> 00:04:03.870
Asexual reproduction
involves only one parent

00:04:03.870 --> 00:04:07.900
meaning the parent and offspring
will have identical genes.

00:04:07.900 --> 00:04:10.850
Sexual reproduction involves two parents

00:04:10.850 --> 00:04:13.750
and results in offspring
that are genetically unique

00:04:13.750 --> 00:04:16.230
compared to either
parent and this all goes

00:04:16.230 --> 00:04:18.620
to show how fantastically unique life

00:04:18.620 --> 00:04:19.930
on earth is.

00:04:19.930 --> 00:04:21.600
Though organisms may differ

00:04:21.600 --> 00:04:23.860
in the ways that they've
been able to reproduce

00:04:23.860 --> 00:04:25.070
as seen in the examples

00:04:25.070 --> 00:04:29.300
between bacteria, succulents,
starfish, and dogs,

00:04:29.300 --> 00:04:32.370
these organisms, as
with all living things,

00:04:32.370 --> 00:04:35.160
share the ability to create more life

00:04:35.160 --> 00:04:36.830
just as all life has shared

00:04:36.830 --> 00:04:39.153
for billions of years here on this planet.