The rock cycle

WEBVTT
Kind: captions
Language: en

00:00:00.170 --> 00:00:01.100
- [Instructor] Have you ever tried

00:00:01.100 --> 00:00:03.490
to hold a staring contest with a rock?

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If you did, you might not have
expected that all that time

00:00:06.500 --> 00:00:08.370
you were staring at one of the sneakiest

00:00:08.370 --> 00:00:10.470
shape-shifters in the world.

00:00:10.470 --> 00:00:13.570
No, rocks don't shapeshift into unicorns,

00:00:13.570 --> 00:00:16.530
but they do change shape and composition.

00:00:16.530 --> 00:00:18.450
Sometimes they change quickly,

00:00:18.450 --> 00:00:20.110
like when an interrupting volcano

00:00:20.110 --> 00:00:22.340
launches molten rock into the air.

00:00:22.340 --> 00:00:24.290
And sometimes they change slowly,

00:00:24.290 --> 00:00:26.400
like when a rock is heated and compressed

00:00:26.400 --> 00:00:29.770
in the earth for thousands
to millions of years.

00:00:29.770 --> 00:00:31.480
When geologists stare at a rock,

00:00:31.480 --> 00:00:33.760
they can figure out the rocks composition

00:00:33.760 --> 00:00:36.280
and tell the story of how it was created.

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And it turns out rocks can be
made in many different ways.

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When put it the right
combination of heat and pressure,

00:00:42.930 --> 00:00:45.460
rocks can become molten and liquid.

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When this molten rock
cools and becomes solid,

00:00:48.480 --> 00:00:50.960
we call the rock it makes igneous rock.

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This term comes from
the Latin word igneus,

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which means fiery or burning hot.

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Igneous rocks make up more
than 90% of the Earth's crust.

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One common kind of
igneous rock is granite,

00:01:02.630 --> 00:01:04.620
which you've probably seen in bridges,

00:01:04.620 --> 00:01:06.560
buildings, and countertops.

00:01:06.560 --> 00:01:09.390
Another kind of igneous rock is obsidian,

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which is smooth and glassy,

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and is sometimes used
to make knife weights.

00:01:13.740 --> 00:01:16.260
Both of these rocks were
made of molten rock.

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So why do they look so different?

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Well, granite was made from magma,

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which is molten rock that exists

00:01:22.940 --> 00:01:24.560
below the surface of the earth.

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Magma tends to cool slowly underground,

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which gives time for the elements in it

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to form large crystals.

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And this obsidian rock was made from lava,

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which is molten rock that
flows above the ground.

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Lava tends to cool quickly,

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which causes the rocks
it forms like obsidian,

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tuff smaller crystals.

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I always remember the difference

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between magma and lava like this.

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I keep my lava lamp above the ground,

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just like lava is above the ground.

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If I buried my lava lamp in the ground,

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then I can call it a magma lamp.

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Once an igneous rock is
created, its journey isn't over.

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The rock might begin to change

00:02:00.320 --> 00:02:02.000
through a process called weathering.

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This is when water, weather,
wind, and other physical forces

00:02:05.850 --> 00:02:07.100
chip away at a rock

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and cause little pieces to break off.

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These little particles
are called sediments.

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The sediment from our igneous rock

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can be moved around by wind and water.

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This is called erosion.

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Eventually, the sediment
will settle down somewhere.

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Maybe at the bottom of an ocean or a lake,

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and it might join other
sediment from other rocks,

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crushed up shells, and plant matter.

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And over time, this
sediment will become a rock.

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Rocks that are formed from sediments

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are called, you guessed
it, sedimentary rocks.

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But how does sedimentary goop

00:02:37.960 --> 00:02:40.290
at the bottom of the lake become a rock?

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Well, it goes through a
process called lithification.

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Lith comes from the Greek word for stone.

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So you can think of this
process as stonification.

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The first step of lithification
is called deposition.

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This is when sediment is
deposited in a new location

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and it spreads out to form a layer.

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As more and more layers are created,

00:02:59.690 --> 00:03:02.473
the layers underneath them
become squished together.

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This is called compaction.

00:03:05.470 --> 00:03:07.640
When water moves to
the layers of sediment,

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it can carry dissolve minerals with it.

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The water can leave these minerals

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in between the sediment particles,

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which makes everything stick together.

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This cementing of sediment
is called cementation.

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Limestone is a sedimentary
rock that is made with sediment

00:03:22.320 --> 00:03:24.950
that contains a lot of
calcium carbonate in it

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goes through lithification.

00:03:26.930 --> 00:03:29.280
But once the sedimentary
rock has been created,

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it doesn't mean that it is done changing.

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Sometimes a rock is
squeezed or heated so much

00:03:34.570 --> 00:03:37.720
that the minerals inside it
actually change composition.

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It is now a metamorphic rock.

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You might've heard of
the word metamorphosis,

00:03:42.440 --> 00:03:44.040
which describes when something changes

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from one form and structure to another.

00:03:46.180 --> 00:03:48.700
Like when a caterpillar
turns into a butterfly.

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Metamorphic rocks are made
when igneous, sedimentary,

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or even other metamorphic rocks

00:03:53.746 --> 00:03:57.790
change form and structure
because of heat and pressure.

00:03:57.790 --> 00:04:00.070
For example, when the
sedimentary rock, limestone,

00:04:00.070 --> 00:04:02.030
gets put under a lot of heat and pressure,

00:04:02.030 --> 00:04:03.690
it can turn into marble,

00:04:03.690 --> 00:04:06.850
but metamorphic rocks still
may not be done changing.

00:04:06.850 --> 00:04:09.970
Rocks can actually keep
on changing forever.

00:04:09.970 --> 00:04:12.926
Igneous and metamorphic rocks
can become sedimentary rocks

00:04:12.926 --> 00:04:15.330
if they're broken apart into sediments

00:04:15.330 --> 00:04:17.060
and go through lithification.

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And metamorphic rocks
and sedimentary rocks

00:04:19.850 --> 00:04:22.210
can become igneous rocks
when they are melted

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and then cools.

00:04:23.280 --> 00:04:25.530
And igneous rocks and sedimentary rocks

00:04:25.530 --> 00:04:27.110
can become metamorphic rocks

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when they're exposed to
high heat and pressure.

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This is called the rock cycle.

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So maybe next time you get
the chance to stare at a rock.

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See if you can figure
out whether it's igneous,

00:04:36.630 --> 00:04:38.680
metamorphic, or sedimentary.

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And when rocks changed so much,

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who knows what kind of rock it'll be next.


The water cycle

WEBVTT
Kind: captions
Language: en

00:00:00.360 --> 00:00:02.360
- [Instructor] Did you know
that the water you drink

00:00:02.360 --> 00:00:05.540
is actually the same
water that dinosaurs drank

00:00:05.540 --> 00:00:08.810
over 65 million years ago?

00:00:08.810 --> 00:00:10.350
It might be hard to believe

00:00:10.350 --> 00:00:14.070
but your water is actually
really, really old.

00:00:14.070 --> 00:00:18.080
In fact, water on Earth is
much older than the dinosaurs.

00:00:18.080 --> 00:00:20.300
Scientists estimate
that the water on Earth

00:00:20.300 --> 00:00:24.000
is at least 4.6 billion years old.

00:00:24.000 --> 00:00:26.520
And the amount of water on Earth today,

00:00:26.520 --> 00:00:29.460
in lakes, rivers, oceans, glaciers,

00:00:29.460 --> 00:00:32.190
even under the ground
and up in the clouds,

00:00:32.190 --> 00:00:33.600
it's about the same as it was

00:00:33.600 --> 00:00:35.980
millions and millions of years ago.

00:00:35.980 --> 00:00:38.220
That's because water is recycled.

00:00:38.220 --> 00:00:40.583
It just gets used again and again.

00:00:41.580 --> 00:00:43.690
And that brings us to the water cycle,

00:00:43.690 --> 00:00:46.170
which is how water continuously moves

00:00:46.170 --> 00:00:49.590
from the ground to the
atmosphere and back again.

00:00:49.590 --> 00:00:53.890
And as water moves through
the cycle, it changes form.

00:00:53.890 --> 00:00:56.870
In fact, water is the
only substance on Earth

00:00:56.870 --> 00:00:59.530
that naturally exists in three states,

00:00:59.530 --> 00:01:02.180
solid, liquid, and gas.

00:01:02.180 --> 00:01:05.160
Have you seen water in all
of its different states?

00:01:05.160 --> 00:01:07.420
Maybe on a hot day, you'll add some ice,

00:01:07.420 --> 00:01:09.470
which is water in its solid state,

00:01:09.470 --> 00:01:11.380
to a glass of liquid water.

00:01:11.380 --> 00:01:13.620
Or maybe when you take out some food

00:01:13.620 --> 00:01:15.460
that you've heated in the microwave,

00:01:15.460 --> 00:01:17.830
you'll see steam coming off of the food,

00:01:17.830 --> 00:01:20.913
which is water in its
gas state as water vapor.

00:01:21.820 --> 00:01:23.010
When you think of water,

00:01:23.010 --> 00:01:25.720
you might think of the wide open ocean.

00:01:25.720 --> 00:01:29.710
Over 95% of all the water
on Earth is in the ocean,

00:01:29.710 --> 00:01:33.150
so this is a great place to
start with the water cycle.

00:01:33.150 --> 00:01:35.960
Here, energy from the sun warms up water

00:01:35.960 --> 00:01:37.690
on the surface of the ocean

00:01:37.690 --> 00:01:40.260
enough to turn it into water vapor.

00:01:40.260 --> 00:01:42.730
This is called evaporation.

00:01:42.730 --> 00:01:44.890
This water vapor is less dense,

00:01:44.890 --> 00:01:47.690
meaning it's lighter, than liquid water,

00:01:47.690 --> 00:01:50.770
so it rises up and up into the atmosphere.

00:01:50.770 --> 00:01:53.440
However, as the water vapor rises,

00:01:53.440 --> 00:01:56.000
the temperature in the atmosphere cools.

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In turn, the water vapor condenses

00:01:58.290 --> 00:02:00.670
into tiny liquid water droplets,

00:02:00.670 --> 00:02:03.770
or, as we see them, clouds.

00:02:03.770 --> 00:02:06.210
This is called condensation.

00:02:06.210 --> 00:02:10.540
Air currents then move these
clouds all around the Earth.

00:02:10.540 --> 00:02:14.180
As a cloud collects more and
more liquid water droplets,

00:02:14.180 --> 00:02:16.330
the water may be released from the cloud,

00:02:16.330 --> 00:02:17.820
pulled down by gravity,

00:02:17.820 --> 00:02:19.840
and then return to the ocean or land

00:02:19.840 --> 00:02:22.050
as precipitation, like rain.

00:02:22.050 --> 00:02:23.780
If it's really cold, though,

00:02:23.780 --> 00:02:27.230
the water drops may
crystallize and become snow.

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The snow will fall to the ground

00:02:28.940 --> 00:02:31.070
and eventually melt back into a liquid

00:02:31.070 --> 00:02:34.880
and run off into a lake or
river, pulled down by gravity,

00:02:34.880 --> 00:02:36.970
which flows back into the ocean

00:02:36.970 --> 00:02:39.253
where the whole process starts over again.

00:02:40.150 --> 00:02:43.090
But that's just one path water can take

00:02:43.090 --> 00:02:44.600
through the water cycle.

00:02:44.600 --> 00:02:47.130
It's like a choose your own adventure.

00:02:47.130 --> 00:02:50.320
Instead of snow melting and
running off into a river,

00:02:50.320 --> 00:02:53.670
the snow could become part
of an icy cold glacier

00:02:53.670 --> 00:02:56.430
and stay there for a long, long time,

00:02:56.430 --> 00:02:58.660
for thousands of years.

00:02:58.660 --> 00:03:02.870
Or rain can seep into the
ground and become groundwater,

00:03:02.870 --> 00:03:05.860
where it's then absorbed by plant roots.

00:03:05.860 --> 00:03:08.260
In turn, through transpiration,

00:03:08.260 --> 00:03:10.090
the water absorbed by the plants

00:03:10.090 --> 00:03:12.550
can transition to water vapor

00:03:12.550 --> 00:03:14.550
and leave directly through the leaves

00:03:14.550 --> 00:03:17.150
via tiny holes called stomata

00:03:17.150 --> 00:03:18.913
and return to the atmosphere.

00:03:19.850 --> 00:03:23.250
Or instead of being
absorbed by plant roots,

00:03:23.250 --> 00:03:27.030
the groundwater can work its
way to an underground aquifer

00:03:27.030 --> 00:03:29.953
or a lake, river, or even the ocean.

00:03:31.040 --> 00:03:33.770
There are many different paths for water

00:03:33.770 --> 00:03:37.350
and the water cycle can
be very complicated.

00:03:37.350 --> 00:03:41.060
But it really comes down
to something very simple.

00:03:41.060 --> 00:03:42.700
The amount of water on Earth

00:03:42.700 --> 00:03:44.670
stays pretty constant over time

00:03:44.670 --> 00:03:46.860
and moves from place to place,

00:03:46.860 --> 00:03:49.520
sometimes transitioning between phases,

00:03:49.520 --> 00:03:52.570
depending on things
like weather, geography,

00:03:52.570 --> 00:03:54.693
solar energy, and gravity.

00:03:55.770 --> 00:03:59.220
Now, we know that water is
essential to life on Earth

00:03:59.220 --> 00:04:02.300
and fresh water is an
especially limited resource

00:04:02.300 --> 00:04:04.620
for a growing world population.

00:04:04.620 --> 00:04:07.560
Changes in the water
cycle can impact everyone

00:04:07.560 --> 00:04:09.990
through the economy, energy production,

00:04:09.990 --> 00:04:13.740
health, recreation
transportation, agriculture,

00:04:13.740 --> 00:04:15.980
and of course drinking water.

00:04:15.980 --> 00:04:18.550
And that's why understanding
the water cycle

00:04:18.550 --> 00:04:20.350
is so important.

00:04:20.350 --> 00:04:22.270
That, and it's pretty cool to know

00:04:22.270 --> 00:04:25.220
that you drink the same
water as dinosaurs did.

00:04:25.220 --> 00:04:26.303
Until next time.


Earth's place in the universe

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:01.230
- [Narrator] Hello, everyone.

00:00:01.230 --> 00:00:02.690
Today, we are going to be talking about

00:00:02.690 --> 00:00:05.420
Earth's place in space.

00:00:05.420 --> 00:00:07.490
So for as long as there have been humans,

00:00:07.490 --> 00:00:09.240
we've been looking up at the stars,

00:00:09.240 --> 00:00:12.660
and wondering about our
place in the universe.

00:00:12.660 --> 00:00:15.480
Our understanding about
this has improved over time,

00:00:15.480 --> 00:00:17.410
and we have developed models

00:00:17.410 --> 00:00:21.320
that can help us understand
something as vast as space.

00:00:21.320 --> 00:00:25.320
Now, models are just a way of
representing a system of ideas

00:00:25.320 --> 00:00:29.260
that help us identify and
understand patterns that we see.

00:00:29.260 --> 00:00:31.540
Models are a tool that can explain,

00:00:31.540 --> 00:00:35.690
and predict what we see in
the world and space around us.

00:00:35.690 --> 00:00:39.330
And as we gain new information,
we can update our models.

00:00:39.330 --> 00:00:42.220
So what kind of model might we construct

00:00:42.220 --> 00:00:46.660
about how Earth interacts with
other bodies in the universe?

00:00:46.660 --> 00:00:48.260
To begin with, every day,

00:00:48.260 --> 00:00:51.730
we can see the sun rise in
the east, and set in the west,

00:00:51.730 --> 00:00:55.230
and other objects in the sky
follow a similar pattern.

00:00:55.230 --> 00:00:57.470
It was logical then for early models

00:00:57.470 --> 00:01:00.350
to consider the Earth
as a stationary object,

00:01:00.350 --> 00:01:03.800
around which all of the universe revolves.

00:01:03.800 --> 00:01:06.350
This is called a geocentric model,

00:01:06.350 --> 00:01:09.720
geo for Earth, and centric for center.

00:01:09.720 --> 00:01:12.090
And this geocentric model was quite good

00:01:12.090 --> 00:01:14.580
at explaining a lot of the
things that we see in the sky,

00:01:14.580 --> 00:01:18.070
like the apparent motion
of the sun and the stars.

00:01:18.070 --> 00:01:21.670
But there were issues with
this geocentric model.

00:01:21.670 --> 00:01:24.740
For example, the motions of
other planets in the sky.

00:01:24.740 --> 00:01:27.910
A planet like Jupiter might
sometimes move backwards

00:01:27.910 --> 00:01:29.460
in the opposite direction,

00:01:29.460 --> 00:01:31.420
which isn't really very well explained

00:01:31.420 --> 00:01:33.770
by this geocentric model.

00:01:33.770 --> 00:01:36.650
Now, when a model doesn't match
our observations like this,

00:01:36.650 --> 00:01:39.790
we can add new pieces
to improve the model.

00:01:39.790 --> 00:01:42.310
So astronomers working
with the geocentric model

00:01:42.310 --> 00:01:44.500
did this by adding smaller cycles

00:01:44.500 --> 00:01:47.820
within the planets'
orbits around the Earth.

00:01:47.820 --> 00:01:50.900
Adding these cycles did help
match the geocentric model

00:01:50.900 --> 00:01:52.430
to the observations,

00:01:52.430 --> 00:01:54.280
but there were many of
these cycles required,

00:01:54.280 --> 00:01:56.010
and there wasn't a good explanation

00:01:56.010 --> 00:01:57.470
for why these cycles existed.

00:01:57.470 --> 00:01:59.850
And there wasn't very
much reasoning for them,

00:01:59.850 --> 00:02:01.522
and they made the model very complicated,

00:02:01.522 --> 00:02:03.563
and not particularly useful.

00:02:04.580 --> 00:02:06.720
Let's pause and talk a
little bit about motion,

00:02:06.720 --> 00:02:09.343
specifically apparent versus actual.

00:02:10.470 --> 00:02:11.970
Imagine you're sitting in a car,

00:02:11.970 --> 00:02:13.750
and driving through a forest.

00:02:13.750 --> 00:02:16.380
To your perspective, as
you look out the window,

00:02:16.380 --> 00:02:18.980
the trees seem to be whizzing by,

00:02:18.980 --> 00:02:21.300
but trees, of course,
are rooted to the ground.

00:02:21.300 --> 00:02:22.840
It's actually you that are moving

00:02:22.840 --> 00:02:25.060
relative to the surface of the Earth.

00:02:25.060 --> 00:02:29.380
This is the difference between
apparent and actual motion.

00:02:29.380 --> 00:02:32.050
So back to our geocentric model.

00:02:32.050 --> 00:02:34.710
Another way to explain some of the issues

00:02:34.710 --> 00:02:36.470
with a model like the geocentric model,

00:02:36.470 --> 00:02:39.480
besides adding evermore
complicated features to it,

00:02:39.480 --> 00:02:42.410
is to in fact, just come
up with a new model.

00:02:42.410 --> 00:02:43.970
And this is what astronomers did.

00:02:43.970 --> 00:02:44.961
The new model that was proposed

00:02:44.961 --> 00:02:49.563
to replace the geocentric model
was the heliocentric model.

00:02:50.652 --> 00:02:53.750
In this model, the Earth
and all the other planets

00:02:53.750 --> 00:02:56.400
actually revolve around the sun.

00:02:56.400 --> 00:02:58.480
Helio means sun.

00:02:58.480 --> 00:03:01.220
This heliocentric model
didn't need complicated

00:03:01.220 --> 00:03:02.400
and unexplained cycles

00:03:02.400 --> 00:03:05.220
to explain the way the other
planets moved across the sky.

00:03:05.220 --> 00:03:08.610
It was an expected outcome
of the planets' orbits.

00:03:08.610 --> 00:03:09.930
Now you may be wondering,

00:03:09.930 --> 00:03:12.130
in this model, the sun is stationary.

00:03:12.130 --> 00:03:13.560
So why does it seem to be

00:03:13.560 --> 00:03:16.190
moving across the Earth's sky each day?

00:03:16.190 --> 00:03:18.480
This is actually also easily explained,

00:03:18.480 --> 00:03:20.160
because the motion of the sun in the sky

00:03:20.160 --> 00:03:23.760
is not actual motion,
it is apparent motion.

00:03:23.760 --> 00:03:26.370
Not only is the Earth
revolving around the sun,

00:03:26.370 --> 00:03:28.010
revolving means orbiting,

00:03:28.010 --> 00:03:31.020
but the Earth is also
spinning on its own axis.

00:03:31.020 --> 00:03:32.670
And so as the surface of the Earth

00:03:32.670 --> 00:03:34.610
moves with its spinning motion,

00:03:34.610 --> 00:03:38.400
it makes it appear as if the
sun is moving across the sky.

00:03:38.400 --> 00:03:39.690
The spinning of the Earth

00:03:39.690 --> 00:03:41.790
actually explains why celestial objects

00:03:41.790 --> 00:03:44.790
appear to rise and set
over the course of a day,

00:03:44.790 --> 00:03:46.890
while the revolution, or orbit,

00:03:46.890 --> 00:03:49.470
around the sun explains
the motion of those objects

00:03:49.470 --> 00:03:51.170
over the course of a year.

00:03:51.170 --> 00:03:53.910
It's important to remember that
while the heliocentric model

00:03:53.910 --> 00:03:55.700
does a better job of explaining

00:03:55.700 --> 00:03:57.180
and predicting our solar system,

00:03:57.180 --> 00:04:00.770
which is what we want models
to do, it is still a model,

00:04:00.770 --> 00:04:03.940
and not a perfect recreation of reality.

00:04:03.940 --> 00:04:06.110
For example, while the heliocentric model

00:04:06.110 --> 00:04:08.320
considers the sun as stationary,

00:04:08.320 --> 00:04:10.950
we know now that the sun
is actually just one star

00:04:10.950 --> 00:04:14.090
of many billions orbiting
the center of our own galaxy.

00:04:14.090 --> 00:04:17.060
And so the sun, along with
the rest of the solar system,

00:04:17.060 --> 00:04:19.290
is in fact, moving.

00:04:19.290 --> 00:04:20.640
To summarize, in this video,

00:04:20.640 --> 00:04:22.610
we talked about how we can use models

00:04:22.610 --> 00:04:25.110
to help us understand
what we see in the sky,

00:04:25.110 --> 00:04:27.670
and Earth's place in space.

00:04:27.670 --> 00:04:28.890
As we learn more,

00:04:28.890 --> 00:04:30.100
we improve our models,

00:04:30.100 --> 00:04:32.170
and we can develop new
ones that do a better job

00:04:32.170 --> 00:04:33.870
of explaining our observations,

00:04:33.870 --> 00:04:35.730
and predicting the world around us,

00:04:35.730 --> 00:04:37.690
such as the change from a geocentric model

00:04:37.690 --> 00:04:40.020
to a heliocentric model.

00:04:40.020 --> 00:04:42.420
The Earth then is a planet
that orbits the sun,

00:04:42.420 --> 00:04:44.450
like the other planets
of the solar system.

00:04:44.450 --> 00:04:46.960
And the sun appears to
move across the sky,

00:04:46.960 --> 00:04:50.300
because the Earth spins on its axis.

00:04:50.300 --> 00:04:51.133
Thanks for watching,

00:04:51.133 --> 00:04:53.463
and I hope you learned a
little bit of something.


Organization in the human body

WEBVTT
Kind: captions
Language: en

00:00:00.290 --> 00:00:01.410
- [Instructor] Have you ever thought about

00:00:01.410 --> 00:00:04.260
how incredible the human body is?

00:00:04.260 --> 00:00:06.210
For example, just to name a few things

00:00:06.210 --> 00:00:08.220
that your body's already been doing today.

00:00:08.220 --> 00:00:11.220
You are using your lungs
to take breaths in and out,

00:00:11.220 --> 00:00:13.430
your heart's beating without stopping.

00:00:13.430 --> 00:00:16.100
And your brain is coordinating
your body's functions,

00:00:16.100 --> 00:00:20.040
and at the same time, helping
you understand this video.

00:00:20.040 --> 00:00:22.600
All these body parts are made up of cells,

00:00:22.600 --> 00:00:26.560
which as you might remember,
are the smallest units of life.

00:00:26.560 --> 00:00:29.330
And it's so amazing
that trillions of cells,

00:00:29.330 --> 00:00:31.870
without thoughts or
intentions of their own,

00:00:31.870 --> 00:00:33.620
can come together to form something

00:00:33.620 --> 00:00:36.340
as complex as the human body.

00:00:36.340 --> 00:00:38.460
To help us understand how this occurs,

00:00:38.460 --> 00:00:41.560
we have to understand how
the body is organized.

00:00:41.560 --> 00:00:45.170
The human body has a
hierarchical organization,

00:00:45.170 --> 00:00:47.510
meaning it's made up of nested layers,

00:00:47.510 --> 00:00:50.150
each one more complex than the last.

00:00:50.150 --> 00:00:54.110
In this case, four different
layers make up this hierarchy.

00:00:54.110 --> 00:00:56.510
Cells, which make up tissues.

00:00:56.510 --> 00:00:58.630
Tissues, which make up organs.

00:00:58.630 --> 00:01:01.080
Organs, which make up organ systems.

00:01:01.080 --> 00:01:04.150
And finally organ systems,
which help the human body

00:01:04.150 --> 00:01:06.040
function as a whole.

00:01:06.040 --> 00:01:08.290
So let's start with cells and tissues.

00:01:08.290 --> 00:01:10.570
Cells are the smallest unit of life,

00:01:10.570 --> 00:01:13.250
and the most basic level of organization

00:01:13.250 --> 00:01:14.800
in the human body.

00:01:14.800 --> 00:01:18.740
In the human body, not all
cells look or work the same.

00:01:18.740 --> 00:01:20.810
Instead, they're specialized

00:01:20.810 --> 00:01:22.850
to carry out different functions.

00:01:22.850 --> 00:01:26.960
After cells, the next level
of organization is tissues.

00:01:26.960 --> 00:01:31.790
A tissue is a collection of
similar, specialized cells.

00:01:31.790 --> 00:01:34.840
And all of the cells that make
up a tissue are like a team.

00:01:34.840 --> 00:01:38.100
They work together to ensure
the tissue works properly.

00:01:38.100 --> 00:01:40.550
For instance, this image shows a section

00:01:40.550 --> 00:01:42.650
of the type of epithelial tissue

00:01:42.650 --> 00:01:45.140
that lines the inside of your mouth.

00:01:45.140 --> 00:01:48.950
This particular tissue is
made up of epithelial cells,

00:01:48.950 --> 00:01:51.330
which are specialized to
help protect your mouth

00:01:51.330 --> 00:01:52.920
from wear and tear.

00:01:52.920 --> 00:01:55.740
So the next time you're
eating a pointy tortilla chip,

00:01:55.740 --> 00:02:00.030
remember how important
this epithelial tissue is.

00:02:00.030 --> 00:02:03.240
Next up are organs and organ systems.

00:02:03.240 --> 00:02:06.570
So organs are structures
that are made up of multiple

00:02:06.570 --> 00:02:09.530
different types of tissues,
which all work together

00:02:09.530 --> 00:02:11.320
to help the organ function.

00:02:11.320 --> 00:02:14.970
And an organ system is a group
of organs that work together

00:02:14.970 --> 00:02:18.280
to carry out complex
functions for the body.

00:02:18.280 --> 00:02:21.410
For instance, the lungs
shown here in the diagram

00:02:21.410 --> 00:02:23.870
are made up of several tissue types

00:02:23.870 --> 00:02:26.920
that help them expand and contract.

00:02:26.920 --> 00:02:29.690
These tissue types
include epithelial tissue,

00:02:29.690 --> 00:02:32.490
which is the same type of
tissue we talked about earlier

00:02:32.490 --> 00:02:35.640
in the mouth, and connective tissue.

00:02:35.640 --> 00:02:38.170
And these tissues work
together so that the lungs

00:02:38.170 --> 00:02:41.100
can carry out their role
in the respiratory system,

00:02:41.100 --> 00:02:43.380
which is the organ system that allows us

00:02:43.380 --> 00:02:45.470
to respire or breathe.

00:02:45.470 --> 00:02:49.040
The respiratory system is
made up of multiple organs,

00:02:49.040 --> 00:02:51.650
including the lungs, the trachea,

00:02:51.650 --> 00:02:53.890
the nose and the diaphragm.

00:02:53.890 --> 00:02:55.820
When we breathe, our diaphragm

00:02:55.820 --> 00:02:58.670
which is this muscle
right here, contracts.

00:02:58.670 --> 00:03:01.080
Air is pulled through
our nose and trachea,

00:03:01.080 --> 00:03:02.810
and into our lungs.

00:03:02.810 --> 00:03:06.540
Here, gas exchange happens
and our bodies take in oxygen

00:03:06.540 --> 00:03:08.770
and get rid of carbon dioxide.

00:03:08.770 --> 00:03:12.340
Then our diaphragm relaxes and we exhale.

00:03:12.340 --> 00:03:15.050
The respiratory system,
and other organ systems

00:03:15.050 --> 00:03:17.730
in the body, carry out specific functions

00:03:17.730 --> 00:03:19.910
that work together to keep us alive.

00:03:19.910 --> 00:03:23.820
And they do this mostly
without us even realizing it.

00:03:23.820 --> 00:03:26.190
So it might get a little
tricky to remember

00:03:26.190 --> 00:03:30.500
how all four levels of
organization cells, tissues,

00:03:30.500 --> 00:03:33.490
organs and organ systems
relate to each other.

00:03:33.490 --> 00:03:35.870
I like to think of these
four different levels,

00:03:35.870 --> 00:03:37.740
almost like the Russian nesting dolls

00:03:37.740 --> 00:03:39.710
that fit one inside another.

00:03:39.710 --> 00:03:42.630
With cells being the
smallest doll on the inside.

00:03:42.630 --> 00:03:46.640
So cells make up tissues.
Tissues make up organs.

00:03:46.640 --> 00:03:49.680
And organs make up organ systems.

00:03:49.680 --> 00:03:51.640
All of these components come together

00:03:51.640 --> 00:03:54.060
to make up the human body.

00:03:54.060 --> 00:03:56.680
So I hope you've learned
more about how our body's

00:03:56.680 --> 00:04:00.290
organization helps us
thrive and stay alive.

00:04:00.290 --> 00:04:03.750
So now use your brain to
tell your muscular system

00:04:03.750 --> 00:04:07.180
to move your arm and give
yourself a pat on the back.

00:04:07.180 --> 00:04:09.490
Because your body and its organized

00:04:09.490 --> 00:04:12.893
hierarchical system is really awesome.


Cell parts and their functions

WEBVTT
Kind: captions
Language: en

00:00:00.130 --> 00:00:02.200
- [Instructor] So let's
imagine this scenario.

00:00:02.200 --> 00:00:03.210
It's cold outside

00:00:03.210 --> 00:00:05.830
and we want to make a nice hot bowl

00:00:05.830 --> 00:00:07.550
of chicken noodle soup.

00:00:07.550 --> 00:00:10.200
Well, we'd probably need to
get the ingredients first.

00:00:10.200 --> 00:00:11.860
We need some chicken bones

00:00:11.860 --> 00:00:14.930
to give the broth that
distinct chicken flavor,

00:00:14.930 --> 00:00:18.090
some noodles to add
that starchy component,

00:00:18.090 --> 00:00:21.050
carrots and onions to give
some sweetness and color.

00:00:21.050 --> 00:00:24.170
And of course, salt and
pepper to provide seasoning.

00:00:24.170 --> 00:00:26.040
All of these ingredients
would come together

00:00:26.040 --> 00:00:27.580
to make our chicken noodle soup

00:00:27.580 --> 00:00:30.530
the comfort food that so many people love,

00:00:30.530 --> 00:00:32.950
but this video is supposed
to be about cells.

00:00:32.950 --> 00:00:34.460
You know, those tiny things

00:00:34.460 --> 00:00:36.670
that make up all living things on earth.

00:00:36.670 --> 00:00:40.030
So why am I telling
you about chicken soup?

00:00:40.030 --> 00:00:42.790
Well, just like how each
ingredient in chicken soup

00:00:42.790 --> 00:00:45.930
adds something unique to
the soup's overall flavor

00:00:45.930 --> 00:00:48.230
and texture, a cell's different parts

00:00:48.230 --> 00:00:50.720
add something unique and necessary

00:00:50.720 --> 00:00:53.410
for the overall functioning of the cell.

00:00:53.410 --> 00:00:55.790
So, let's take a look at
some of the structures

00:00:55.790 --> 00:00:58.560
inside a cell and see how
their functions come together

00:00:58.560 --> 00:01:03.050
to allow cells to carry out
all the processes of life.

00:01:03.050 --> 00:01:04.890
So let's explore the parts of a cell

00:01:04.890 --> 00:01:06.830
starting with the cell's surface.

00:01:06.830 --> 00:01:09.690
Cells are separated from
their outside environment

00:01:09.690 --> 00:01:11.730
by a cell membrane.

00:01:11.730 --> 00:01:14.250
You can think of the cell
membrane like a fortress gate,

00:01:14.250 --> 00:01:18.020
because it regulates what
comes into and out of the cell,

00:01:18.020 --> 00:01:19.400
and contained within the cell

00:01:19.400 --> 00:01:22.350
is a jelly-like substance
that fills out the cell

00:01:22.350 --> 00:01:24.660
and contains its internal parts,

00:01:24.660 --> 00:01:27.110
this jelly and all the
structures within it

00:01:27.110 --> 00:01:29.790
make up the cell cytoplasm.

00:01:29.790 --> 00:01:31.020
Unlike chicken soup,

00:01:31.020 --> 00:01:32.730
the cell parts in the cytoplasm

00:01:32.730 --> 00:01:34.300
are not just floating around.

00:01:34.300 --> 00:01:36.760
Instead, they're organized
and held in place

00:01:36.760 --> 00:01:39.280
by an internal structural network.

00:01:39.280 --> 00:01:41.790
Some of the parts contained
within the cytoplasm

00:01:41.790 --> 00:01:43.760
are called organelles.

00:01:43.760 --> 00:01:46.180
So what exactly are organelles?

00:01:46.180 --> 00:01:48.880
Well, organelles are small
compartments in the cell

00:01:48.880 --> 00:01:51.700
that have different
structures and functions.

00:01:51.700 --> 00:01:54.740
The word organelle
basically means, mini organ.

00:01:54.740 --> 00:01:57.910
And just like how our bodies
are made up of different organs

00:01:57.910 --> 00:02:00.350
that work together to help us stay alive,

00:02:00.350 --> 00:02:02.890
cells contain different
organelles that work together

00:02:02.890 --> 00:02:05.670
to get things done inside the cell.

00:02:05.670 --> 00:02:08.570
For example, these jellybean
shaped organelles here

00:02:08.570 --> 00:02:10.830
are little energy producing factories

00:02:10.830 --> 00:02:12.730
called mitochondria.

00:02:12.730 --> 00:02:15.230
So mitochondria use chemical reactions

00:02:15.230 --> 00:02:17.110
to break down sugar molecules

00:02:17.110 --> 00:02:19.160
in order to release energy that the cell

00:02:19.160 --> 00:02:21.270
can use for other tasks.

00:02:21.270 --> 00:02:24.460
Another really amazing
organelle is the nucleus.

00:02:24.460 --> 00:02:27.790
You can think of the nucleus
as the information database

00:02:27.790 --> 00:02:28.690
of the cell.

00:02:28.690 --> 00:02:32.290
It contains DNA which
includes the cell's genes.

00:02:32.290 --> 00:02:34.290
Genes are special instructions

00:02:34.290 --> 00:02:37.163
that the cell uses to
carry out its functions.

00:02:38.550 --> 00:02:40.600
Moving over to a plant cell,

00:02:40.600 --> 00:02:44.420
we can see these green
organelles called chloroplasts.

00:02:44.420 --> 00:02:48.020
You might remember that plants
carry out photosynthesis.

00:02:48.020 --> 00:02:51.160
Well, chloroplasts are the
organelle's responsible

00:02:51.160 --> 00:02:52.610
for this process.

00:02:52.610 --> 00:02:55.810
Plants need food to live,
just like animals do.

00:02:55.810 --> 00:02:58.080
And chloroplasts use photosynthesis

00:02:58.080 --> 00:03:01.640
to produce sugars that
plant cells use as food.

00:03:01.640 --> 00:03:04.590
Plant cells also have a layer
outside their cell membrane

00:03:04.590 --> 00:03:05.680
called the cell wall,

00:03:05.680 --> 00:03:08.270
which helps provide
structure for the cell.

00:03:08.270 --> 00:03:11.320
So as you can see, there
are so many different parts

00:03:11.320 --> 00:03:12.930
that make up a single cell.

00:03:12.930 --> 00:03:15.740
There are many, many
organelles present in cells,

00:03:15.740 --> 00:03:19.010
way more than the handful
I mentioned in this video.

00:03:19.010 --> 00:03:20.810
And what's even more mind blowing

00:03:20.810 --> 00:03:23.640
is that these diagrams are
only simplified versions

00:03:23.640 --> 00:03:25.840
of what cells actually look like.

00:03:25.840 --> 00:03:27.210
And just to give you an idea,

00:03:27.210 --> 00:03:30.600
here's a picture of what
a real cell looks like.

00:03:30.600 --> 00:03:32.160
So when we're talking about cells

00:03:32.160 --> 00:03:34.290
and using these diagrams as references,

00:03:34.290 --> 00:03:37.330
keep in mind that these pictures
are only simplified models

00:03:37.330 --> 00:03:38.970
of the real thing.

00:03:38.970 --> 00:03:40.750
To wrap up this video on cell parts,

00:03:40.750 --> 00:03:44.100
let's revisit our delicious
bowl of chicken noodle soup

00:03:44.100 --> 00:03:45.800
that I mentioned at the beginning.

00:03:45.800 --> 00:03:47.160
Each ingredient that we added

00:03:47.160 --> 00:03:49.510
had a unique function that contributed

00:03:49.510 --> 00:03:51.980
to the soup's taste and texture.

00:03:51.980 --> 00:03:54.500
And similarly, our cell's ingredients,

00:03:54.500 --> 00:03:56.560
its organelles and structures,

00:03:56.560 --> 00:03:58.790
each contribute a unique function

00:03:58.790 --> 00:04:00.210
that helps the cell carry out

00:04:00.210 --> 00:04:02.690
all the tasks necessary for life.

00:04:02.690 --> 00:04:04.680
So the next time you find yourself

00:04:04.680 --> 00:04:06.690
in front of a bowl of noodle soup,

00:04:06.690 --> 00:04:10.110
just imagine that you're
eating one enormous cell.

00:04:10.110 --> 00:04:12.823
Now, isn't that something to noodle on?


Cells and Organisms

WEBVTT
Kind: captions
Language: en

00:00:00.120 --> 00:00:01.010
- [Narrator] Hi, everyone.

00:00:01.010 --> 00:00:01.843
In this video,

00:00:01.843 --> 00:00:03.170
we are going to be talking about

00:00:03.170 --> 00:00:06.060
one of the most fascinating
and complex features

00:00:06.060 --> 00:00:08.630
of life on Earth, cells.

00:00:08.630 --> 00:00:09.610
But before we do,

00:00:09.610 --> 00:00:12.920
I'd like to take us way back
to when I was a little kid.

00:00:12.920 --> 00:00:14.650
Now I know that for me, at least,

00:00:14.650 --> 00:00:17.100
I had a great time playing
with toy building blocks,

00:00:17.100 --> 00:00:18.920
and creating things out of them.

00:00:18.920 --> 00:00:21.940
I used blocks of
different shapes and sizes

00:00:21.940 --> 00:00:24.350
to make all kinds of things like houses,

00:00:24.350 --> 00:00:27.750
cars, even spaceships, and airplanes.

00:00:27.750 --> 00:00:28.700
You're probably thinking,

00:00:28.700 --> 00:00:31.120
what does this have to do with cells?

00:00:31.120 --> 00:00:34.200
Well, cells are considered
the building blocks of life.

00:00:34.200 --> 00:00:37.290
Like my blocks, cells can
come in a variety of shapes,

00:00:37.290 --> 00:00:39.570
and they have different features too.

00:00:39.570 --> 00:00:41.240
They can also stand alone,

00:00:41.240 --> 00:00:43.920
or they can come together
to build something larger.

00:00:43.920 --> 00:00:47.930
So let's dive deeper into this
fascinating topic of cells.

00:00:47.930 --> 00:00:49.978
So all living things, or organisms,

00:00:49.978 --> 00:00:52.650
like you, me, your pet dog,

00:00:52.650 --> 00:00:55.280
the birds in the sky, the fish in the sea,

00:00:55.280 --> 00:00:59.980
all organisms are made of
these basic units called cells.

00:00:59.980 --> 00:01:03.960
Take this moss plant, for
example, if we zoom way in,

00:01:03.960 --> 00:01:07.700
we can see that it's actually
made up of many smaller units.

00:01:07.700 --> 00:01:09.890
These units are cells.

00:01:09.890 --> 00:01:12.510
Each cell contains a flurry of activity,

00:01:12.510 --> 00:01:13.858
as it works to carry out the functions

00:01:13.858 --> 00:01:16.500
that keep the organism alive.

00:01:16.500 --> 00:01:19.780
In fact, cells are the smallest
unit that can carry out

00:01:19.780 --> 00:01:22.400
all the tasks necessary for life.

00:01:22.400 --> 00:01:25.890
For instance, all cells can
take up nutrients and water,

00:01:25.890 --> 00:01:28.700
get rid of waste, use energy,

00:01:28.700 --> 00:01:30.241
and interact with the things around them

00:01:30.241 --> 00:01:32.500
in their environment.

00:01:32.500 --> 00:01:35.250
These functions, plus many
others that cells carry out,

00:01:35.250 --> 00:01:37.680
are what make life possible.

00:01:37.680 --> 00:01:39.240
There are many different kinds of cells.

00:01:39.240 --> 00:01:40.618
For instance, take a look at these cells

00:01:40.618 --> 00:01:43.050
that make up an onion's outer skin,

00:01:43.050 --> 00:01:45.060
or these really cool red blood cells,

00:01:45.060 --> 00:01:47.120
or even these bacterial cells.

00:01:47.120 --> 00:01:49.840
This type of bacteria is called e-coli,

00:01:49.840 --> 00:01:52.050
which you might've heard
can be a safety hazard

00:01:52.050 --> 00:01:53.370
found in our food.

00:01:53.370 --> 00:01:55.630
So cells are fascinating to look at,

00:01:55.630 --> 00:01:58.620
but we generally can't see
them with our eyes alone.

00:01:58.620 --> 00:01:59.960
Most cells are so small

00:01:59.960 --> 00:02:02.340
that we need a microscope to see them.

00:02:02.340 --> 00:02:04.620
In fact, all of these
pictures of cells here

00:02:04.620 --> 00:02:07.750
were taken with the aid of microscopes.

00:02:07.750 --> 00:02:09.810
And something else that I find really cool

00:02:09.810 --> 00:02:13.500
is that some organisms are
made up of only a single cell,

00:02:13.500 --> 00:02:16.400
while others are made up of many cells.

00:02:16.400 --> 00:02:18.720
So organisms that are made up of one cell

00:02:18.720 --> 00:02:20.440
are called unicellular,

00:02:20.440 --> 00:02:23.230
and organisms that are
made up of many cells

00:02:23.230 --> 00:02:25.130
are called multicellular.

00:02:25.130 --> 00:02:27.540
Uni telling us that
there is only one cell,

00:02:27.540 --> 00:02:30.890
and multi telling us that
there are many cells.

00:02:30.890 --> 00:02:33.410
So an example of a unicellular organism

00:02:33.410 --> 00:02:37.000
would be the e-coli bacteria
that I mentioned a minute ago.

00:02:37.000 --> 00:02:39.330
Each bacterium is a single cell

00:02:39.330 --> 00:02:42.847
that's responsible for taking
in nutrients, reproducing,

00:02:42.847 --> 00:02:45.890
and doing all the things
that it needs to stay alive.

00:02:45.890 --> 00:02:48.310
So an example of a multicellular organism

00:02:48.310 --> 00:02:51.910
would be you, me, or
most any other organism

00:02:51.910 --> 00:02:54.150
that you can see with the naked eye.

00:02:54.150 --> 00:02:56.220
And the cells of multicellular organisms

00:02:56.220 --> 00:03:00.000
are often specialized to
carry out specific functions.

00:03:00.000 --> 00:03:01.090
So for example,

00:03:01.090 --> 00:03:04.080
some cells help the
organism absorb nutrients,

00:03:04.080 --> 00:03:06.270
while others transmit information,

00:03:06.270 --> 00:03:10.050
or defend against bacteria and viruses.

00:03:10.050 --> 00:03:11.510
So going back to our comparison

00:03:11.510 --> 00:03:13.490
between building blocks and cells,

00:03:13.490 --> 00:03:15.990
specialized cells are like
different building blocks

00:03:15.990 --> 00:03:19.630
of different sizes, shapes, and colors.

00:03:19.630 --> 00:03:20.780
And these different blocks

00:03:20.780 --> 00:03:22.710
can come together to
build something larger,

00:03:22.710 --> 00:03:24.400
like this airplane here.

00:03:24.400 --> 00:03:26.730
Similarly, cells with different structures

00:03:26.730 --> 00:03:29.740
and functions come together
to make something larger,

00:03:29.740 --> 00:03:33.063
an organism like this
adorable kitten right here.

00:03:34.150 --> 00:03:35.970
So to sum up cells and organisms,

00:03:35.970 --> 00:03:39.530
today, we learned that cells
are the smallest unit of life.

00:03:39.530 --> 00:03:42.770
We talked about how all
organisms are made up of cells,

00:03:42.770 --> 00:03:46.580
and that organisms can be
unicellular or multicellular.

00:03:46.580 --> 00:03:48.750
So I hope that now you
have a good understanding

00:03:48.750 --> 00:03:50.160
of cells and organisms,

00:03:50.160 --> 00:03:52.900
as well as a new perspective
about building blocks,

00:03:52.900 --> 00:03:56.323
not the toys, but the cells
that make up life itself.


Subtracting with place value blocks (regrouping)

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:01.860
- [Instructor] What we
want to do in this video

00:00:01.860 --> 00:00:06.760
is figure out what 438 minus 272 is

00:00:06.760 --> 00:00:08.930
and to help us think about that

00:00:08.930 --> 00:00:13.550
we have these place value
blocks right over here.

00:00:13.550 --> 00:00:15.630
So you can see 438.

00:00:15.630 --> 00:00:20.170
We have four hundreds, 100, 200, 300, 400.

00:00:20.170 --> 00:00:23.950
We have three tens, one, two, three

00:00:23.950 --> 00:00:25.750
and then we have eight ones.

00:00:25.750 --> 00:00:28.370
You can count those eight
ones right over there.

00:00:28.370 --> 00:00:30.710
From that, we're going to
take away two hundreds,

00:00:30.710 --> 00:00:32.810
so that's 200 right over there,

00:00:32.810 --> 00:00:37.310
seven tens or 70 right
over here, and two ones.

00:00:37.310 --> 00:00:38.290
So pause this video

00:00:38.290 --> 00:00:41.040
and see if you can figure
out what this is going to be.

00:00:41.950 --> 00:00:42.783
All right.

00:00:42.783 --> 00:00:45.400
Now let's work through this together.

00:00:45.400 --> 00:00:48.730
So first of all, we could
start in the ones place

00:00:48.730 --> 00:00:51.430
and we can see we have eight ones

00:00:51.430 --> 00:00:53.070
and then we're gonna take away two ones.

00:00:53.070 --> 00:00:55.250
So that's pretty straight forward.

00:00:55.250 --> 00:00:59.863
We're just going to be left
with six ones right over here.

00:01:00.740 --> 00:01:02.860
Now let's go to the tens place.

00:01:02.860 --> 00:01:04.770
Now the tens place is interesting.

00:01:04.770 --> 00:01:06.270
We have three tens here

00:01:06.270 --> 00:01:08.040
and we're trying to take away from that

00:01:08.040 --> 00:01:12.140
one, two, three, four,
five, six, seven tens.

00:01:12.140 --> 00:01:15.760
So how do you take seven
tens from three tens?

00:01:15.760 --> 00:01:20.760
Well, luckily we can regroup
from the hundreds place.

00:01:20.890 --> 00:01:25.890
What if we were to take
this piece right over here

00:01:26.280 --> 00:01:28.490
from the hundreds to the tens place

00:01:28.490 --> 00:01:31.750
and now this is going to be
the equivalent of 10 tens.

00:01:31.750 --> 00:01:34.250
So let me represent it that way.

00:01:34.250 --> 00:01:36.470
Once again, I took a hundreds.

00:01:36.470 --> 00:01:38.210
That's the same thing as one, two, three

00:01:38.210 --> 00:01:42.380
four, five, six, seven,
eight, nine, 10 tens.

00:01:42.380 --> 00:01:43.340
Well, this is useful now,

00:01:43.340 --> 00:01:45.960
because now I have 10 plus three tens,

00:01:45.960 --> 00:01:47.820
or you could say I have 13 tens

00:01:47.820 --> 00:01:50.520
and now I can take away
seven tens from that.

00:01:50.520 --> 00:01:51.920
So let's do that.

00:01:51.920 --> 00:01:56.920
Let's take away one, two,
three, four, five, six, seven

00:02:00.120 --> 00:02:05.060
and what we are left with
is six tens right over here.

00:02:05.060 --> 00:02:08.990
So now I have six tens left, six ones left

00:02:08.990 --> 00:02:11.100
and in the hundreds,
I have three hundreds.

00:02:11.100 --> 00:02:12.270
I'm gonna take away two of them.

00:02:12.270 --> 00:02:15.330
So I'm gonna take away 100 and 200.

00:02:15.330 --> 00:02:17.550
So I'm left with just 100 there.

00:02:17.550 --> 00:02:21.710
So I'm left with one hundred,
six tens and six ones.

00:02:21.710 --> 00:02:26.297
So this is one hundred, six
tens and six ones, or 166.


Using probability to make fair decisions

WEBVTT
Kind: captions
Language: en

00:00:00.260 --> 00:00:01.970
- [Instructor] We're told
that Roberto and Jocelyn

00:00:01.970 --> 00:00:05.420
decide to roll a pair
of fair six-sided dice

00:00:05.420 --> 00:00:08.107
to determine who has to
dust their apartment.

00:00:08.107 --> 00:00:11.730
If the sum is seven,
then Roberto will dust.

00:00:11.730 --> 00:00:15.840
If the sum is 10 or 11,
then Jocelyn will dust.

00:00:15.840 --> 00:00:19.860
If the sum is anything
else, they'll roll again.

00:00:19.860 --> 00:00:22.589
Is this a fair way to decide who dusts?

00:00:22.589 --> 00:00:24.730
Why or why not?

00:00:24.730 --> 00:00:25.950
So pause this video and see

00:00:25.950 --> 00:00:28.989
if you can figure this out
before we do it together.

00:00:28.989 --> 00:00:31.130
All right, now let's do this together.

00:00:31.130 --> 00:00:33.050
So what I wanna do is
make a table that shows

00:00:33.050 --> 00:00:35.600
all of the different scenarios for rolling

00:00:37.559 --> 00:00:40.610
two fair six-sided dice.

00:00:40.610 --> 00:00:44.800
So let me make columns for roll one.

00:00:44.800 --> 00:00:48.140
So that is when you get a one.

00:00:48.140 --> 00:00:49.520
This is when you get a two.

00:00:49.520 --> 00:00:51.287
This is when you get a three.

00:00:51.287 --> 00:00:53.680
This is when you get a four.

00:00:53.680 --> 00:00:55.520
This is when you get a five.

00:00:55.520 --> 00:00:58.880
And then, this is when you get a six.

00:00:58.880 --> 00:01:02.290
And then here, let's do the other die.

00:01:02.290 --> 00:01:04.350
So this is when you get a one.

00:01:04.350 --> 00:01:06.820
This is when you get a two.

00:01:06.820 --> 00:01:08.790
This is when you get a three.

00:01:08.790 --> 00:01:10.766
This is when you get a four.

00:01:10.766 --> 00:01:13.150
This is when you get a five.

00:01:13.150 --> 00:01:15.680
And then, this is when you get a six.

00:01:15.680 --> 00:01:16.830
So one way to think about it

00:01:16.830 --> 00:01:21.370
is this is roll one

00:01:21.370 --> 00:01:22.790
or let me write it this way,

00:01:22.790 --> 00:01:25.400
d1 and d2.

00:01:25.400 --> 00:01:28.753
This could be a one, a two,
a three, a five or a six.

00:01:29.812 --> 00:01:33.700
And this could be a one,
a two, a three, a four,

00:01:33.700 --> 00:01:36.070
a five or a six.

00:01:36.070 --> 00:01:40.210
Now what we could do is
fill in these 36 squares

00:01:40.210 --> 00:01:41.530
to figure out what the sum is.

00:01:41.530 --> 00:01:42.380
Actually, let me just do that

00:01:42.380 --> 00:01:43.600
and I'll try to do it really fast,

00:01:43.600 --> 00:01:44.670
one + one is two.

00:01:44.670 --> 00:01:49.150
So it's three, four, five, six, seven.

00:01:49.150 --> 00:01:53.070
This is three, four,
five, six, seven, eight.

00:01:53.070 --> 00:01:57.430
This is four, five,
six, seven, eight, nine.

00:01:57.430 --> 00:02:02.030
This is five, six, seven, eight, nine, 10.

00:02:02.030 --> 00:02:06.970
This is six, seven, eight, nine, 10, 11.

00:02:06.970 --> 00:02:07.890
Last but not least,

00:02:07.890 --> 00:02:11.950
seven, eight, nine, 10, 11 and 12,

00:02:11.950 --> 00:02:13.721
took a little less time than I suspected.

00:02:13.721 --> 00:02:15.610
All right, let's think
about this scenario.

00:02:15.610 --> 00:02:18.740
If the sum is seven,
then Roberto will dust.

00:02:18.740 --> 00:02:20.750
So where is the sum seven?

00:02:20.750 --> 00:02:24.680
So we have that ones, twice, three times,

00:02:24.680 --> 00:02:27.250
four, five, six.

00:02:27.250 --> 00:02:30.990
So six out of, so six of these outcomes

00:02:30.990 --> 00:02:32.560
result in a sum of seven.

00:02:32.560 --> 00:02:36.290
And how many possible equally
likely outcomes are there?

00:02:36.290 --> 00:02:38.470
Well, there are six times six

00:02:38.470 --> 00:02:41.630
equally possible outcomes or 36.

00:02:41.630 --> 00:02:43.108
So six out of the 36

00:02:43.108 --> 00:02:44.730
or this is another way of saying

00:02:44.730 --> 00:02:48.920
there's a 1/6 probability
that Roberto will dust.

00:02:48.920 --> 00:02:51.590
And then, let's think
about the 10s or 11s.

00:02:51.590 --> 00:02:53.480
If the sum is 10 or 11,

00:02:53.480 --> 00:02:56.023
then Jocelyn will dust.

00:02:56.860 --> 00:02:58.530
So 10 or 11,

00:02:58.530 --> 00:03:01.180
so we have one, two,

00:03:01.180 --> 00:03:05.100
three, four, five.

00:03:05.100 --> 00:03:10.100
So this is only happening
five out of the 36 times.

00:03:10.120 --> 00:03:11.610
So in any given roll,

00:03:11.610 --> 00:03:14.230
it's a higher probability that Roberto

00:03:14.230 --> 00:03:16.810
will dust than Jocelyn will dust.

00:03:16.810 --> 00:03:18.470
And of course, if neither of these happen,

00:03:18.470 --> 00:03:19.740
they are going to roll again.

00:03:19.740 --> 00:03:20.920
But on that second roll,

00:03:20.920 --> 00:03:23.630
there's a higher probability
that Roberto will dust

00:03:23.630 --> 00:03:24.860
than Jocelyn will dust.

00:03:24.860 --> 00:03:27.280
So in general, this is not fair.

00:03:27.280 --> 00:03:30.720
There's a higher probability
that Roberto dusts.

00:03:30.720 --> 00:03:32.933
So this is our choice.


3 Minute Breather for Teachers

WEBVTT
Kind: captions
Language: en

00:00:00.330 --> 00:00:04.553
- Welcome, teachers, for
this short guided meditation.

00:00:06.170 --> 00:00:07.880
Remind yourself that meditation,

00:00:07.880 --> 00:00:10.240
there's no right way to do it.

00:00:10.240 --> 00:00:14.900
It's just an opportunity
to still your mind,

00:00:14.900 --> 00:00:19.430
take a break from all the
thoughts that you normally have,

00:00:19.430 --> 00:00:22.580
the planning, the to-do's of the future,

00:00:22.580 --> 00:00:23.793
thoughts of the past,

00:00:25.090 --> 00:00:28.803
and just be in the moment, and be still.

00:00:30.720 --> 00:00:33.930
So let's start by taking a few deep

00:00:33.930 --> 00:00:37.323
and controlled breaths
together in through our nose.

00:00:40.110 --> 00:00:40.943
Hold.

00:00:46.650 --> 00:00:48.473
And out through our mouths.

00:00:56.190 --> 00:00:57.493
In through our nose.

00:01:00.240 --> 00:01:01.073
Hold.

00:01:09.380 --> 00:01:10.980
And then out through your mouth.

00:01:16.590 --> 00:01:19.690
Now I encourage you to continue to breathe

00:01:19.690 --> 00:01:23.473
in a deep and controlled way,

00:01:24.460 --> 00:01:28.233
but as you do so, try to
put a smile on your face.

00:01:29.440 --> 00:01:31.373
It might feel a little artificial,

00:01:32.830 --> 00:01:35.090
but I promise it'll actually feel good.

00:01:35.090 --> 00:01:38.470
Even if your mood might not
have made you want to smile,

00:01:38.470 --> 00:01:41.370
just put a big cheesy smile on your face

00:01:41.370 --> 00:01:42.963
as you continue to breathe in.

00:01:48.240 --> 00:01:49.073
And out.

00:01:58.150 --> 00:02:00.250
So as you go through the rest of your day,

00:02:01.310 --> 00:02:03.833
encourage you to take breaks like this,

00:02:05.370 --> 00:02:08.373
moment of pause, moment of stillness,

00:02:09.760 --> 00:02:12.233
approached with a sense of acceptance,

00:02:13.520 --> 00:02:18.253
a sense of curiosity,
even a sense of humor.

00:02:21.470 --> 00:02:23.643
And remind yourself that as a teacher,

00:02:24.900 --> 00:02:27.313
you give so much of yourself to others,

00:02:28.940 --> 00:02:30.940
but you need to have a source of energy.

00:02:32.560 --> 00:02:34.600
And so for their sake,

00:02:34.600 --> 00:02:36.900
it's important that you
take care of yourself.

00:02:39.470 --> 00:02:42.143
It's important that you
give your mind a break,

00:02:43.917 --> 00:02:45.490
and be in the moment,

00:02:45.490 --> 00:02:48.953
in a moment of stillness and acceptance.

00:02:51.610 --> 00:02:52.770
And maybe in a little way,

00:02:52.770 --> 00:02:56.870
resolve and refresh
everything that's going on

00:02:56.870 --> 00:03:01.523
to tackle the day, the
weeks, the months ahead.

00:03:05.148 --> 00:03:06.065
Thank you.


Inequalities word problems

WEBVTT
Kind: captions
Language: en

00:00:03.340 --> 00:00:04.310
- [Instructor] We're told that Eric

00:00:04.310 --> 00:00:05.800
is shorter than Priti.

00:00:05.800 --> 00:00:09.470
Priti is 158 centimeters tall.

00:00:09.470 --> 00:00:12.160
Write an inequality that
compares Eric's height

00:00:12.160 --> 00:00:15.640
in centimeters, E, to Priti's height.

00:00:15.640 --> 00:00:18.340
Pause this video and
see if you can do that.

00:00:18.340 --> 00:00:20.620
Alright, so we have Eric's height,

00:00:20.620 --> 00:00:23.780
which we are using the
variable capital E for,

00:00:23.780 --> 00:00:24.860
And how does it compare?

00:00:24.860 --> 00:00:27.710
It says Eric is shorter than Priti.

00:00:27.710 --> 00:00:31.640
So Eric's height is going to be less than

00:00:31.640 --> 00:00:36.640
whatever Priti's height is,
which is 158 centimeters.

00:00:37.570 --> 00:00:39.320
You could think about
it on a number line too.

00:00:39.320 --> 00:00:41.680
If I were to draw a number line like this,

00:00:41.680 --> 00:00:46.680
and this is 158
centimeters, Priti's height,

00:00:46.780 --> 00:00:51.350
Eric's is gonna be less than
that 'cause he is shorter.

00:00:51.350 --> 00:00:55.200
So it would be all of the
values that are to the left of,

00:00:55.200 --> 00:00:56.860
let me do this in another color,

00:00:56.860 --> 00:00:59.330
that are less than that.

00:00:59.330 --> 00:01:00.790
Just like that.

00:01:00.790 --> 00:01:02.763
Let's do another example.

00:01:05.310 --> 00:01:09.030
Here we are told that Sydney wears skirts

00:01:09.030 --> 00:01:14.030
when the temperature is warmer
than 25 degrees Celsius.

00:01:14.740 --> 00:01:17.800
Write an inequality that describes T,

00:01:17.800 --> 00:01:21.890
the temperatures at which
Sydney wears skirts.

00:01:21.890 --> 00:01:23.180
So again, pause this video and see

00:01:23.180 --> 00:01:24.943
if you can have a go at that.

00:01:26.440 --> 00:01:29.810
Alright. So when does Sydney wear skirts?

00:01:29.810 --> 00:01:34.100
When the temperature is warmer
than 25 degrees Celsius.

00:01:34.100 --> 00:01:36.680
Now, warmer means that
the temperature is higher

00:01:36.680 --> 00:01:38.550
than 25 degrees Celsius,

00:01:38.550 --> 00:01:43.350
or that the temperature is
greater than 25 degrees Celsius.

00:01:43.350 --> 00:01:46.630
And we're using capital
T to denote temperature.

00:01:46.630 --> 00:01:51.260
So we would say capital
T, this needs to be higher

00:01:51.260 --> 00:01:56.260
than 25 degrees, or greater
than 25 degrees Celsius.

00:01:56.890 --> 00:02:00.460
So T is greater than 25.

00:02:00.460 --> 00:02:03.580
Let's do one last example here.

00:02:03.580 --> 00:02:08.580
So here we are told that Lola
and Hayley are running a race.

00:02:10.350 --> 00:02:13.610
Lola finishes the race in 53 seconds.

00:02:13.610 --> 00:02:16.950
Hayley finishes after Lola.

00:02:16.950 --> 00:02:19.500
Write an inequality that represents H,

00:02:19.500 --> 00:02:21.970
Hayley's finish time in seconds.

00:02:21.970 --> 00:02:25.360
Pause the video and see if
you can think about this.

00:02:25.360 --> 00:02:28.110
Alright, so how does
Hayley compare to Lola?

00:02:28.110 --> 00:02:30.800
Hayley finishes after Lola.

00:02:30.800 --> 00:02:33.070
So what does that mean
about Hayley's time?

00:02:33.070 --> 00:02:36.470
Well, that means that Hayley
is going to take more time

00:02:36.470 --> 00:02:38.370
than Lola to finish the race.

00:02:38.370 --> 00:02:41.530
So whatever Lola's time is, Hayley's time

00:02:41.530 --> 00:02:46.170
is going to be longer,
or more, or greater than.

00:02:46.170 --> 00:02:50.620
So Hayley's time is going to
be greater than Lola's time,

00:02:50.620 --> 00:02:52.300
which is 53 seconds,

00:02:52.300 --> 00:02:55.253
because Hayley finishes after.


Finding mistakes in one-step equations

WEBVTT
Kind: captions
Language: en

00:00:00.400 --> 00:00:01.240
- [Instructor] We're told that Lisa

00:00:01.240 --> 00:00:03.290
tried to solve an equation.

00:00:03.290 --> 00:00:07.070
See, 42 is equal to 6a, or six times a.

00:00:07.070 --> 00:00:09.360
And then we can see her steps here.

00:00:09.360 --> 00:00:12.520
And they say, where did
Lisa make her first mistake?

00:00:12.520 --> 00:00:14.850
So pause this video, and see
if you can figure that out.

00:00:14.850 --> 00:00:17.150
And it might be possible
she made no mistakes.

00:00:18.640 --> 00:00:19.910
All right.

00:00:19.910 --> 00:00:22.360
Well, we know she ends
up with seven equals six,

00:00:22.360 --> 00:00:26.200
which is sketchy, so let's
see what happened here.

00:00:26.200 --> 00:00:29.320
So right over here, it looks like,

00:00:29.320 --> 00:00:31.100
well, she did something
a little bit strange.

00:00:31.100 --> 00:00:33.510
She divided the left-hand side by six,

00:00:33.510 --> 00:00:35.990
and the right hand side by a.

00:00:35.990 --> 00:00:38.300
You don't want to divide
two sides of an equation

00:00:38.300 --> 00:00:40.090
by two different things.

00:00:40.090 --> 00:00:42.150
Then it's no longer
going to be an equation.

00:00:42.150 --> 00:00:43.767
The equality won't hold.

00:00:43.767 --> 00:00:46.710
An algebraically legitimate thing

00:00:46.710 --> 00:00:49.100
is to do the same thing to both sides,

00:00:49.100 --> 00:00:50.510
but she didn't do it here.

00:00:50.510 --> 00:00:54.320
So this is where she
made her first mistake.

00:00:54.320 --> 00:00:56.940
Let's give another example here.

00:00:56.940 --> 00:01:00.010
So here it says that Jin
tried to solve an equation.

00:01:00.010 --> 00:01:03.780
All right, x plus 4.7 is equal to 11.2.

00:01:03.780 --> 00:01:05.980
Where did Jin make his first mistake?

00:01:05.980 --> 00:01:08.730
Pause this video, and
try to figure it out.

00:01:08.730 --> 00:01:09.563
All right,

00:01:09.563 --> 00:01:11.510
so it looks like in order to isolate the x

00:01:11.510 --> 00:01:16.510
on the left-hand side, Jin is
subtracting 4.7 from the left,

00:01:16.550 --> 00:01:21.080
and then also subtracting
4.7 from the right.

00:01:21.080 --> 00:01:24.540
So that is looking good, doing
the same thing to both sides,

00:01:24.540 --> 00:01:26.920
subtracting 4.7 from both sides.

00:01:26.920 --> 00:01:29.675
And then over here on the left-hand side,

00:01:29.675 --> 00:01:31.368
these two would cancel.

00:01:31.368 --> 00:01:33.760
So you'd be left with just an x,

00:01:33.760 --> 00:01:37.123
and let's see, 11.2 minus 4.7.

00:01:38.325 --> 00:01:42.577
11.2 minus four would be 7.2,

00:01:44.650 --> 00:01:47.250
and then minus the 0.7 would be 6.5.

00:01:47.250 --> 00:01:50.870
So this is where Jin made his mistake,

00:01:50.870 --> 00:01:53.550
on the calculating part.

00:01:53.550 --> 00:01:55.900
Let's do another example,
this is a lot of fun.

00:01:56.960 --> 00:02:00.304
So here we are told that Marina
tried to solve an equation,

00:02:00.304 --> 00:02:01.580
and we need to figure out

00:02:01.580 --> 00:02:04.770
where Marina made her first mistake.

00:02:04.770 --> 00:02:09.360
All right, one-sixth is
equal to two-thirds, why?

00:02:09.360 --> 00:02:11.260
So the first step,

00:02:11.260 --> 00:02:14.680
or the first thing that
Marina did right over here

00:02:14.680 --> 00:02:18.630
is to multiply both sides of this equation

00:02:18.630 --> 00:02:21.640
by the reciprocal of two-thirds,
which is three halves.

00:02:21.640 --> 00:02:23.990
Multiplied the left-hand
side by three halves,

00:02:23.990 --> 00:02:26.520
multiplied the right-hand
side by three halves,

00:02:26.520 --> 00:02:29.660
which is a very reasonable thing to do.

00:02:29.660 --> 00:02:30.997
We're doing the same thing to both sides,

00:02:30.997 --> 00:02:33.130
multiplying by three halves.

00:02:33.130 --> 00:02:36.130
And then when we go over here, let's see,

00:02:36.130 --> 00:02:38.920
three halves times one-sixth.

00:02:38.920 --> 00:02:42.370
We could divide the numerator
and the denominator by three.

00:02:42.370 --> 00:02:44.960
So it's gonna be one over two.

00:02:44.960 --> 00:02:47.240
So that indeed is going to
be one half times one half,

00:02:47.240 --> 00:02:49.540
which is one-fourth, so that checks out.

00:02:49.540 --> 00:02:50.530
And on this side,

00:02:50.530 --> 00:02:52.290
if you multiply three
halves times two-thirds,

00:02:52.290 --> 00:02:54.660
that's going to be one,
so this checks out.

00:02:54.660 --> 00:02:57.950
So it actually looks like
Marina did everything correctly.

00:02:57.950 --> 00:03:02.950
So no mistake, no mistake for Marina.

00:03:03.300 --> 00:03:05.853
Let's do one last example.

00:03:07.380 --> 00:03:10.570
So here, Taylor is trying
to solve an equation.

00:03:10.570 --> 00:03:14.210
And so where did Taylor
first get tripped up?

00:03:14.210 --> 00:03:16.293
N minus 2.7 is equal to 6.7.

00:03:17.450 --> 00:03:20.220
In order to isolate this N over here,

00:03:20.220 --> 00:03:24.030
I would add 2.7 to both sides,

00:03:24.030 --> 00:03:26.960
but that's not what Taylor did.

00:03:26.960 --> 00:03:31.750
Taylor subtracted 2.7 from both sides.

00:03:31.750 --> 00:03:34.460
So the first place that
Taylor starts to trip up,

00:03:34.460 --> 00:03:39.000
or move in the wrong
direction is right over here.

00:03:39.000 --> 00:03:43.750
Now, what Taylor did is not
algebraically incorrect.

00:03:43.750 --> 00:03:48.750
You would end up with n
minus 5.4 is equal to four,

00:03:49.870 --> 00:03:52.290
but it's not going to help
you solve this equation.

00:03:52.290 --> 00:03:53.980
You just replaced this equation

00:03:53.980 --> 00:03:55.830
with another equivalent equation

00:03:55.830 --> 00:03:59.440
that is no simpler than the one before.

00:03:59.440 --> 00:04:00.273
And then of course,

00:04:00.273 --> 00:04:02.810
instead of getting n
minus 5.4 equals four,

00:04:02.810 --> 00:04:06.030
Taylor calculated incorrectly as well.

00:04:06.030 --> 00:04:07.890
But where they first
started to get tripped up,

00:04:07.890 --> 00:04:09.670
or at least not move
in the right direction

00:04:09.670 --> 00:04:11.113
would be right over here.


One-step multiplication equations: fractional coefficients

WEBVTT
Kind: captions
Language: en

00:00:00.770 --> 00:00:02.440
- Let's say that we have the equation,

00:00:02.440 --> 00:00:06.730
two-fifths X is equal to 10.

00:00:06.730 --> 00:00:08.703
How would you go about solving that?

00:00:09.640 --> 00:00:11.230
Well, you might be thinking to yourself,

00:00:11.230 --> 00:00:12.980
it would be nice if we just had an X

00:00:12.980 --> 00:00:15.620
on the left-hand side
instead of a two-fifths X,

00:00:15.620 --> 00:00:17.820
or if the coefficient on the X were one

00:00:17.820 --> 00:00:19.120
instead of a two-fifths.

00:00:19.120 --> 00:00:21.400
And the way that we might do that,

00:00:21.400 --> 00:00:22.730
is if we were to multiply

00:00:22.730 --> 00:00:27.440
both sides of this
equation by five halves.

00:00:27.440 --> 00:00:29.490
Why five halves?

00:00:29.490 --> 00:00:30.670
Well, five halves,

00:00:30.670 --> 00:00:31.503
if you notice,

00:00:31.503 --> 00:00:33.880
when I multiply five
halves times two-fifths,

00:00:33.880 --> 00:00:35.540
it's going to get us to one.

00:00:35.540 --> 00:00:37.417
Five times two is 10,

00:00:37.417 --> 00:00:39.140
two times five is 10.

00:00:39.140 --> 00:00:41.460
So it's going to be 10 over 10 or one,

00:00:41.460 --> 00:00:44.800
or you could think about
five divided by five is one,

00:00:44.800 --> 00:00:47.220
two divided by two is one.

00:00:47.220 --> 00:00:48.670
And you might say, "Is that magical?

00:00:48.670 --> 00:00:51.100
How did you think of five halves?"

00:00:51.100 --> 00:00:53.670
Well, five halves is just
the reciprocal of two-fifths.

00:00:53.670 --> 00:00:56.420
I just swapped the numerator
and the denominator

00:00:56.420 --> 00:00:57.600
to get five halves.

00:00:57.600 --> 00:00:59.960
And then why did I multiply
it times the right-hand side?

00:00:59.960 --> 00:01:01.247
Well, anything I do to the left hand,

00:01:01.247 --> 00:01:03.640
I also want to do to the right hand.

00:01:03.640 --> 00:01:07.460
So the left-hand side
simplifies to this is all one.

00:01:07.460 --> 00:01:10.792
So it's just going to be X is equal to,

00:01:10.792 --> 00:01:14.470
or we could say one X is
equal to 10 times five halves.

00:01:14.470 --> 00:01:17.020
That's the same thing as 50 halves.

00:01:17.020 --> 00:01:19.410
I could write it this way, 50 over two,

00:01:19.410 --> 00:01:22.910
which is the same thing as 25.

00:01:22.910 --> 00:01:24.160
Let's do another example.

00:01:25.010 --> 00:01:26.410
Let's say we have the equation,

00:01:26.410 --> 00:01:28.010
14 is equal

00:01:28.010 --> 00:01:30.660
to seven-thirds B.

00:01:30.660 --> 00:01:32.533
See if you can solve this.

00:01:33.460 --> 00:01:34.600
Well, once again,

00:01:34.600 --> 00:01:36.080
it'd be nice if the coefficient

00:01:36.080 --> 00:01:38.030
on the B weren't seven-thirds,

00:01:38.030 --> 00:01:39.410
but instead were just a one.

00:01:39.410 --> 00:01:42.160
If it's just B is equal to something.

00:01:42.160 --> 00:01:43.580
Well, we know how to do that.

00:01:43.580 --> 00:01:46.330
We can multiply both
sides of this equation

00:01:46.330 --> 00:01:50.040
times the reciprocal
of the coefficient on B

00:01:50.040 --> 00:01:52.050
times the reciprocal of seven-thirds.

00:01:52.050 --> 00:01:54.210
What's the reciprocal of seven-thirds?

00:01:54.210 --> 00:01:56.060
Well, the denominator
will become the numerator.

00:01:56.060 --> 00:01:57.960
The numerator becomes a denominator.

00:01:57.960 --> 00:02:00.700
It's going to be three-sevenths.

00:02:00.700 --> 00:02:01.533
Now, of course,

00:02:01.533 --> 00:02:03.020
I can't just do it on one side.

00:02:03.020 --> 00:02:05.540
I have to do it on both sides.

00:02:05.540 --> 00:02:08.920
So on the right-hand
side of this equation,

00:02:08.920 --> 00:02:10.460
three divided by three is one,

00:02:10.460 --> 00:02:11.870
seven divided by seven is one.

00:02:11.870 --> 00:02:13.390
Those all cancel out to one.

00:02:13.390 --> 00:02:15.030
So you're just left with one B

00:02:15.030 --> 00:02:17.510
or just to B and 30,

00:02:17.510 --> 00:02:20.206
or three-sevenths times 14,

00:02:20.206 --> 00:02:23.690
you might see this as 14 over one.

00:02:23.690 --> 00:02:24.790
And you could say okay,

00:02:24.790 --> 00:02:28.801
this is going to be three
times 14 over seven times one,

00:02:28.801 --> 00:02:29.730
or you could say,

00:02:29.730 --> 00:02:33.770
hey, let's divide both a numerator
and denominator by seven.

00:02:33.770 --> 00:02:36.280
So this could be two.
And this could be one.

00:02:36.280 --> 00:02:39.893
So your left with three
times two over one times one

00:02:39.893 --> 00:02:43.200
which is just going to be equal to six.

00:02:43.200 --> 00:02:45.550
Let's do another example.

00:02:45.550 --> 00:02:47.020
Let's say

00:02:47.020 --> 00:02:48.620
that we had

00:02:48.620 --> 00:02:51.530
one sixth A

00:02:51.530 --> 00:02:54.710
is equal to two-thirds.

00:02:54.710 --> 00:02:57.363
How could we think about solving for A.

00:02:58.380 --> 00:02:59.680
Well, once again, it would be nice,

00:02:59.680 --> 00:03:03.410
if this one-sixth were to become a one

00:03:03.410 --> 00:03:05.980
and we could do that by multiplying by 6.

00:03:05.980 --> 00:03:09.150
Six-sixths is the same thing as one.

00:03:09.150 --> 00:03:11.300
And to make it clear that
this is the reciprocal,

00:03:11.300 --> 00:03:15.120
we could just write six wholes as six ones

00:03:15.120 --> 00:03:18.350
or six wholes when you multiply these,

00:03:18.350 --> 00:03:20.080
this is all going to be equal to one.

00:03:20.080 --> 00:03:23.610
So you're left with one
A on the left-hand side,

00:03:23.610 --> 00:03:25.470
but of course, you can't just
do it on the left-hand side.

00:03:25.470 --> 00:03:28.840
You have to also do it
on the right-hand side.

00:03:28.840 --> 00:03:31.540
So A is going to be equal to,

00:03:31.540 --> 00:03:35.760
over here we could say two
times six over three times one.

00:03:35.760 --> 00:03:38.560
So that would be twelve-thirds

00:03:38.560 --> 00:03:39.620
or we could say,

00:03:39.620 --> 00:03:42.060
look, six and three are
both divisible by three.

00:03:42.060 --> 00:03:43.582
So six divided by three is two,

00:03:43.582 --> 00:03:45.585
three divided by three is one,

00:03:45.585 --> 00:03:48.940
two times two is four over one times one.

00:03:48.940 --> 00:03:53.053
So it's going to be four wholes
or just four and we're done.


Analyzing relationships between variables using tables and equations

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:03.850
- [Narrator] We're told Rava
is researching an electric car.

00:00:03.850 --> 00:00:07.710
She finds this graph,
which shows how much range,

00:00:07.710 --> 00:00:09.430
measured in kilometers,

00:00:09.430 --> 00:00:13.500
the car gains based on charging time.

00:00:13.500 --> 00:00:15.330
All right, and they say, first,

00:00:15.330 --> 00:00:18.410
fill in the missing
values in the table below.

00:00:18.410 --> 00:00:21.070
And if you are so
inspired, pause this video,

00:00:21.070 --> 00:00:24.070
and see if you can have
a go at that as well.

00:00:24.070 --> 00:00:25.540
All right, well they give us a few points,

00:00:25.540 --> 00:00:27.600
and I'm assuming these
are points on a line.

00:00:27.600 --> 00:00:31.790
And we can see when the
charging time is 15 minutes,

00:00:31.790 --> 00:00:33.540
the range is 180.

00:00:33.540 --> 00:00:36.430
So we could see when the
charging time is 15 minutes,

00:00:36.430 --> 00:00:38.920
the range is 180.

00:00:38.920 --> 00:00:43.030
We can see when the
charging time is 30 minutes,

00:00:43.030 --> 00:00:48.030
the range is 360 kilometers,
so I could write that there.

00:00:48.570 --> 00:00:53.570
And then we see when the
charging time is 45 minutes,

00:00:54.400 --> 00:00:59.270
the range is 540 kilometers.

00:00:59.270 --> 00:01:01.380
So that's all nice.

00:01:01.380 --> 00:01:03.390
But then they give us a
few other points here.

00:01:03.390 --> 00:01:07.200
They say what happens when
we are at T equals 10,

00:01:07.200 --> 00:01:10.940
or T equals one, which
aren't easy to pick out here?

00:01:10.940 --> 00:01:12.490
But this is where it might be useful,

00:01:12.490 --> 00:01:13.970
if we assume that this is a line,

00:01:13.970 --> 00:01:17.020
what is the relationship between these?

00:01:17.020 --> 00:01:19.910
So let's see, to go from 15 to 180,

00:01:19.910 --> 00:01:22.110
it looks like you're multiplying by 12.

00:01:22.110 --> 00:01:26.080
To go from 30 to 360, it looks
like we're multiplying by 12.

00:01:26.080 --> 00:01:28.420
To go from 45 to 540,

00:01:28.420 --> 00:01:31.260
it looks like we are multiplying by 12.

00:01:31.260 --> 00:01:34.130
So assuming K is just
going to be 12 times T,

00:01:34.130 --> 00:01:37.500
we know that when T equals one, K is 12,

00:01:37.500 --> 00:01:42.063
and when T equals 10, 10 times 12 is 120.

00:01:43.100 --> 00:01:45.530
All right, now the second part,
they say write an equation

00:01:45.530 --> 00:01:49.000
Rava can use to find out
how much charging time, T,

00:01:49.000 --> 00:01:54.000
it takes to gain any number
of kilometers in range, K.

00:01:54.460 --> 00:01:56.660
All right, well we already
established a relationship.

00:01:56.660 --> 00:02:01.660
We said that K is equal
to 12 times whatever T is.

00:02:02.640 --> 00:02:05.540
That's what we just established
in this table up here,

00:02:05.540 --> 00:02:06.870
but that's not what they want.

00:02:06.870 --> 00:02:09.500
They wanna find out how
much charging time, T,

00:02:09.500 --> 00:02:13.660
it takes to gain any number
of kilometers in range, K.

00:02:13.660 --> 00:02:17.050
So what we need to do here is solve for T.

00:02:17.050 --> 00:02:19.380
So let's divide both sides by 12

00:02:20.430 --> 00:02:23.820
to just have a T by itself
on the right-hand side.

00:02:23.820 --> 00:02:28.500
And we are going to be left
with T is equal to K over 12.

00:02:28.500 --> 00:02:31.010
T is equal to K over 12 and notice,

00:02:31.010 --> 00:02:34.070
you could put any number of
kilometers of range in here

00:02:34.070 --> 00:02:36.110
and you're essentially just
going to divide it by 12,

00:02:36.110 --> 00:02:38.110
and that will give you
how much charging time.

00:02:38.110 --> 00:02:41.130
And I guess this would assume
an infinitely large battery,

00:02:41.130 --> 00:02:42.900
which we know doesn't exist.

00:02:42.900 --> 00:02:45.380
But for the sake of this
problem, here we have it.

00:02:45.380 --> 00:02:47.883
Here is the equation Rava can use.


Writing equations for relationships between quantities

WEBVTT
Kind: captions
Language: en

00:00:00.250 --> 00:00:02.270
- [Narrator] We're told
Amad is going to walk

00:00:02.270 --> 00:00:06.030
20 kilometers for a charity fundraiser.

00:00:06.030 --> 00:00:07.290
In the first part of
this question, they say,

00:00:07.290 --> 00:00:10.980
write an equation that
represents how many hours, t,

00:00:10.980 --> 00:00:15.140
the walk will take if Amad
walks at a constant rate

00:00:15.140 --> 00:00:17.760
of r kilometers per hour.

00:00:17.760 --> 00:00:20.720
Pause this video and see if
you could have a go at that.

00:00:20.720 --> 00:00:23.120
All right, now let's work
through this together.

00:00:23.120 --> 00:00:25.050
So you might be familiar with the notion

00:00:25.050 --> 00:00:29.270
that distance is equal to rate times time.

00:00:29.270 --> 00:00:31.558
For example, if you were to walk at a rate

00:00:31.558 --> 00:00:35.100
of five kilometers per hour

00:00:35.100 --> 00:00:36.900
for two hours,

00:00:36.900 --> 00:00:40.180
you would say five times two,
five kilometers per hour,

00:00:40.180 --> 00:00:43.890
times two hours, would
give you 10 kilometers.

00:00:43.890 --> 00:00:45.210
Now in this situation,

00:00:45.210 --> 00:00:48.880
they've given us the number of kilometers

00:00:48.880 --> 00:00:50.610
or the distance in this situation,

00:00:50.610 --> 00:00:53.090
so in this situation d is equal to 20.

00:00:53.090 --> 00:00:55.840
So 20 is going to be equal to our rate,

00:00:55.840 --> 00:00:58.740
which we are told is going
to be r kilometers per hour,

00:00:58.740 --> 00:01:02.600
times our time, which is t hours.

00:01:02.600 --> 00:01:04.890
Now they're asking us for an equation

00:01:04.890 --> 00:01:08.330
that represents how many
hours the walk will take

00:01:08.330 --> 00:01:11.340
if Amad walks at a constant rate of r.

00:01:11.340 --> 00:01:12.750
So the way that it's phrased,

00:01:12.750 --> 00:01:15.960
it sounds like they
want us to solve for t,

00:01:15.960 --> 00:01:19.510
where t is going to be equal
to some expression here

00:01:19.510 --> 00:01:23.500
that deals with r and
probably some other things,

00:01:23.500 --> 00:01:27.690
so if we put in any r here,
then we can get the time.

00:01:27.690 --> 00:01:29.450
So if we know what the rate is,

00:01:29.450 --> 00:01:30.760
if you put that in here,

00:01:30.760 --> 00:01:32.460
because it's already solved for t,

00:01:32.460 --> 00:01:34.540
we'll be able to solve for that time.

00:01:34.540 --> 00:01:37.340
You could think of r as
the independent variable

00:01:37.340 --> 00:01:39.260
that you could try
different values out for,

00:01:39.260 --> 00:01:41.050
and that t is the dependent variable.

00:01:41.050 --> 00:01:44.100
It's the thing that we have solved for.

00:01:44.100 --> 00:01:45.080
So let's do that.

00:01:45.080 --> 00:01:49.870
Let's rewrite this expression
here by solving for t

00:01:49.870 --> 00:01:52.040
and I could do it right over here.

00:01:52.040 --> 00:01:55.080
If I have 20 is equal to rt,

00:01:55.080 --> 00:01:58.270
if I wanna solve for t, what can I do?

00:01:58.270 --> 00:02:01.033
Well, I could divide both sides by r.

00:02:01.970 --> 00:02:03.970
If I do that on the right-hand side,

00:02:03.970 --> 00:02:05.360
then I'm just left with a t here,

00:02:05.360 --> 00:02:07.620
because an r divided by r is just one.

00:02:07.620 --> 00:02:09.410
And on the left, I have 20 over r,

00:02:09.410 --> 00:02:13.900
so I have t is equal to 20 over r

00:02:13.900 --> 00:02:14.733
and we're done.

00:02:14.733 --> 00:02:17.675
This will tell us how many hours Amad

00:02:17.675 --> 00:02:20.590
will take to walk based on the rate.

00:02:20.590 --> 00:02:21.423
You give me a rate.

00:02:21.423 --> 00:02:22.620
I'm just gonna divide 20 by that

00:02:22.620 --> 00:02:24.210
and I'm going to give you t.

00:02:24.210 --> 00:02:25.720
You might say, why is this useful?

00:02:25.720 --> 00:02:28.150
Well, this is useful because
now that we have it written

00:02:28.150 --> 00:02:30.940
this way, any time
someone gives an r to you,

00:02:30.940 --> 00:02:33.103
you just take 20 divided
by that and it essentially

00:02:33.103 --> 00:02:36.320
is already gonna solve
for what your time is,

00:02:36.320 --> 00:02:40.010
how long Amad's gonna have to walk.

00:02:40.010 --> 00:02:42.610
Question two, how many
hours will the walk take

00:02:42.610 --> 00:02:44.500
if Amad walks at a constant rate

00:02:44.500 --> 00:02:46.640
of 6 kilometers per hour?

00:02:46.640 --> 00:02:48.020
Well, here is an example of that,

00:02:48.020 --> 00:02:50.030
where they are giving us the actual rate

00:02:50.030 --> 00:02:51.320
and they want the time.

00:02:51.320 --> 00:02:54.620
So we just take the 6
and replace it in for r,

00:02:54.620 --> 00:02:58.280
so we get t is equal to 20 over 6,

00:02:58.280 --> 00:03:01.710
which is 3 and 1/3 hours,

00:03:01.710 --> 00:03:04.500
which would be the same thing
as 3 hours and 20 minutes,

00:03:04.500 --> 00:03:06.360
depending on how you wanna view it.

00:03:06.360 --> 00:03:08.163
Let's do another example here.

00:03:09.550 --> 00:03:12.100
So here we're told at the end of each day,

00:03:12.100 --> 00:03:14.390
a restaurant makes soup
with whatever amount

00:03:14.390 --> 00:03:16.610
of vegetable stock is unused that day.

00:03:16.610 --> 00:03:18.630
Let me re-center this a little bit.

00:03:18.630 --> 00:03:22.950
The soup recipe calls for
400 milliliters of water

00:03:22.950 --> 00:03:27.330
for every 500 milliliters
of vegetable stock.

00:03:27.330 --> 00:03:30.810
Write an equation that
represents how much water

00:03:30.810 --> 00:03:34.400
the restaurant should use,
and we'll use the variable w,

00:03:34.400 --> 00:03:38.070
with any amount of vegetable stock, v.

00:03:38.070 --> 00:03:40.660
All right, and then we'll do
part two right after that,

00:03:40.660 --> 00:03:43.040
so let's look at this,
400 milliliters of water

00:03:43.040 --> 00:03:45.400
for every 500 milliliters
of vegetable stock.

00:03:45.400 --> 00:03:47.350
And so to get my head around this,

00:03:47.350 --> 00:03:48.970
I like just to think about,

00:03:48.970 --> 00:03:50.480
let's put a little table here,

00:03:50.480 --> 00:03:52.880
and so you could say amount of water,

00:03:52.880 --> 00:03:54.250
let me write it this way,

00:03:54.250 --> 00:03:58.720
water and vegetable stock,

00:03:58.720 --> 00:04:01.093
vegetable stock.

00:04:02.100 --> 00:04:05.120
So for every 500 milliliters
of vegetable stock,

00:04:05.120 --> 00:04:07.680
so if you had 500 milliliters
of vegetable stock,

00:04:07.680 --> 00:04:09.180
and I won't write the milliliters,

00:04:09.180 --> 00:04:11.870
then you're going to have
400 milliliters of water.

00:04:11.870 --> 00:04:15.580
If you had 1,000 here,
which is two times that,

00:04:15.580 --> 00:04:17.120
well, you're gonna have
twice as much water,

00:04:17.120 --> 00:04:19.140
which is going to be 800.

00:04:19.140 --> 00:04:22.080
And so you can see this
relationship that's forming.

00:04:22.080 --> 00:04:24.580
No matter what the vegetable stock is,

00:04:24.580 --> 00:04:28.360
if you essentially take 4/5 of that,

00:04:28.360 --> 00:04:29.910
that is the amount of water.

00:04:29.910 --> 00:04:32.350
You take 4/5, that is the amount of water.

00:04:32.350 --> 00:04:35.360
So if you had only 5
milliliters of vegetable stock,

00:04:35.360 --> 00:04:39.150
you take 4/5, you get the amount of water.

00:04:39.150 --> 00:04:42.610
So another way to think
about it is the water

00:04:42.610 --> 00:04:44.560
that you need to use is going to be 4/5

00:04:45.680 --> 00:04:48.570
of the amount of vegetable stock

00:04:48.570 --> 00:04:50.690
that you are going to be using,

00:04:50.690 --> 00:04:53.870
and so actually we just did part one.

00:04:53.870 --> 00:04:56.090
We wrote an equation that
represents how much water

00:04:56.090 --> 00:04:59.280
the restaurant should use with
any amount of vegetable stock

00:04:59.280 --> 00:05:00.650
and the way that they phrased it,

00:05:00.650 --> 00:05:05.310
we're solving for w given
some v that you might have.

00:05:05.310 --> 00:05:07.330
And since we're solving for w here,

00:05:07.330 --> 00:05:09.450
we would consider w the dependent variable

00:05:09.450 --> 00:05:10.680
and v as the independent variable.

00:05:10.680 --> 00:05:12.880
You can give me different vs

00:05:12.880 --> 00:05:15.730
and then I can put that into
this little equation here,

00:05:15.730 --> 00:05:17.850
and I can solve for the w,

00:05:17.850 --> 00:05:19.890
so we've done the first part.

00:05:19.890 --> 00:05:23.230
If there are 800 milliliters
of unused vegetable stock,

00:05:23.230 --> 00:05:27.160
how much water should the
restaurant use to make soup?

00:05:27.160 --> 00:05:29.720
Well, we can just take this 800

00:05:29.720 --> 00:05:32.740
and substitute it in for
v to figure that out.

00:05:32.740 --> 00:05:34.770
In this situation, the
amount of water to use

00:05:34.770 --> 00:05:39.770
is 4/5 times 800,

00:05:40.020 --> 00:05:44.280
and that's going to be,
let's see, 800 divided by 5,

00:05:44.280 --> 00:05:49.280
100 divided by 5 is 20 and so,

00:05:49.290 --> 00:05:50.330
and then you're gonna have 8 of those,

00:05:50.330 --> 00:05:54.550
so it's 160, so this was 160 times 4

00:05:54.550 --> 00:05:58.560
is equal to 640 milliliters,

00:05:58.560 --> 00:06:00.203
and we are done.


Dependent & independent variables

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:03.280
- [Teacher] Let's say that
you love to eat apples,

00:00:03.280 --> 00:00:06.360
and you are going to buy a apples,

00:00:06.360 --> 00:00:08.250
so a is the number of apples,

00:00:08.250 --> 00:00:11.100
number of apples,

00:00:11.100 --> 00:00:12.410
but you also have a budget,

00:00:12.410 --> 00:00:13.880
so you have to care about costs,

00:00:13.880 --> 00:00:17.990
so let's say C is equal to the total cost,

00:00:17.990 --> 00:00:21.530
and let's say that the
price of an apple is $2,

00:00:21.530 --> 00:00:24.483
so $2 per apple.

00:00:25.530 --> 00:00:28.950
There's several ways that we
can express the relationship

00:00:28.950 --> 00:00:31.840
between the total cost
and the number of apples.

00:00:31.840 --> 00:00:34.930
One way is if we solve for the total cost,

00:00:34.930 --> 00:00:38.400
and we say, okay, the total
cost is gonna be $2 per apple

00:00:38.400 --> 00:00:40.250
times the number of apples,

00:00:40.250 --> 00:00:41.403
so it's going to be 2a.

00:00:43.210 --> 00:00:46.270
Another way that we could rewrite this

00:00:46.270 --> 00:00:49.440
if we were to divide both
sides of this by two,

00:00:49.440 --> 00:00:52.730
we would get that the number of apples

00:00:52.730 --> 00:00:57.730
is equal to cost over two.

00:00:57.900 --> 00:01:00.700
These are equivalent
expressions I should say

00:01:00.700 --> 00:01:02.470
these are equivalent equations,

00:01:02.470 --> 00:01:04.310
but the way they've been written,

00:01:04.310 --> 00:01:06.770
make it useful for different scenarios.

00:01:06.770 --> 00:01:09.360
For example, on the left-hand side here,

00:01:09.360 --> 00:01:11.760
it's really easy to try out different As

00:01:11.760 --> 00:01:14.680
and then think about how
that will affect the cost,

00:01:14.680 --> 00:01:16.790
and so when it's written like this,

00:01:16.790 --> 00:01:18.030
we would call the variable

00:01:18.030 --> 00:01:19.930
that it's easy to try
out different values,

00:01:19.930 --> 00:01:22.880
we would call that the
independent variable,

00:01:22.880 --> 00:01:25.580
independent variable,

00:01:25.580 --> 00:01:28.870
and then the one that we
are essentially solving for

00:01:28.870 --> 00:01:30.420
that we then spit out a value

00:01:30.420 --> 00:01:32.780
after we compute using
the independent variable,

00:01:32.780 --> 00:01:34.860
you call that the dependent variable.

00:01:34.860 --> 00:01:36.280
You could view it as,

00:01:36.280 --> 00:01:37.960
look in this situation,

00:01:37.960 --> 00:01:40.970
the cost is dependent
on the number of apples

00:01:40.970 --> 00:01:42.580
you choose to eat.

00:01:42.580 --> 00:01:44.180
Now, when we wrote it over here,

00:01:44.180 --> 00:01:45.380
this looks a little bit different.

00:01:45.380 --> 00:01:48.900
Now the number of apples is solved for,

00:01:48.900 --> 00:01:52.890
and we compute how many
apples based on the cost,

00:01:52.890 --> 00:01:55.660
so this would be a scenario
where you have a budget

00:01:55.660 --> 00:01:57.310
and you tell me what the budget is

00:01:57.310 --> 00:01:59.350
and I could tell you the number of apples.

00:01:59.350 --> 00:02:00.640
So in this situation,

00:02:00.640 --> 00:02:02.660
C is the independent variable,

00:02:02.660 --> 00:02:04.740
and since we have solved for a,

00:02:04.740 --> 00:02:07.170
a is the dependent variable.

00:02:07.170 --> 00:02:09.700
This is useful if I give
you a number of apples

00:02:09.700 --> 00:02:11.200
and you want to know the total cost,

00:02:11.200 --> 00:02:14.000
and this is useful if
you have a certain cost

00:02:14.000 --> 00:02:17.993
and then you want to find
out the number of apples.


Writing expressions with parentheses

WEBVTT
Kind: captions
Language: en

00:00:00.150 --> 00:00:01.470
- [Narrator] We have
two different statements

00:00:01.470 --> 00:00:02.303
written in English

00:00:02.303 --> 00:00:04.800
that I would like you to pause this video

00:00:04.800 --> 00:00:07.373
and try to write as an
algebraic expression.

00:00:08.230 --> 00:00:10.650
All right, now let's
work on this first one.

00:00:10.650 --> 00:00:12.374
So you might be tempted to
say, all right, I have five.

00:00:12.374 --> 00:00:14.300
So let me just write a five,

00:00:14.300 --> 00:00:15.960
times and I'll write a dot

00:00:15.960 --> 00:00:17.420
because when we're dealing with algebra,

00:00:17.420 --> 00:00:19.970
if you write a traditional
multiplication sign,

00:00:19.970 --> 00:00:21.630
it can get confused with an X.

00:00:21.630 --> 00:00:23.120
So five times

00:00:23.120 --> 00:00:24.730
the difference of X and two.

00:00:24.730 --> 00:00:25.980
The difference of X and two,

00:00:25.980 --> 00:00:30.050
we could write as X minus two,

00:00:30.050 --> 00:00:32.460
but this expression has a problem

00:00:32.460 --> 00:00:33.990
because whoever's interpreting it,

00:00:33.990 --> 00:00:35.730
if they're following order of operations,

00:00:35.730 --> 00:00:36.920
which they should,

00:00:36.920 --> 00:00:38.510
that would mean that they would multiply

00:00:38.510 --> 00:00:39.970
the five and the X first

00:00:39.970 --> 00:00:41.600
and then subtract two.

00:00:41.600 --> 00:00:43.390
But that's not what's
going on in the sentence.

00:00:43.390 --> 00:00:45.030
It's five times,

00:00:45.030 --> 00:00:47.290
not X, but the difference of X and two.

00:00:47.290 --> 00:00:48.950
So what you need to do is

00:00:48.950 --> 00:00:50.590
put parentheses here

00:00:50.590 --> 00:00:52.240
to make sure that you take the difference

00:00:52.240 --> 00:00:53.730
of X and two first,

00:00:53.730 --> 00:00:56.480
and then multiply that by five.

00:00:56.480 --> 00:00:58.100
Now, with that in mind,

00:00:58.100 --> 00:01:00.440
let's tackle this example right over here,

00:01:00.440 --> 00:01:02.603
10 times the sum of Y and three.

00:01:03.460 --> 00:01:04.293
Well, once again,

00:01:04.293 --> 00:01:07.000
if you just wrote 10 times

00:01:07.000 --> 00:01:08.030
the sum

00:01:08.030 --> 00:01:09.690
of Y and three,

00:01:09.690 --> 00:01:11.520
you'll run into the same problem.

00:01:11.520 --> 00:01:13.070
someone would interpret this as,

00:01:13.070 --> 00:01:14.879
hey, maybe I should
multiply 10 and Y first,

00:01:14.879 --> 00:01:17.800
because that's what order of
operations would tell me to do,

00:01:17.800 --> 00:01:18.750
but that's not what we want.

00:01:18.750 --> 00:01:20.780
We want 10 times, not just Y,

00:01:20.780 --> 00:01:23.050
but the sum of Y and three.

00:01:23.050 --> 00:01:24.590
So that's where the parentheses

00:01:24.590 --> 00:01:26.260
are really important to make sure

00:01:26.260 --> 00:01:28.930
that we take the sum of Y and three first

00:01:28.930 --> 00:01:31.263
and then multiply that by 10.


Writing algebraic subtraction expressions

WEBVTT
Kind: captions
Language: en

00:00:00.120 --> 00:00:01.550
- [Instructor] We have
different statements here

00:00:01.550 --> 00:00:05.240
that can each be expressed
as an algebraic expression,

00:00:05.240 --> 00:00:07.110
and as you might have guessed,

00:00:07.110 --> 00:00:09.750
I would love you to pause this video

00:00:09.750 --> 00:00:12.480
and try to write each of these statements

00:00:12.480 --> 00:00:15.273
as an algebraic expression
before we do it together.

00:00:16.700 --> 00:00:19.360
All right, now let's work on it together.

00:00:19.360 --> 00:00:24.360
So this first statement,
we have two less than x.

00:00:24.410 --> 00:00:27.390
So my brain thinks, all
right, let me start with x,

00:00:27.390 --> 00:00:29.340
and how am I going to
get two less than that?

00:00:29.340 --> 00:00:31.920
Well, I'm going to subtract two.

00:00:31.920 --> 00:00:33.630
And this is an interesting example

00:00:33.630 --> 00:00:35.580
because you see the order that we see it

00:00:35.580 --> 00:00:37.840
in the sentence is not the order

00:00:37.840 --> 00:00:39.450
that we would necessarily write it

00:00:39.450 --> 00:00:41.300
in the expression right over here.

00:00:41.300 --> 00:00:44.380
Very important to think
about, what is going on here?

00:00:44.380 --> 00:00:47.290
What is being described?

00:00:47.290 --> 00:00:51.340
Now, this next statement,
y fewer than three.

00:00:51.340 --> 00:00:54.760
Well, in my mind, I'm
going to start with three

00:00:54.760 --> 00:00:57.060
and I'm going to be y fewer than that.

00:00:57.060 --> 00:00:58.760
So I'm gonna start with three

00:00:58.760 --> 00:01:02.480
and then I'm going to
be y fewer than that.

00:01:02.480 --> 00:01:04.420
Now, these first two
statements are similar

00:01:04.420 --> 00:01:06.760
in that you have something
less than something else

00:01:06.760 --> 00:01:08.930
or something fewer than something else.

00:01:08.930 --> 00:01:11.963
They just swapped the
number and the variable.

00:01:12.850 --> 00:01:17.850
Now, this third statement,
x decreased by five.

00:01:18.580 --> 00:01:20.710
So my mind is thinking,
what am I starting with?

00:01:20.710 --> 00:01:24.810
I'm starting with an x and
I'm decreasing it by five.

00:01:24.810 --> 00:01:26.670
So I can do that as minus five,

00:01:26.670 --> 00:01:28.793
or I'm gonna take five away from it.


Evaluating expressions like 5x² & ⅓(6)ˣ

WEBVTT
Kind: captions
Language: en

00:00:00.120 --> 00:00:02.050
- [Instructor] What I
want you to do is evaluate

00:00:02.050 --> 00:00:04.340
the expression 5x squared

00:00:04.340 --> 00:00:07.150
when x is equal to three.

00:00:07.150 --> 00:00:09.100
Pause this video and have a go at that.

00:00:10.530 --> 00:00:12.220
All right, well, we just have to think

00:00:12.220 --> 00:00:14.050
about every place we see an x,

00:00:14.050 --> 00:00:16.000
we'll now replace it with a three.

00:00:16.000 --> 00:00:18.500
So this is going to be
equivalent to five times,

00:00:18.500 --> 00:00:19.780
instead of x squared,

00:00:19.780 --> 00:00:23.800
it's going to be five times three squared.

00:00:23.800 --> 00:00:25.500
And we know from order of operations,

00:00:25.500 --> 00:00:26.980
we do the exponents first.

00:00:26.980 --> 00:00:28.520
That's why I actually put a parentheses

00:00:28.520 --> 00:00:31.060
around the three squared
to just make that clear.

00:00:31.060 --> 00:00:33.940
And three squared is,
of course, equal to nine

00:00:33.940 --> 00:00:38.750
and five times nine is equal to 45.

00:00:38.750 --> 00:00:41.810
Let's do another example
that's a little bit different.

00:00:41.810 --> 00:00:44.610
Let's say I have the expression 1/3

00:00:44.610 --> 00:00:49.000
times six to the x power,

00:00:49.000 --> 00:00:53.800
and I want to evaluate it
when x is equal to two.

00:00:53.800 --> 00:00:56.443
Pause the video again and
see if you can work that out.

00:00:57.300 --> 00:00:59.590
Well, once again, everywhere
where we see an x,

00:00:59.590 --> 00:01:00.980
we'll replace that with a two.

00:01:00.980 --> 00:01:02.320
So this is going to be the same thing

00:01:02.320 --> 00:01:06.880
as 1/3 times six squared.

00:01:06.880 --> 00:01:10.360
Where we saw the x, we now
replace that with a two.

00:01:10.360 --> 00:01:12.780
And so this is going to be equal to,

00:01:12.780 --> 00:01:15.560
we do the exponent first,
order of operations,

00:01:15.560 --> 00:01:17.190
so it's going to be 1/3

00:01:17.190 --> 00:01:20.790
times six squared is 36,

00:01:20.790 --> 00:01:24.603
and 1/3 of 36 is equal to 12.

00:01:24.603 --> 00:01:25.771
And we're done!