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Math 3: The Wonderful World of Scaling (Maps) 62 Views


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Description:

Scale models aren't just for planes, trains, and Star Wars action figures... time to talk about maps.

Language:
English Language

Transcript

00:03

[Dino and Coop singing]

00:12

If you've ever been on a road trip, you've probably seen your fair share of maps. [Man holding map with wife and child standing outside of their car]

00:16

You've probably also seen your fair share of gas station bathrooms, but we're not going

00:20

to cover those in this video… [Man walks into gas station bathroom]

00:21

things we've seen….

00:23

Ahem.

00:25

Instead, we'll be thinking about maps, and how they're a kind of scaled image.

00:28

A scaled image is a representation of something… [Barbie dolls either side of a weighing scale]

00:31

…but it's either much smaller…

00:32

…or much larger than that original thing.

00:35

Either way, all of the different parts of the image keep the same relative size to each [Man stood in bedroom with a poster of himself behind him]

00:39

other.

00:40

For example, if you make a scaled image of an elephant's head that's smaller than its

00:43

actual head, its ears will still be really big compared to the rest of its face. [An elephant standing beside a picture of another elephant]

00:47

Though if the elephant's a bit self-conscious, a scaled image isn't gonna help them out.

00:52

Maybe some big earmuffs would do the trick? [Elephant wearing giant ear muffs]

00:54

Scaled images are really important when it comes to making maps.

00:57

Take a look at this map of the United States.

00:59

At a glance, we can see the mountain ranges in the west… [Map of the United State showing the western mountain ranges]

01:02

…as well as the long coastline of the east.

01:05

Without a map, the only way you'd be able to see all that stuff at once is if you were

01:09

in space. [Astronaut floating in space looking down on Earth]

01:10

Though unless you've got hundreds of millions of dollars lying around that you're willing

01:13

to spend on a space vacay, you might wanna stick with the two buck map.

01:17

Okay, let's think about Lake Michigan, one of the Great Lakes. [Finger points to Lake Michigan on a map]

01:20

If you travelled there and stood on its shores, you'd be able to see that it's huge, with

01:25

big waves, like an ocean, but it'd be hard to tell much else about it. [Man holding surfboard on Lake Michigan shoreline]

01:29

On the other hand, if we were to look at a scaled image of Lake Michigan on a map, we'd

01:33

learn all sorts of stuff.

01:35

Since scaled images are exactly like the originals, just a different size, we'd learn that Lake [Woman points to scaled image of Lake Michigan]

01:39

Michigan is long and narrow, just like it is on the map.

01:43

Plus, since different parts of a scaled image have the same size relative to each other,

01:47

we'd also be able to tell that Lake Michigan is bigger than Lake Erie… [Lake Michigan and Lake Erie circled on the map]

01:51

…but much smaller than Lake Superior.

01:53

Good luck figuring all that out from the middle of Lake Michigan. [Woman stood on a boat in Lake Michigan]

01:56

All you'll learn there is that it's not very fun being wet and cold in the middle of a

02:00

lake, but you probably could have guessed that.

02:02

Similarly, Rhode Island might seem pretty huge if you're walking around it…[Woman walking down the streets of Rhode Island]

02:05

…but if we take a look at a map, we see that it's tiny!

02:09

Well…tiny compared to California.

02:10

A good map shows the real relative sizes of everything on it. [Map of United States with California circled]

02:14

And that's that!

02:15

Now if you'd excuse us, we've got a giant pair of earmuffs to make! [Man wearing giant pair of ear muffs]

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