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```Introduction to area and unit squares（面積と単位正方形の基礎）

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So we've got two figures right over here, and
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ここに図形が 2 つあります。それぞれ画面で見て、どのくら
I want to think about how much space they
いの広さがあるでしょう
And this idea of how much space something
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takes up on a surface. This idea is area.
どれほどの広さかを問われたにときに必要なのが、面積と
いう考え方です
So, right when you look at it, it looks pretty
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clear that this purple figure takes up more
パッと見て分かるように、ピンク紫のほうが、青よりも広い

space on my screen than this blue figure,
but how do we actually measure it? How do
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we actually know how much more area this
それは、どのように測ればいいのでしょう。具体的にピンク

purple figure takes up than this blue one?
Well, one way to do it would be to define a
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そこで、広さの基準となるものを決めます
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この正方形は、どんな単位でも構いません。これ 1 つが
unit amount of area.
So, for example, I could create a square over
here,
And this square, whatever units we're using,
we could say its one unit, Its width right over
1 単位面積で、横の長さが 1 単位
here is one unit,
and its height over here is one unit.
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こちらの縦も 1 単位の長さです
We could call this a unit square. A unit
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これを、単位正方形と呼びます。単位正方形です
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square.
So, one way to measure the area of these
figures is to figure out how many unit

squares I could cover this thing with without
う方法があります
overlapping
and
while
staying
in
the
boundaries.
So let's try to do that. Let's try to cover each
of
these
with unit squares,
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ではこの 2 つに、単位正方形がいくつ入るかを調べ、面

and then
essentially, we'll have a measure of area.
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まずは青いほうから
So we could put 1,
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ここに 1 つ目
2
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2
3, 3,
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3、3 つ目
4
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4
5
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5
5 unit squares.
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1:36

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1, 2, 3, 4, 5。単位正方形が 5 つ分です。分かりやす
Let me write this down. So we
got
1, 2, 3, 4, 5 unit squares -- and I could draw
the boundary between those unit squares a
く境目を書きますよ
little bit clearer -so we have 5 unit squares.
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And so we could say that this figure right
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こういう場合、この図形の面積は、5 単位面積ある、と
over here has an area - the area is five.

1/3
We could say five unit squares, but the more
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typical way of saying it is that you have 5

square, 5 square units.
That's the area over here. Now let's do the
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same thing with this purple figure. So with
この図形の次は、こっちのピンク紫のほうの面積を求めま
しょう
the purple figure,
I could put 1,
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まずは 1 つ目
2,
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2
3
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3
4,
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4
5,
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5
6
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6
7,
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7
8,
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8
9,
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9
10 of these unit squares I can cover. They're
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10。単位正方形が 10 個分です。このように単位正方
not overlapping, or I'm trying pretty close to

not make them overlap, but you see you can

fit ten of them, and let me draw the
boundary between them,
so you can see a little bit clearer.
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そのほうがわかりやすいですね
So, that's the boundary between my unit
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Between my unit squares. So, there you go,
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and we can count them.
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ここで数えます
1,2,3,4,5,6,7
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1,2,3,4,5,6,7
8 , 9 , 10
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8 , 9 , 10
So we could say the area -- and let me divide
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こちらの面積は…こっちも分かりやすく、境目を黒で書き
squares.
these with the black boundary too, it makes

things a little bit clearer than blue -So the area here for the purple figure
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こちらのピンク紫の面積は
we could say the area here is equal to 10, 10
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square, square units.
So what we have here - we have an idea of
るということです
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さてここで、面積が求められました
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こちらのほうが、大きいと目測することもできますが、これ
how much space something takes up on a
surface,
and you could eyeball it, say, "Hey this takes
up more space." But now we've come up
で面積を求めることができるようになったわけです
with a way of measuring it.
We can define a unit square-- here it's a 1
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unit by 1 unit -- in the future we'll see that it
この 1 単位掛ける 1 単位の単位正方形を、例えば、1

could be a could be a unit centimeter, a 1
1 メートルとして 1 平方メートル。1 単位を 1 フィートとし
centimeter by 1 centimeter square; it could
て、1 平方フィートで測れます
be a 1 meter by 1 meter square; it could be a
2/3
1 foot by 1 foot square;
but then we can use that to actually measure
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さて、このようして面積を測っていったところ
This thing has an area of 5 square units;
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この面積は 5 単位面積
this thing has an area of 10 square units.
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こっちは 10 単位面積です
So this one we can actually say has twice the
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よって、具体的にこっちのほうが 2 倍広い、ピンク紫のほ
the area of things.
area - the purple figure had twice the area -
うは 10 単位面積あって、青いほうと比べて 2 倍の面積
it's 10 square units - as the blue figure. It
を持つということが示せます
takes up twice the amount of space on the
screen.
Translator: Ai Kubota