Name: 【TED-Ed】「1」是「1」…還是？ One is one ... or is it? - Christopher Danielson
Uploaded: 2013-07-04T15:25:57.000Z
Duration: 3 min 55 s

Which is correct -- a dozen eggs is? Or a dozen eggs are?

哪個是正確的──a dozen eggs "is" 或者 a dozen eggs "are"？

and my teachers making a big deal about the unit.

我們老師教了很多關於數量單位詞。

And I never really got that, until one day I was in the grocery store,

但我從沒有學會，直到有一天我到雜貨店，

and I wanted to buy an apple, but I couldn't buy one apple.

我想買一顆蘋果（an apple）， 不過我卻不能買「一」蘋果  （one apple）。

這表示我必須買一整袋的蘋果。

所以我做了，我買了一整袋的蘋果，

I took it home, I took one apple out of the bag, and I cut it up.

我把它拿回家，我從袋子拿出一顆蘋果並切開，

Well, they all are, of course, and that's what my elementary teachers were trying to tell me.

好吧，他們都是，當然，而且 那正是我小學老師一直試著告訴我的。

Because this is the important idea behind

whole number place value, decimal place value and fractions.

Our whole number system depends on being able to change what we count as one.

我們所使用的數字系統要能夠轉換我們所熟悉的「一」。

Our whole number system depends on being able to change units.

我們所使用的數字系統要能夠轉換「單位」。

we take a bunch of things and we put them together to make a bigger thing,

我們把一大堆的東西放在一起，讓他們變成更大的東西。

We take 12 eggs, put them together to make a group,

我們把十二顆雞蛋放在一起，組合成一組，

a deck of cards, a pair of shoes, a jazz quartet

一副牌、一雙鞋、爵士四重奏，

and, of course, Barbie and Ken make a couple.

當然還有，芭比和肯尼組合成一對情侶。

because we don't get a whole bunch of slices from a whole bunch of different bakeries

因為我們不會從不同的麵包店拿一片片切好的麵包

將它們放在一起變成一條麵包。

No, we start with a loaf of bread and we cut it into smaller pieces

不是這樣，我們是把一條麵包切成更小的麵包

called slices, so each slice of bread is a partitioned unit.

並叫它「一片」麵包，所以每一片麵包就是一個分割單位。

Other examples of partitioned units include

a square of a chocolate bar, a section of an orange

The important thing about units is that once we've made a new unit,

重要的是，一旦我們創造新的單位，

we can treat it just like we did the old unit.

我們就能用跟舊的單位同樣的方法使用它。

We can compose composed units, and we can partition partitioned units.

我們可以組成組合單位，也可以分成分割單位。

and then those packs get put together in sets of four

So when I buy one box of toaster pastries,

And when I share a slice of pizza with a friend,

當我跟我的朋友分享一片披薩，

we have to cut it into two smaller pieces.

我們必須將它切成更小的兩個。

但這些到底跟數學有甚麼關係？

數學中，所有東西都是確定的。

Two plus two equals four, and one is just one.

and we count up to nine -- one, two, three, four, five, six, seven, eight, nine.

一直數到9──1、2、3、4、5、6、7、8、9。

And then we get to 10, and in order to write 10,

接下來我們數到10了，而為了寫下10這個數字，

其中的1就表示我們有了一個群組，

and the zero helps us remember that it means one group, not one thing.

而0幫助我們記得這是指一組，而不是一個。

just like a dozen eggs, just like an egg,

就像一打雞蛋，就像一顆雞蛋，

So when I think about 100, it's like the box of toaster pastries.

所以當我們在想100是什麼的時候，它就像那一盒零食。

那就取決於那個「一」是指甚麼，

So think about all the times in math when you write the number one.

所以碰到數學需要寫「一」的時候，要一直想著這件事。

不管這個「一」是放在哪個位置，

no matter how many things that one represents,

不管這個「一」裡有多少東西，