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

哪個是正確的──a dozen eggs &quot;is&quot; 或者 a dozen eggs &quot;are&quot;？

• I remember being in elementary school,

我記得當我在小學的時候，

• 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。

• So I did. I bought one bag of apples,

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，

• And then I ate one slice.

然後吃了一片。

• One bag, one apple, one slice.

一袋、一顆、一片。

• Which of these is the real one?

哪一個才是真實的那一個？

• 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

因為這是一個重要的概念關於

• whole number place value, decimal place value and fractions.

整數位、小數點位與分數。

• 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」。

• There are two ways to change units.

有兩個方式能夠轉換單位。

• We can compose, and we can partition.

我們可以組合，也可以分割。

• When we compose units,

當我們組合多個單位時，

• 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。

• like a dozen eggs.

就像一打雞蛋一樣。

• 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，

• and we call that group a dozen.

然後我們叫這一組「一打」。

• A dozen eggs is a composed unit.

一打雞蛋就是一種組合單位。

• Other examples of composed units include

其他組合單位的例子包括：

• 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。

但想想看一條麵包。

• That's not a composed unit,

那不是一種組合單位，

• 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

• and put them together to make a loaf.

將它們放在一起變成一條麵包。

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

其他分割單位的例子包括：

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

一塊巧克力、一片柳橙，

• and a slice of pizza.

還有一片披薩。

• 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。

想想看那些零食。

• They come in packs of two,

他們兩片包成一袋，

• and then those packs get put together in sets of four

然後再把四袋放在一起

• to make a box.

變成一盒。

• So when I buy one box of toaster pastries,

所以當我買一盒零食時，

• am I buying one thing,

我是買了「一個」？

• four things, or eight things?

「四個」？還是「八個」？

• It depends on the unit.

這取決於單位。

• One box, four packs, eight pastries.

一盒、四袋、八片。

• 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。

• So a box of toaster pastries

所以一盒零食

• is composed of composed units,

是一個組合單位的組成，

• and when I split a slice of pizza,

而當我切開一片披薩時，

• I'm partitioning a partitioned unit.

我正在切出一個分割單位。

• But what does that have to do with math?

但這些到底跟數學有甚麼關係？

• In math, everything is certain.

數學中，所有東西都是確定的。

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

2+2=4，1就是1。

• But that's not really right.

但那不全然正確。

• One isn't always one.

1不一定永遠是1。

• Here's why: We start counting at one,

這就是原因：我們從1開始數，

• 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，

• we write a one and a zero.

我們寫了一個1和一個0。

• That one means that we have one group,

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。

• But 10, just like one,

但是10，就像1，

• just like a dozen eggs, just like an egg,

就像一打雞蛋，就像一顆雞蛋，

• 10 is a unit.

10是一個單位。

• And 10 tens make 100.

而十個10變成100。

• 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。

• Is 100 one thing,

100是一個東西？

• 10 things

10個？

• or 100 things?

或是100個？

• And that depends on what one is,

那就取決於那個「一」是指甚麼，

• it depends on what the unit is.

也就是單位是什麼。

• 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。

• No matter what place that one is in,

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，

• one is.

「一」就是...

(Music)

(音樂)

B1 中級 中文 TED-Ed 單位 麵包 組合 雞蛋 零食

# 【TED-Ed】「1」是「1」…還是？ One is one ... or is it? - Christopher Danielson

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VoiceTube 發佈於 2013 年 07 月 04 日