TED演讲:一就是一吗(1)

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　　I remember being in elementary school, and my teachers making a big deal about the unit. 我记得上小学的时候，我们老师教了很多数量单位词。

　　And I never really got that, until one day I was in the grocery store, and I wanted to buy an apple, 但我从没有学会，直到有一天，我到杂货店买苹果（an apple），

　　but I couldn't buy one apple. I had to buy a whole bag of apples. 不过我不能买一个（one apple），而是必须买一整袋。

　　So I did. I bought one bag of apples, I took it home, I took one apple out of the bag, and I cut it up. 于是我买了一整袋苹果，把它拿回了家，我从袋子拿出一颗苹果并切开。

　　And then I ate one slice. 然后吃了一片。

　　One bag, one apple, one slice. Which of these is the real "one"? 一袋、一颗、一片。哪个才是真实的“一个”？

　　Well, they all are of course, and that's what my elementary teachers were trying to tell me. 好吧，它们当然都是，这正是我的小学老师一直试图告诉我的。

　　Because this is the important idea behind whole number place value, decimal¹ place value and fractions². 因为这是一个关于整数、小数与分数的重要概念。

　　Our whole number system depends on being able to change what we count as "one". 我们所使用的整个数字系统要转换我们所熟悉的“一”。

　　Our whole number system depends on being able to change units. 我们所使用的数字系统要能够转换成单位。

　　There are two ways to change units. 有两个方式能够转换单位。

　　We can compose, and we can partition³. 我们可以组合，也可以分割。

　　When we compose units, we take a bunch of things, 当我们组合单位时，

　　we put them together to make a bigger thing, like a dozen eggs. 把一大堆东西放在一起，让它们变得更大，比如一打鸡蛋。

　　We take 12 eggs, put them together to make a group, and we call that group a dozen. 我们把十二颗鸡蛋放在一起，组成一组，然后我们叫这一组为一打。

　　A dozen eggs is a composed unit. 一打鸡蛋就是一种组合单位。

　　Other examples of composed units include a deck⁴ of cards, a pair of shoes, 其他组合单位的例子包括：一副牌、一双鞋、

　　a jazz quartet and of course, Barbie and Ken⁵ make a couple. 爵士四重奏。当然还有芭比和肯尼组成的一对情侣。

　　But think about a loaf of bread. 但想想一条面包。

　　That's not a composed unit, because we don't get a bunch of slices from a bunch of different bakeries 它不是一种组合单位，因为我们不会从不同的面包店拿一堆面包片放在一起，

　　and put them together to make a loaf. 变成一条面包。

　　No, we start with a loaf of bread and we cut it into smaller pieces called slices, 我们不这样做，而是把一条面包切得更小，并叫它为一片面包，

　　so each slice of bread is a partitioned⁶ unit. 所以每一片面包就是一个分割单位。

　　Other examples of partitioned units include a square of a chocolate bar, a section of an orange and a slice of pizza. 其他分割单位的例子包括：一块巧克力、一片柳橙，还有一片披萨

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