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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 "is" 或者 a dozen eggs "are"?

  • 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)。

  • I had to buy a whole bag of apples.

    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。

  • But think about a loaf of bread.

    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。

  • 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

    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。

  • Think about toaster pastries.

    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...

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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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