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

  • I remember being in elementary school,

  • and my teachers making a big deal about the unit.

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

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

  • I had to buy a whole bag of apples.

  • 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.

  • And then I ate one slice.

  • One bag, one apple, one slice.

  • Which of these is the real one?

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

  • 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.

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

  • There are two ways to change units.

  • We can compose, and we can partition.

  • When we compose units,

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

  • like a dozen eggs.

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

  • and we call that group a dozen.

  • A dozen eggs is a composed unit.

  • Other examples of composed units include

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

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

  • But think about a loaf of bread.

  • That's not a composed unit,

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

  • and put them together to make a loaf.

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

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

  • Other examples of partitioned units include

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

  • and a slice of pizza.

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

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

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

  • Think about toaster pastries.

  • They come in packs of two,

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

  • to make a box.

  • So when I buy one box of toaster pastries,

  • am I buying one thing,

  • four things, or eight things?

  • It depends on the unit.

  • One box, four packs, eight pastries.

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

  • we have to cut it into two smaller pieces.

  • So a box of toaster pastries

  • is composed of composed units,

  • and when I split a slice of pizza,

  • I'm partitioning a partitioned unit.

  • But what does that have to do with math?

  • In math, everything is certain.

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

  • But that's not really right.

  • One isn't always one.

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

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

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

  • we write a one and a zero.

  • That one means that we have one group,

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

  • But 10, just like one,

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

  • 10 is a unit.

  • And 10 tens make 100.

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

  • Is 100 one thing,

  • 10 things

  • or 100 things?

  • And that depends on what one is,

  • it depends on what the unit is.

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

  • No matter what place that one is in,

  • no matter how many things that one represents,

  • one is.


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B1 TED-Ed unit composed dozen slice toaster

【TED-Ed】One is one ... or is it? - Christopher Danielson

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    VoiceTube posted on 2013/07/04
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