One is one ... or is it?

Translator: Jordina Nogués Graell Reviewer: Paula García

Which is correct: "A dozen eggs is?" Or "A dozen eggs are?"

Quin és correcte: «Una dotzena d'ous és?» o «Una dotzena d'ous són?»

I remember being in elementary school,

Recordo estar a primària,

and my teachers making a big deal about the unit.

els professors parlaven de la importància de la unitat.

And I never really got that,

Mai no ho vaig entendre,

until one day, I was in the grocery store,

fins que un dia, estava al supermercat

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

i volia comprar una poma, però no en podia comprar una.

I had to buy a whole bag of apples.

So I did. I bought one bag of apples,

Així que vaig comprar una bossa,

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

la vaig dur a casa, vaig treure una poma i la vaig tallar.

And then I ate one slice.

One bag, one apple, one slice.

Which of these is the real "one"?

Quin d'aquests és l'«u» real?

Well, they all are of course,

and that's what my elementary teachers were trying to tell me.

és el que els meus professors m'intentaven dir.

Because this is the important idea behind whole number place value,

És la idea que hi ha darrera del valor posicional,

de la xifra decimal i de les fraccions.

decimal place value and fractions.

Our whole number system depends

on being able to change what we count as "one".

de poder canviar el que anomenem «u».

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

There are two ways to change units.

Hi ha dues maneres de canviar les unitats:

We can compose, and we can partition.

les podem compondre i les podem partir.

When we compose units,

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

agafem grups de coses i les posem juntes per fer-ne una de més gran;

like a dozen eggs.

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

Agafem 12 ous i els ajuntem per fer un grup

and we call that group a dozen.

al que anomenem una dotzena.

A dozen eggs is a composed unit.

Other examples of composed units

Altres exemples d'unitats compostes són:

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

una baralla de cartes, un parell de sabates, un quartet de jazz

and of course, Barbie and Ken make a couple.

i, és clar, la Barbie i en Ken, que són parella.

But think about a loaf of bread.

Però penseu en un pa de motlle.

That's not a composed unit,

No és una unitat composta,

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

and put them together to make a loaf.

i els posem junts per fer un pa de motlle.

No, we start with a loaf of bread

No, tenim un pa de motlle,

and we cut it into smaller pieces called slices,

el tallem en trossos més petits, anomenats llesques,

so each slice of bread is a partitioned unit.

cada llesca de pa és una unitat partida.

Other examples of partitioned units

Altres exemples d'unitats partides són:

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

una presa de xocolata, un grill de taronja

and a slice of pizza.

o un tall de pizza.

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

L'important de les unitats és que una vegada n'hem fet de noves,

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

les podem tractar, com la unitat antiga.

We can compose composed units,

Podem compondre unitats compostes,

and we can partition partitioned units.

Think about toaster pastries.

Penseu en les galetes farcides.

They come in packs of two,

and then those packs get put together in sets of four

i aquests paquets es posen junts en jocs de quatre

to make a box.

So when I buy one box of toaster pastries,

Quan compro una caixa d'aquestes galetes,

am I buying one thing,

four things, or eight things?

It depends on the unit.

One box, four packs, eight pastries.

Una caixa, quatre paquets, vuit galetes.

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

I si comparteixo un tall de pizza amb un amic,

we have to cut "it" into two smaller pieces.

So a box of toaster pastries is composed of composed units,

Una caixa de galetes farcides està composta d'unitats compostes,

and when I split a slice of pizza,

quan divideixo un tall de pizza,

I'm partitioning a partitioned unit.

But what does that have to do with math?

Però, què té a veure això amb les mates?

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,

El motiu: comencem a comptar a partir de l'u,

and we count up to nine: 1, 2, 3, 4, 5, 6, 7, 8, 9,

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

i després ve el 10, i per escriure 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.

que és un grup, no una cosa.

But 10, just like one,

just like a dozen eggs,

just like an egg,

10 is a unit.

And 10 tens make 100.

I 10 vegades 10 fan 100.

So when I think about 100,

Quan penso en 100,

it's like the box of toaster pastries.

és com la caixa de galetes.

Is 100 one thing,

10 things

or 100 things?

And that depends on what "one" is,

it depends on what the unit is.

depèn del què és la unitat.

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

Penseu en cada vegada que, a mates, heu escrit el número u.

No matter what place that one is in,

Sense importar en quin lloc està aquest u,

no matter how many things that one represents,

sense importar quantes coses representa aquest u,

one is.

l'u hi és.