One is one ... or is it?

Prevoditelj: Ivan Stamenković Recezent: Senzos Osijek

(Glazba)

Što je točno -- tucet jaja je? Ili tucet jaja su?

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

Sjećam se kada sam bio u osnovnoj školi,

I remember being in elementary school,

and my teachers making a big deal about the unit.

i učitelji su radili veliku stvar oko jedinice.

I nikad to nisam shvatio, dok jednog dana nisam bio u trgovini,

And I never really got that,

until one day, I was in the grocery store,

i htio sam kupiti jabuku, ali nisam mogao kupiti jednu jabuku.

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

I had to buy a whole bag of apples.

Morao sam kupiti vreću jabuka.

So I did. I bought one bag of apples,

Tako da sam kupio jednu vreću jabuka,

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

odnio sam je kući, uzeo jednu jabuku iz vrećice, i izrezao je.

I onda sam pojeo jednu krišku.

And then I ate one slice.

Jedna vreća, jedna jabuka, jedna kriška.

One bag, one apple, one slice.

Which of these is the real "one"?

Koja od ovih je prava?

Pa, sve su, naravno, i to je ono što su mi učitelji u osnovnoj školi govorili.

Well, they all are of course,

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

Jer ovo je važna ideja iza

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

cijele vrijednosti poožaja broja, decimalne vrijednosti i razlomaka.

decimal place value and fractions.

Our whole number system depends

Naš čitav sustav brojeva ovisan je o mijenjanju toga što brojimo kao jedan.

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

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

Naš čitav sustav ovisi o mjenjanju jedinica.

Postoje dva načina mjenjanja jedinica.

There are two ways to change units.

We can compose, and we can partition.

Možemo sklapati, i razdvajati.

Kada sklapamo jedinice,

When we compose units,

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

uzimamo hrpu stvari i stavljamo ih u veću stvar,

like a dozen eggs.

kao tucet jaja.

Uzmemo 12 jaja, stavimo ih skupa i napravimo grupu,

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

and we call that group a dozen.

i zovemo tu grupu tucet.

Tucet jaja je sklopljena jedinica.

A dozen eggs is a composed unit.

Drugi primjeri sklopljenih jedinica uključuju

Other examples of composed units

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

špil karata, par cipela, jazz kvartet

i naravno, Barbie I Ken čine par.

and of course, Barbie and Ken make a couple.

Ali razmislite o štruci kruha.

But think about a loaf of bread.

That's not a composed unit,

To nije sklopljena jedinica,

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

jer ne dobijemo mnoštvo kriški od mnoštva različitih pekara

and put them together to make a loaf.

i sklapamo ih da dobijemo štrucu.

No, we start with a loaf of bread

Ne, počnemo sa štrucom, i režemo ju na manje dijelove

and we cut it into smaller pieces called slices,

nazvane kriške, tako da je svaka kriška kruha razdvojena jedinica.

so each slice of bread is a partitioned unit.

Drugi primjeri razdvojenih jedinica uključuju

Other examples of partitioned units

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

kocku čokolade, ili dio naranče,

krišku pizze.

and a slice of pizza.

Važna stvar s jedinicama je kad smo napravili novu jedinicu,

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.

možemo je tretirati kao i staru.

We can compose composed units,

Možemo ih sklapati, i možemo ih razdvajati.

and we can partition partitioned units.

Think about toaster pastries.

Razmislite o tost kruhu.

Dolaze u paketima od dva

They come in packs of two,

i onda se ti paketi stavljaju kao setovi od četiri

and then those packs get put together in sets of four

to make a box.

da bi napravili kutiju.

So when I buy one box of toaster pastries,

Dakle, kada kupujem kutiju

kupujem li jednu stvar,

am I buying one thing,

četiri ili osam stvari?

four things, or eight things?

Ovisi o jedinici.

It depends on the unit.

One box, four packs, eight pastries.

Jedna kutija, četiri paketića, osam peciva.

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

I kada dijelim krišku pizze s prijateljem,

moramo je podijeliti na dva manja dijela.

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

Dakle kutija peciva za toster

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

je sastavljena od sklopljenih jedinica,

i kada podijelim pizzu,

and when I split a slice of pizza,

I'm partitioning a partitioned unit.

dijelim razdvojenu jedinicu.

But what does that have to do with math?

Ali kakve to veze ima s matematikom?

U matematici, sve je sigurno.

In math, everything is certain.

Two plus two equals four,

Dva plus dva je četiri, a jedan je uvijek jedan.

and one is just one.

Ali to zapravo nije točno.

But that's not really right.

One isn't always one.

Jedan nije uvijek jedan.

Here's why: we start counting at one,

Evo zašto: Počnemo brojati kod jedan,

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

i brojimo do devet -- jedan, dva, tri, četiri, pet, šest, sedam, osam, devet.

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

I onda dođemo do 10, i da napišemo 10,

we write a one

pišemo jedan i nula.

and a zero.

To znači da imamo jednu grupu,

That one means that we have one group,

and the zero helps us remember

i ta nula nas podsjeća da to označava jednu grupu, ne jednu stvar.

that it means one group, not one thing.

Ali 10, baš kao i jedan,

But 10, just like one,

just like a dozen eggs,

kao i tucet jaja, i jaje,

just like an egg,

10 is a unit.

10 je jedinica.

i 10 desetki čini 100.

And 10 tens make 100.

So when I think about 100,

Kada razmišljam o 100, to je kao kutija peciva za toster.

it's like the box of toaster pastries.

Is 100 one thing,

Je li 100 jedna stvar,

10 stvari

10 things

or 100 things?

ili 100 stvari?

And that depends on what "one" is,

I to ovisi o onome što je jedan,

it depends on what the unit is.

ovisi o tome što je jedinica.

Razmislite kada u matematici pišete broj jedan.

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

Bez obzira na kojem mjestu je jedinica,

No matter what place that one is in,

no matter how many things that one represents,

bez obzira koliko stvari jedinica predstavlja

jedinica jest.

one is.