Doubling and Sharing

Imagine you have 3 cookies and your friend gives you 3 more cookies — the very same amount again. That special kind of adding, where you add an amount to itself, has its own name: doubling.

Doubling isn't a new trick — it's just addition you already know, with a shortcut name for one particular kind of sum: adding a number to itself.

duck duck duck + duck duck duck = 6 ducks

We say "double 3 is 6", and we write it just like any other sum:

3 + 3 = 6

You can use your fingers to double a small number — hold up 3 fingers on one hand, then 3 more on the other hand, and count all the fingers up. Doubling with toys, counters or fingers works exactly the same way every time: make the amount, then make it again, then count everything.

Watch a double happen

Step through the picture below. First you'll see one group, then the very same amount appears again next to it, and finally the two groups join up into the total. Press Refresh for a brand-new number to double.

Doubles to know

These little doubles come up all the time, so it's worth getting to know them well:

Number	Double
1	1 + 1 = 2
2	2 + 2 = 4
3	3 + 3 = 6
4	4 + 4 = 8
5	5 + 5 = 10
6	6 + 6 = 12

Look back at the table — every single answer is an even number: 2, 4, 6, 8, 10, 12. That's not an accident! An even number is exactly one that can be split into two equal piles. When you double a number, you build it from two equal piles on purpose — so the answer can always be split straight back into those same two equal piles. Doubling and "splitting into two equal groups" are really the same idea, seen from opposite ends.

Sharing equally

Doubling puts two equal groups together. Sharing does the opposite: it starts with one pile and splits it into equal groups.

Imagine you have 10 strawberries to share between 2 friends, fairly, so nobody feels left out. The safe way to do it is to deal them out one at a time, just like dealing playing cards — one to the first friend, one to the second friend, one back to the first friend, and so on — until every strawberry has gone to somebody. When you finish dealing 10 strawberries between 2 friends this way, each friend ends up with exactly 5.

The same idea works for any small pile and any small number of friends. Share 12 toy cars between 3 friends by dealing one at a time, round and round, and each friend ends up with 4 cars.

Watch the dealing happen below, one item at a time, then read off how many each friend gets. Press Refresh for a new sharing problem.

Grouping — sharing's twin

There's a second question hiding inside the very same picture. Instead of asking "how many does each friend get?", we can ask "how many groups can I make?" — this is called equal grouping.

Say you have 8 apples and you want to pack them into bags, with 2 apples in every bag. How many bags do you need?

apple apple | apple apple | apple apple | apple apple

Deal the apples into pairs the same way you dealt the strawberries: two together, two together, two together, two together — that makes 4 bags.

Sharing and grouping use exactly the same numbers — 8 apples split into equal piles of 2 — but they answer opposite questions:

Sharing asks: I know how many friends (or bags) there are — how many go in each one?
Grouping asks: I know how many go in each pile — how many piles can I make?

Two traps that catch out new sharers and doublers:

When sharing, you must deal one at a time, going all the way round. Don't just scoop a big handful for the first friend and hope there's enough left for everyone else — that's how someone ends up with too many and someone else with too few, or nothing at all!
Doubling is not the same as "add one more". Double 3 means 3 + 3 = 6, not 3 + 1 = 4. Doubling adds the whole amount again, not just one extra.

Later on you'll learn a much faster way to work out bigger groups-of-groups — arranging things in neat rows and columns called Arrays and the Area Model — but doubling and sharing are where it all begins.