Division as Sharing

If 12 sweets are shared equally between 3 people, how many does each get?

That question is written 12 ÷ 3.

Division splits a total into equal groups. The symbol is ÷.

The answer has a name too.

Quotient is the answer to a division.

Equal is the whole point

Sharing 12 as 5, 4 and 3 is not division. The shares have to match.

Sharing out fairly

You have 12 sweets and 3 friends. Deal them out one at a time, going round and round, until they run out. Each friend ends up with 4. That is 12 ÷ 3 = 4. Dealing is a real procedure you can carry out with objects, which is why sharing is the first meaning of division children meet.

The other meaning: making groups

There is a second question that also gives 12 ÷ 3. Instead of "12 shared between 3 people", ask "how many groups of 3 can I make from 12?" The answer is again 4. These two questions feel completely different but the same division answers both. Noticing this is a real step forward.

When it does not come out evenly

Share 13 sweets between 3 friends and each gets 4 with one left over. That leftover is called a remainder. Grade 3 mostly uses divisions that come out exactly, but knowing leftovers exist stops you assuming every division is tidy.