Basic division

Division in arithmetic is the reverse of multiplication. So it’s probably a good idea if your child has some understanding of how to multiply numbers before beginning on any real study of division. For a few ideas about helping your child understand the basic concepts of multiplication, you might like to read the page Introducing multiplication. You can then reinforce the concept by helping him understand various multiplication tricks and patterns, if you wish.

However, in its simplest form, division is sometimes known as ‘sharing’. As soon as your child understands how numbers work, it’s good to use basic mathematical language in everyday situations, as suggested on the page maths for toddlers. If you have four children playing together, and four biscuits, then if they share them fairly, each child will have one biscuit.

Obvious? It is to adults, but not necessarily to small children. If your child is interested in the idea of sharing, you could try asking how many biscuits they would each get if there were only two of them. Or only one. Never push it – just throw these ideas into everyday conversation, and when your child is ready to understand the concept, he or she will pick up on it. If you keep it low-key and in the context of food, or games, your child may never know that division can be a difficult concept to some.

Do keep it simple, and reinforce the concepts gently when the opportunity arises. Remember that your child does not know how numbers work, and they’re not always intuitive. If eight biscuits shared amongst four children gives two each, what about eight cakes? Or eight apples? Or eight pennies? Children who have not played with numbers in concrete form at a young age sometimes have no idea that eight of anything divided into four equal parts will always give two of them.

Once your child has the idea that six pieces of chocolate shared between three children gives two each, you can casually introduce the word ‘divided’.  Mathematically, we talk about dividing six by three, which is similar to sharing, though not exactly the same. Don’t worry about your child becoming confused; all language is new to a toddler, and small children have a remarkable knack of grasping language concepts and ambiguities.

Lego bricks for division concepts

If your child likes playing with Lego, then the bricks are very useful manipulative tools for understanding about basic multiplication and division. If you want to put two-bricks along a thin 12-brick, how many will fit?Is it the same every time? Does it make any difference what colour the bricks are? Again, this may seem a ridiculous question from an adult perspective, but remember that a small child does not know automatically how numbers work.

There are other simple dividing games you can play with Lego, of course, depending on your child’s interests. There are six knights and twelve horses. Can we make sure each knight has the same number of horses? There are twenty pieces of treasure, and four chests. How can we divide the treasure equally between the chests?

Dividing with remainders

If you play games like these, you will quickly come across the question of the remainder. Twelve horses can be equally shared between six knights, but what if you only have five knights? Or eleven horses? You may have come across this problem before, if you have a family of four, and buy a pack of six doughnuts. How can we share things when they don’t divide easily?

There’s no need to make it complicated at this stage. Twelve horses divided by five knights means that each knight gets two, and there are two left over. In mathematical language, twelve divided by five is two with a remainder of two. If your child is fascinated by this kind of number game, you can try asking how many more horses would be needed before they could be shared again. But don’t push it. And do remember to play around with different numbers, so your child doesn’t think the remainder is always going to be two!

With six doughnuts and four people, you can give one to each person, and have two left over. Six divided by four is one, with a remainder of two. With your two remaining doughnuts you can painlessly introduce the idea of simple fractions if you wish. Cut each of them into two parts, or halves, and then give one half doughnut to each person. As well as saying that six divided by four is one with a remainder of two, we can also say that six divided by four is one-and-a-half.

Dividing one item between many

Your child may ask what happens if you want to share one item – for instance a cake – between several children. You could, if you wish, start to explain how fractions work – the page fractions for four-year-olds might help you if you’d like some further ideas – or you could just say, simply, that you divide the cake into pieces, and share those.


For more articles about teaching basic maths, see:

Number bonds – beginning addition
Fractions for four-year-olds
Algebra for six-year-olds

Prime numbers and factors

If you have older children, and are concerned about teaching them maths, see:

Maths and the home educated teen
Understanding angles
Simultaneous equations