“I’ll have the smaller half!”

How many times have we said this contradicting statement? Of all the topics in elementary math, fractions is the one that seems to cause the most dread among children and adults alike. Teaching fractions is difficult because for many children, they present the first mathematical stumbling block. Fractions can behave in ways that seem strange at first. For example, every child knows 5 is greater than 4 so they can become confused when told that 1/5 is less than 1/4.

When thinking about how to introduce fractions to your child, it’s important to focus not only on the rules of fractions, but also the meaning behind them. Understanding fractions is the goal.

To understand how to explain fractions to children, we’re going to take a close look at one particular fraction: a half.

### What is a fraction?

Fractions are used to represent smaller pieces (or parts) of a whole. The parts might make up a ‘whole’, which may be one thing, or more than one thing. Sounds confusing, doesn’t it? Let’s use some tasty treats to get our heads around it all.

Here’s a bar of chocolate (yum!) broken into two identical parts. Each part is one half of the overall amount.

This can also be written as 1/2. Let’s break down this notation – warning: some fancy long words are coming!

### Teaching Fractions

When writing a fraction, it helps to get your child to write the denominator first, as this tells us how many equal parts the whole is being divided into (e.g. 2 pieces of chocolate). They can say this out loud as they write it. Then draw the fraction bar (vinculum) which separates the numerator and denominator. Finally, write the numerator which is the top number in a fraction. This shows how many parts we have (e.g. 1 whole chocolate).

Notice how fractions build on simple counting exercises – the key is to know what you are counting at each step. Let’s try another example. This time, our tasty example involves 12 iced biscuits.

There are 12 in all, 6 of which are pink and 6 are blue. We can say that 6 out of 12, or 6/12, are pink. This is the same as 1/2 because one out of every two biscuits is pink. We say that 6/12 and 1/2 are equivalent because they represent the same amount.

### Use different representations

So far we’ve used groups of objects to represent fractions. We can also use lengths. Here’s a train ambling along the tracks without a care in the world.

We can measure the whole length of the train track and say that the train is half way along. In this case, the fraction 1/2 denotes what proportion of the track the train has travelled (for every 2 meters that cover the whole track, it has covered 1 meter).

You can hopefully see that even a really simple fraction like 1/2 can be modeled in different ways. When children are given the opportunity to visualize fractions (particularly more complicated ones) across different situations, they deepen their understanding of how these strange objects behave.

Very soon, your child will learn to recognize ‘one half’ in everyday situations: half a cake, half past twelve, a glass half full. The key to understanding fractions is to build them into other daily routines. Food is a fantastic resource for fractions. You can use pasta pieces or dried beans in place of counters and then have your child draw them as pictures, colouring in different parts to denote various fractions.

### Fun ways to teach fractions around the house

You can also collect lots of different objects from around the house – a dressing gown tie, potato, coin, book, glass of water, bunch of grapes, two apples, piece of paper, and so on – and then identify half of each of these objects. A potato is often irregular in its shape so cutting it in half doesn’t necessarily mean each half will be equal. How would you find half?

Activities like these will help build your child’s grasp of mathematical language. Make sure that your child can explain a) why the two parts are equal and b) what the whole is in this situation.

The most important thing to remember when you’re dealing with fractions is to go slowly and use a variety of representations. It’s always worth taking a bit of extra time to hone the basics!