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Fractions in Year 3 (age 7–8)

In Year 3, your child will learn about tenths, unit fractions and non-unit fractions, and will begin to understand equivalent fractions (fractions that have the same value such as Ìý=Ìý).

The key words for this section areÌýunit fraction,Ìýdenominator,Ìýnumerator, andÌýnumber line.

What your child will learn

Take a look at the National Curriculum expectations for fractions in Year 3 (age 7–8):

How to help at home

There are lots of everyday ways you can help your child to understand fractions. Here are just a few ideas.

1. Make fraction snowflakes

Paper folding can be a great way to explore fractions.

Decorate a piece of paper or card and then ask your child to fold the paper into different equal parts. For example, they could fold the paper into fifths by creating five equal sections. Ask them to show you a fifth, two-fifths, three-fifths, four-fifths, and five-fifths, which they can see is equivalent to a whole.

Challenge your child by giving the paper a value and asking them to work out what the fractions would be worth. What would one fifth represent if the whole paper had a value of 10? As they fold, they may like to cut patterns into the paper to make a ‘snowflake’ and watch the pattern develop as they fold further.

2. Have fun with food

Cake, pizza, or any foods with a regular shape can help children understand what fractions are and how they work. Ask your child questions like, ‘If I cut our cake into 8 pieces, what fraction will each piece be?’

Foods that people eat lots of can help your child understand how to find fractions of amounts. For example:

‘We have 12 fish fingers in the packet. There are 4 of us. What fraction of the fish fingers can we each have? How many fish fingers would that be?’

3. Compare fractions together

In Year 3, your child will compareÌýunit fractionsÌýand fractions with the sameÌýdenominatorÌýby saying which fraction is bigger or smaller – and explaining how they know.

You could show your child fractions likeÌýÌýandÌýÌýand ask them to explain which fraction is bigger.ÌýMany children may incorrectly believe a fifth is bigger than a third because they see a five and know that five is bigger than three. Your child should realise that, with unit fractions, the larger the denominator, the smaller the fraction.

Explain that the whole is divided into 5 equal parts when we talk about a fifth, but 3 equal parts when we talk about a third. If the whole was a cake, you would have less if you hadÌýÌýthan if you hadÌýÌý(demonstrate this with a real cake!). By drawing diagrams like the one below, your child will be able to see thatÌýÌýis larger thanÌý.

4. Fraction countdown

Your child will be expected to putÌýunit fractions in order.ÌýWhen ordering unit fractions, help your child by asking them to think of the whole as an object, such as a cake or plate of sandwiches. This should help them to see that Ìýis smaller thanÌý.ÌýFor example:

‘Would you prefer it if I cut this cake into ten equal pieces and gave you a piece, or if I cut the cut into two equal pieces and gave you a piece?’

Print out theÌý and cut out each fraction card. Take a selection of cards and see if your child can put them all in order, either from largest to smallest or smallest to largest. Are there any equivalent fractions? See if your child can match them up.

5. Make a fraction wall

Equivalent fractions are different fractions that have the same value. In Year 3, your child will learn about equivalent fractions with small denominators using drawings and diagrams.

are a helpful way to explore equivalent fractions. They show fractions visually, which helps children to see that some fractions that are written differently nonetheless have the same value (for example,ÌýÌýhas the same value asÌý,Ìý, and so on).

Why not try making a fraction wall with your child? You could investigate using the computer to make your fraction wall by creating a table and splitting each row into the equal number of parts you need. For example, to represent fifths, you would have to split the whole row into five equal parts.

Alternatively, you can download our below.

6. Adding and subtracting fractions

Try adding and subtracting fractions with the same denominator with your child. Try to do this within a whole, i.e. make sure that the sum uses numbers less than one, including the answer.

Using drawings or diagrams can help your child visualise adding and subtracting fractions. For example:

Ìý+ÌýÌý=Ìý

 

This could be calculated using a diagram like this:

 

 

Your child will first split the whole into five equal parts. Your child can then shade one box to representÌýÌýand two boxes to representÌý. They will then be able to see that the total isÌý.