Year 2 maths · Key Stage 1 · Number – fractions

Year 2 fractions: thirds, quarters and three-quarters

In Year 2 children go beyond halves and quarters. They learn to recognise, name and write one third, one quarter, two quarters and three quarters, and to find these fractions of a shape, a length, a set of objects or a quantity. They also discover that two quarters is the same amount as one half.

Thirds, quarters and equivalent halves, explained

A fraction is one or more equal parts of a whole. The word “equal” matters most: a pizza cut into four unequal slices doesn’t have quarters, however many pieces there are. In Year 2, children say and write 1/3 (one third), 1/4 (one quarter), 2/4 (two quarters) and 3/4 (three quarters). The top number says how many parts we are talking about and the bottom number says how many equal parts the whole has been divided into. Your child may not be asked for the words numerator and denominator yet, but they will see and write fractions in this form.

The “whole” can be many things. It might be a shape cut or folded into equal parts, a length such as a piece of ribbon or a line on a ruler, a set of objects such as 12 counters, or a quantity such as a jug of water. This is why the same fraction can give different amounts: a quarter of 8 sweets is 2, but a quarter of 20 sweets is 5. Children are encouraged to say what the whole is: “one quarter of the 12 counters”.

Finding a fraction of a set is really sharing. To find 1/3 of 12, share the 12 counters equally into 3 groups and look at what is in one group: 4. To find 3/4 of 12, share into 4 equal groups of 3 and take 3 of those groups, which is 9. Children write short number sentences such as 1/2 of 6 = 3. Sharing and grouping connect fractions with the division facts they have been learning, especially in the 2, 5 and 10 times tables, where half of 40 is 20 because 40 ÷ 2 = 20.

Year 2 also introduces equivalence. When a paper strip is folded into quarters, two of the quarters cover exactly the same amount as one half, so 2/4 = 1/2. Children see this with folding, shading and drawing before they meet any rules, and it is the first step towards the equivalent fractions of Key Stage 2. Many schools also count in fractions on a number line, saying 1, 1 1/4, 1 2/4 (or 1 1/2), 1 3/4, 2, so that children see fractions as numbers that sit between whole numbers and can be bigger than one.

Words your child will hear

Whole: The complete shape, length, set of objects or quantity that is being divided.
Equal parts: Parts that are exactly the same size, which every fraction needs.
Third: One of three equal parts of a whole, written 1/3.
Quarter: One of four equal parts of a whole, written 1/4.
Three-quarters: Three of four equal parts, written 3/4.
Half: One of two equal parts, written 1/2. It is worth the same as 2/4.
Equivalent: Worth the same amount, even if it is written differently, like 2/4 and 1/2.

What the National Curriculum says

In Year 2, pupils should be taught to:

Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity
Write simple fractions, for example 1/2 of 6 = 3, and recognise the equivalence of 2/4 and 1/2

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

There are 12 counters. Find 3/4 of them. Then find 2/4 and say what you notice.

The bottom number is 4, so share the 12 counters equally into 4 groups. Deal them out one at a time: each group gets 3.
```
12 counters shared into 4 groups
3 in each group
```
One group is one quarter, so 1/4 of 12 is 3.
1/4
The top number is 3, so take 3 of the groups. 3 groups of 3 is 9, so 3/4 of 12 is 9.
3/4
Now take 2 of the 4 groups: 2/4 of 12 is 3 + 3 = 6. Half of 12 is also 6, because 12 ÷ 2 = 6. So 2/4 and 1/2 are the same amount.
2/4
1/2

3/4 of 12 is 9. 2/4 of 12 is 6, the same as 1/2 of 12, so 2/4 = 1/2.

Common mistakes and how to help

Calling unequal pieces quarters

A child sees a shape split into four parts and says each is a quarter, even though some pieces are much larger. Everyday language often says “a fraction” when it just means a piece.

What helps: Always ask “Are the parts equal?” Fold the shape or lay one piece on top of another to check. Cutting a sandwich into fair and unfair pieces, with an adult doing the cutting, makes the point quickly.

Giving the bottom number as the answer: 1/3 of 12 is 3

The digit 3 is the one that stands out, and in the child’s mind “a third” can slip into “three”.

What helps: Share the 12 counters into 3 groups and count what is in one group. The 3 tells you how many groups, not how many counters in the answer.

Thinking a bigger bottom number means a bigger fraction

With whole numbers 4 is bigger than 3, so 1/4 seems bigger than 1/3.

What helps: Compare two strips of paper of the same length folded into 3 and into 4. More parts means each part is smaller, just as sharing a cake with four people gives a smaller slice than sharing it with three.

Not believing that 2/4 and 1/2 are the same

The numbers 2, 4 and 1, 2 look completely different, so it seems they must be different amounts.

What helps: Fold a strip in half and shade one part. Fold another into quarters and shade two. Put one on top of the other, and the shaded areas match exactly.

How to help at home

Fold paper into fractions. Fold strips of paper into halves, thirds and quarters and colour one part. Folding into thirds is harder than into quarters, so talk about why it needs care. Stack the strips to compare.
Share a set fairly. Put 12 raisins or buttons on the table and ask for a quarter. Your child will share them into four groups and take one. Then ask for three-quarters and compare with half.
Use lengths and liquids. Mark a third of a piece of string or ribbon by folding, or ask your child to pour water until a clear jug or bottle looks about a quarter full, then three quarters full. Use the word “whole” each time, so they say what the fraction is of.
Use fraction language. Talk about “half an hour” and “a quarter of the pizza”, and point out the 1/4 on a set of measuring spoons. Ask “Is that more or less than a half?” when you can.

Builds on

Year 1: Halves and quarters

Leads on to

Year 3: Tenths and equivalent fractions

Everything in Year 2 maths

Updated 20 October 2026.