Year 1 maths · Key Stage 1 · Number – fractions
Year 1 halves and quarters: a guide for parents
Fractions begin in Year 1 with two ideas: a half and a quarter. Children learn that a half is one of two equal parts and a quarter is one of four equal parts, and they find and name them in shapes, lengths and groups of objects. The key word is equal. Getting this right now makes the fractions in Years 2 and 3, from thirds to tenths, much easier to follow.
Halves and quarters, explained
A half is one of two equal parts of a whole, and a quarter is one of four equal parts. The whole can be a shape, such as a square of paper, a length, such as a ribbon, or a group of objects, such as eight counters. Year 1 teachers usually use all three, because children need to see that a half is a relationship, not a particular picture. Half of a pizza and half of a bag of ten marbles are different amounts, but both come from splitting something into two equal parts.
Children meet fractions through things they already do: sharing and grouping. Sharing 8 counters between 2 people gives half each, and sharing between 4 gives each person a quarter. They also fold and cut paper shapes, share out play dough, find half of a length of string, and say how full a jug is when it is half full. These activities connect fractions to the equal sharing and grouping they are learning in multiplication and division, and to the measures they use in the same year.
Children name the fractions in words, such as “a half” and “a quarter”, and may be shown the written forms ½ and ¼. Expect your child to say things like “this shape is split into four equal parts, so each part is a quarter”. They also begin to combine the two ideas: two quarters make a half, and two halves or four quarters make a whole. Formal work on writing fractions, three-quarters and equivalence (that 2/4 is the same as 1/2) belongs to Year 2.
Teachers pay a lot of attention to the word “equal”. A shape cut into two uneven pieces has not been split into halves, however it looks on paper. Children also see halves and quarters in different orientations and in different shapes, so a square can be halved by a vertical line, a horizontal line or a diagonal, and the parts are still halves as long as they are equal. Checking by folding one part on top of the other, or by comparing counters, is the classroom way of proving it.
Words your child will hear
- Whole
- The complete shape, length or group before it is split into parts.
- Half
- One of two equal parts of a whole. Half of 6 is 3.
- Quarter
- One of four equal parts of a whole. A quarter of 8 is 2.
- Equal parts
- Parts that are exactly the same size, or that hold exactly the same number of objects.
- Fraction
- A part of a whole. Halves and quarters are the first fractions children meet.
- Half full
- Describes a container when the liquid fills half its capacity.
What the National Curriculum says
In Year 1, pupils should be taught to:
- Recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity
- Recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity
Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.
A worked example
There are 8 counters. Find half of the counters and a quarter of the counters.
- To find a half, share the 8 counters into 2 equal groups, dealing them out one at a time. Each group has 4 counters. One group is half of the counters.half
- To find a quarter, share the same 8 counters into 4 equal groups. Each group has 2 counters. One group is a quarter of the counters.quarter
- Compare the answers. A half is 4 counters and a quarter is 2 counters. The quarter is smaller than the half, even though the word “four” belongs to quarter. Cutting a whole into more equal parts makes each part smaller.
- Check by putting the parts back. 2 groups of 4 make 8, and 4 groups of 2 make 8. Two quarters (2 and 2) also make 4, which is the same as a half.
Half of 8 is 4. A quarter of 8 is 2.
Common mistakes and how to help
Calling parts halves or quarters when they are not equal
Children focus on the number of pieces, so any shape cut into two pieces is called two halves.
What helps: Always ask “Are the parts equal? How do you know?” Fold the paper so one part sits exactly on top of the other, or match counters one to one. Show a deliberately uneven cut and ask your child to explain what is wrong.
Thinking there is only one way to make a half
Pictures of halves are often split down the middle by a vertical line, so other splits look wrong.
What helps: Fold a paper square into halves in several ways: top to bottom, side to side and corner to corner. Turn the shapes around. All the parts are halves if they match when folded.
Thinking a quarter is bigger than a half because 4 is bigger than 2
Children bring their whole-number thinking to fractions and compare the numbers in the words.
What helps: Share a piece of play dough between 2 people, then between 4. Compare one piece from each. The more people sharing, the smaller each share.
Giving the number of groups as the answer, so a quarter of 8 is 4
To find a quarter you make 4 groups, and the child reports the 4 instead of the number in one group.
What helps: Ask “How many counters are in one group?” Point to a single group and say “one group is a quarter of the counters”. Check by counting the group.
How to help at home
- Fold paper into halves and quarters. Fold a sheet of paper in half, then in half again, and open it up to see four equal parts. Colour in one quarter. Ask which other ways you could fold it to make halves.
- Share food fairly. Cut a sandwich, apple or pancake into halves and quarters yourself, and let your child check the pieces are equal before anyone eats. Ask “Would you like half or a quarter? Which is more?”
- Halve and quarter small groups. Use 8 pasta shapes, building bricks or toy cars: “Give me half.” “Now give me a quarter.” Start with numbers that share evenly, such as 4, 8 and 12, and ask your child to prove each answer.
- Half full, half empty. At the sink, pour water into a clear jug or bottle and stop when it is half full. Share a full jug equally between two matching cups, so each holds half, then between four matching cups, so each holds a quarter. Ask which cups hold more.
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