Fractions of an amount
National Curriculum: this is in the Year 2 programme of study, part of key stage 1 (Years 1 and 2). Schools have to teach the key stage 1 programme by the end of Year 2, and can introduce content earlier or later within it.
Children in Year 2 are 6 or 7, and turn 7 during the school year.
What it is
Finding a fraction of an amount takes two steps. The bottom number says how many equal groups to share the amount into, and the top number says how many of those groups to count. A quarter of 12 is 12 shared into 4 equal groups, which puts 3 in each group, so a quarter of 12 is 3. Three quarters of 12 is three of those groups, so 9.
The first step is a division, which is where fractions and division meet: a quarter of 12 is 12 divided by 4. A child can find a fraction of any amount their division facts reach, so times tables do as much work here as fractions do.
The amount has to stay in view. Half of 8 is 4 and half of 20 is 10, so "a half" is not a number on its own: it is an instruction about the amount it is applied to. What the two numbers in a fraction mean is the idea underneath this one, and it is worth being secure there first.
When children learn it
Year 2 is where the National Curriculum asks children to recognise, find, name and write a third, a quarter, two quarters and three quarters of a length, a shape, a set of objects or a quantity, with three quarters as the first fraction that counts more than one part. Year 3 extends it to unit and non-unit fractions of a set of objects with small denominators, and Year 4 asks for harder fractions of quantities. The two steps stay the same throughout; the numbers get bigger.
What it looks like when it goes wrong
These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.
- Shared into the wrong number of groups. Asked for a quarter of 12, they answer 6. The amount was halved: sharing is happening, but the bottom number is not deciding how many groups to share into. Ask how many groups the 4 is asking for before any sharing starts.
- The bottom number given as the answer. Asked for a quarter of 12, they answer 4. The number that says how many groups to make has been read as the answer. Nothing has been shared out at that point, which is the thing to say back.
- The whole amount given back. Asked for half of 8, they answer 8. The fraction has not acted on the amount at all. This usually means the question is being heard as two separate numbers rather than as an instruction, and it clears up with objects on the table faster than with explanation.
How to help at home
- Share something real: 12 grapes into 4 equal piles. Ask how many piles first, then how many are in one pile. Those two questions are the method.
- Say the division out loud alongside it: a quarter of 12 is 12 divided by 4. Making that link once saves relearning it later.
- For a non-unit fraction, count the groups rather than starting again. Three quarters of 12 is three piles of 3, not a new calculation.
- Ask the same fraction of two different amounts, such as half of 8 and half of 30. A fraction says what to do to an amount; it is not a fixed number.