Halves and quarters
National Curriculum: this is in the Year 1 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 1 are 5 or 6, and turn 6 during the school year.
What it is
A half is 1 of 2 equal parts of something. A quarter is 1 of 4 equal parts. The something can be an object, a shape or an amount: half an apple, half a sheet of paper, half of 8 counters. This is the first fraction work a child does, and it is done by folding, cutting and sharing rather than by writing anything down.
Equal is the word carrying the idea. Two pieces are halves only if they are the same size, so a bar snapped into a big piece and a small piece has two parts and no halves. Quarters work the same way: four parts, all the same size as each other. A child counts parts long before they think to check that the parts match, and the checking is the thing worth practising.
Halves and quarters are linked, and saying so helps: a quarter is half of a half, so folding a sheet in half and then in half again gives quarters. Halving an amount is sharing it into 2 equal groups, which is where finding a fraction of an amount takes over once the numbers grow. Writing the fraction down comes later, with what the top and bottom numbers each mean.
When children learn it
Recognising, finding and naming a half as 1 of 2 equal parts of an object, shape or quantity is a Year 1 requirement, and a quarter as 1 of 4 equal parts sits beside it. Year 2 adds a third, and 2/4 and 3/4, of a length, a shape, a set of objects or a quantity, asks for simple fractions to be written down, such as 1/2 of 6 = 3, and treats 2/4 and 1/2 as the same amount.
A class may meet quarters early in Year 1 or late in Year 2, and both are within what is asked.
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.
- Unequal pieces called halves. A bar cut into one big piece and one small piece, agreed to be halves. Two parts is being treated as the whole of the rule, and the sizes are not being compared at all. Asking which piece they would rather be given settles it faster than saying the parts are not equal.
- A quarter named as a half. A bar cut into 4 equal parts, with one part called a half. The parts are equal and one part is being named, so the idea of a fraction is there; how many parts the whole was cut into is not what is deciding the name. Count the parts aloud before naming one, because that count is where the name comes from.
- An equal split turned down. A bar cut genuinely into 4 equal parts, and asked whether each part is a quarter, they say no. This is usually one picture learned as what a quarter looks like, often a square split into four small squares, with anything cut a different way refused. Cut the same shape into quarters two or three different ways and ask the question each time.
- An amount shared into the wrong number of groups. Asked for half of 8 counters, they deal them into 4 groups and answer 2. Halving a shape can be secure while halving an amount is not, because an amount has to be shared out before any part of it can be named. That is finding a fraction of an amount, the skill that follows this one, where how many groups to make is the first question rather than an afterthought.
How to help at home
- Fold before you cut. Fold a sheet of paper in half, open it out, and ask whether the two parts match. Then fold again for quarters. Checking that the parts are the same size is the skill; the folding is only how you get there.
- Ask for half of things that are not shapes: half of 6 grapes, half of a glass of juice, half of a pile of bricks. A half is 1 of 2 equal parts of whatever is in front of them.
- Cut something into two unequal pieces on purpose and ask whether they are halves. A child who says no, and can say why, has the idea.
- Say the words while sharing. Two equal parts, and one of them is a half. Four equal parts, and one of them is a quarter. The count of the parts is where the name comes from.