For example, this shape is divided into seven equal triangles.

27 of this shape is shaded blue. 57 is shaded pink.

The whole shape is

27 + 57 = 77 = 1

This question is from an old test paper.

Some squares have been shaded.
Shade more squares so that

34 of the shape is shaded white.

What this might look like in the classroom

Question:

Look at this shape.

What fraction is coloured?
Colour in more squares until 34 of the shape is coloured.

Answer:

18 of the shape is coloured.
In order for 34 of the shape to be coloured, any 5 further squares need to be coloured. This will mean that 6 out of 8 squares are coloured. 6 out of 8 can be written as 68. This is equivalent to 34.

Taking this mathematics further

Investigate how concrete materials such as Cuisenaire rods can be used to model fractions.

Take a regular shape such as a regular hexagon. How many different ways can you find to shade exactly one half of it?

Making connections

Early experience of fractions is likely to involve halves and quarters of physical objects such as apples or pizzas. Children may share items such as a biscuit with a friend so that they get half each. They may fold paper shapes to create halves and quarters. Through such early experience, children begin to understand that fractions are created when a whole object is divided into equal parts.

Children often learn to recognise the written symbols for 12, 14 and 34 without understanding the notation.

In order to handle a wider range of unit fractions such as 18, 15 and non−unit fractions such as 23 learners need to develop understanding of the role of the numerator and denominator of a fraction.

Using shapes to model fractions can support learners in developing understanding of equivalent fractions and mixed numbers.

A key concept of fractions is that the parts have to be equal in size. Develop this idea with children with questions such as asking them to identify which of the following shows thirds:

Challenge children to split a square into two sections that are nearly but not quite halves. Get them to explain their reasoning.