A fraction can be represented as part of a shape. For example, this shape is divided into seven equal triangles.

27 of this shape is shaded dark blue.

57 is light blue.

The whole shape is 27 + 57 = 77 = 1

What this might look like in the classroom

Question:
Use fraction strips split into halves, thirds, quarters, fifths, sixths, eighths, tenths, twelfths and sixteenths. Identify fractions which are the same size as:

a. 23

b. 34

Answer:

a. 23 = 46 = 812

b. 34 = 68 = 912 = 1216

Note: Learners can discuss the terminology ‘equivalent fractions’. They may also use a ‘fraction wall’ to check their answers to this question

Taking this mathematics further

A context in which comparing fractions can be explored is questions such as:

Which would you rather have - two fifths of a pizza or a third of a pizza? Three quarters of a chocolate bar or two thirds of a chocolate bar?

Encourage children, as appropriate, to develop more abstract reasoning and not just rely on a visual representation such as a fraction wall.
For example a child might say:

I know that two sixths is the same as a third, and so two fifths must be a bit bigger than two sixths – we’re cutting the pizza into fewer pieces with fifths. So two fifths must be bigger than a third.

Or:

Three quarters of a chocolate bar is a whole chocolate bar with a quarter removed. Two-thirds is a whole bar with a third removed. A third is bigger than a quarter, so three quarters must be bigger than two thirds.

Making connections

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 shade a square into fractions which are very nearly but not quite quarters – get them to justify how they have done this.