Maths: pie charts

A free preview from the Athena Learning Library — the same lesson registered students learn from.

In this lesson: Work out slice angles and group sizes from pie charts, and express a slice as a fraction.

Before you start

A whole circle is 360°. If half of a class chose red in a survey, what angle would the red slice of the pie chart be — and what fraction of the circle is a right angle of 90°?

Watch it happen

Build the pie, slice by slice

Pie chart of favourite colour for 120 children: Red: 25 (75 degrees); Orange: 50 (150 degrees); Purple: 15 (45 degrees); Green: 30 (90 degrees). The slices are added one at a time.

Red joins the pie: 25 of the 120 children. As a fraction of the whole group that is 25/120, which simplifies to 5/24, so its slice takes 25 × 3° = 75° of the 360° circle.

Step 1 of 4

The same pie, labelled with angles

Pie chart of favourite colour for 120 children, labelled with the angle of each slice: Red: 75 degrees; Orange: 150 degrees; Purple: 45 degrees; Green: 90 degrees.

The same results with the key showing angles instead of numbers of children. Each person is worth 360 ÷ 120 = 3° of the circle, so Orange's 50 people take 50 × 3° = 150°.

Your turn: spot the half

Four pies from four surveys. Move the frame onto the pie whose first (blue) slice is exactly half of the whole circle.

Four small pie charts in a grid, labelled Pie A to Pie D. Their first slices are a quarter, a third, a half and three quarters of the circle. A frame surrounds one pie.

Your target:

The idea

A pie chart is a circle split into slices. The whole circle stands for the whole group, and each slice shows one part of that group. A bigger group gets a bigger slice. The angles at the centre of the circle always add up to 360°.

To find the angle for a group, write the group as a fraction of the total, then multiply that fraction by 360°. For example, in a survey of 40 children where 10 walk to school, the fraction is 10/40, which simplifies to 1/4, and 1/4 of 360° is 90°.

You can also work backwards. If you know a slice's angle, divide it by 360° to get its fraction of the whole group, then multiply that fraction by the total number of people to find how many are in the group. Always check that all the slice angles add up to 360°.

Worked example

The pie chart shows pets owned by a class for 36 pupils. What angle is the Rabbit slice, and what fraction of the pupils chose Rabbit?

Pie chart of pets owned by a class for 36 pupils: Cat: 4 (40 degrees); Dog: 9 (90 degrees); Rabbit: 19 (190 degrees); None: 4 (40 degrees).

The whole pie stands for 36 pupils. A full turn is 360°, so each person is worth 360 ÷ 36 = 10° of the circle.
The biggest slice is Rabbit with 19 pupils: 19 × 10° = 190°. The second picture labels every slice with its angle — check they add up to 360°.
As a fraction of the whole group, Rabbit is 19/36.

Answer: 190°, and 19/36 of the pupils.

Try one yourself

On this pie chart of how pupils travel to school (36 pupils), what fraction chose Walk?

Pie chart of how pupils travel to school for 36 pupils: Car: 3 (30 degrees); Walk: 11 (110 degrees); Train: 4 (40 degrees); Bus: 18 (180 degrees).

Watch out

Dividing 360° by the group's number instead of by the total — the fraction must use the whole group as the denominator.
Forgetting to check that all the slice angles add up to 360° at the end.
Leaving a fraction unsimplified — simplifying first, such as 10/40 to 1/4, makes the angle much easier to spot.

Quick check

Try these on your own first — then reveal each answer.

1. On this pie chart, what angle is the Grapes slice?

Pie chart of favourite fruit for 36 children: Orange: 4 (40 degrees); Pear: 8 (80 degrees); Banana: 18 (180 degrees); Grapes: 6 (60 degrees).

2. On this pie chart, how many more pupils chose Cycle than Walk?

Pie chart of how pupils travel to school for 72 pupils: Walk: 12 (60 degrees); Cycle: 36 (180 degrees); Bus: 15 (75 degrees); Car: 9 (45 degrees).

Practise this concept

Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.

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