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Bar graphs and axis scales

Key idea: Read the scale before a bar’s value. The same drawn height can represent a different amount on another scale.

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Enlarged diagram

Read a bar’s height

How many pupils does one gap stand for?

Point to 0, then 5, then 10 on the axis. Each equal gap stands for 5 pupils.

Pupils attending clubs

Read the number of pupils on the vertical axis.

A: Art; B: Music; C: Drama. Equal gaps mean equal increases. Every bar starts at zero.
Figure data

This table is included in print while it is open.

Bar positions on the value axis
KeyClubEqual gaps from zero
AArt1 gap
BMusic2 gaps
CDrama3 gaps

Follow Drama’s bar to the axis. Three gaps, five pupils per gap: 15 pupils. Read the height to count pupils. The width does not count pupils.

How much does one gap stand for?

Practise: Primary 3 Mathematics Bar graphs and different axis scales practice · Primary 3 MathematicsPractise: Primary 5 Foundation Mathematics Tables, bar graphs and line graphs practice · Primary 5 Foundation Mathematics

Check your understanding 1

Compare and combine the clubs

Each pupil attends only one of these clubs. Use the bar values to answer in pupils.

Pupils attending clubs

The vertical axis counts pupils. Use the key below the graph to find each club.

A: Art; B: Music; C: Drama. Keep using five pupils per gap.
Figure data

This table is included in print while it is open.

Bar positions on the value axis
KeyClubEqual gaps from zero
AArt1 gap
BMusic2 gaps
CDrama3 gaps
Show answerHide answer

Drama has 10 more pupils: 15-5 = 10. Music and Art have 15 pupils altogether: 10 + 5 = 15. Two extra gaps mean ten extra pupils, not two.

Read a changed scale

What does this graph’s scale tell you?

A new graph can use a different value for each gap. Read its axis again.

Check your understanding 2

Read the bar between labelled marks

Find the value of one labelled gap. Then read Drama’s bar.

Attendance with a different scale

Use the table to find each bar’s end between labelled axis marks.

A: Art; B: Music; C: Drama. Drama’s bar ends halfway between 30 and 40.
Figure data

This table is included in print while it is open.

Bar positions on the value axis
KeyClubEqual gaps from zero
AArt1 and a half gaps
BMusic3 gaps
CDrama3 and a half gaps
Show answerHide answer

10 pupils per labelled gap. Half a gap stands for 5 pupils. Drama’s bar represents 35 pupils: 30 + 5 = 35.

Do the two scales count the same amount?

Check your understanding 3

Compare the Tuesday bars

Both Tuesday bars are three gaps high from zero. Use each axis scale to enter the number of books.

Library 1: books borrowed

Read this library’s scale. Then compare its Tuesday bar with the next graph.

A: Monday; B: Tuesday. The graphs use the same drawing size. Check their axis numbers.
Figure data

This table is included in print while it is open.

Bar positions on the value axis
KeyDayEqual gaps from zero
AMonday2 gaps
BTuesday3 gaps

Library 2: books borrowed

Use this library's own scale to read its Tuesday bar.

A: Monday; B: Tuesday. Tuesday is B in each graph.
Figure data

This table is included in print while it is open.

Bar positions on the value axis
KeyDayEqual gaps from zero
AMonday2 gaps
BTuesday3 gaps
Why can the two Tuesday bars mean different totals?
Show answerHide answer

Library 1: 15 books. Library 2: 30 books. The drawn bar heights match. Each gap stands for a different number of books. Point to 5 and 10 on the axes to compare.

Which way does the number scale run?

Practise: Primary 3 Mathematics Bar graphs and different axis scales practice · Primary 3 MathematicsPractise: Primary 5 Foundation Mathematics Tables, bar graphs and line graphs practice · Primary 5 Foundation Mathematics

Check your understanding 4

Read a graph turned the other way

This graph records books borrowed. Find the extra books on Wednesday and the combined Monday–Tuesday total.

Books borrowed on three days

Read the number of books along the horizontal axis. Its endpoints and equally spaced gaps determine the scale.

A: Monday; B: Tuesday; C: Wednesday
Figure data

This table is included in print while it is open.

Bar positions on the value axis
KeyDayEqual gaps from zero
AMonday2 gaps
BTuesday3 gaps
CWednesday5 gaps
Show answerHide answer

Six gaps from 0 to 36: 6 books per gap. Monday: 12. Tuesday: 18. Wednesday: 30.

18 more books on Wednesday than Monday: 30-12 = 18. 30 books altogether on Monday and Tuesday: 12 + 18 = 30.

Which question can this graph answer?

Check what the graph tells you

A graph counts books borrowed on each day. Does it tell you which day pupils spent the most time reading? Choose the reason.

What can we conclude about time spent reading?
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No. It counts books borrowed. It does not show time spent reading. The club graphs count how many pupils came. They do not tell you which club pupils like best. Use counts to answer questions about how many. You need other facts to find time or favourite clubs.

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