Integers on number lines | Year 6

01 / LEARN

Understand the idea.

Read the interval

Before reading a marked point, find what one interval represents. Equal spaces must represent equal changes in value. Count the gaps between labelled ticks, rather than counting the ticks themselves, to find the scale.

For example, from $- 4$ to $2$ is a change of six units. If there are three equal gaps between them, each gap is worth $6 \div 3 = 2$ units. Not every number line uses one-unit intervals.

Keep the scale across zero

The scale continues through zero without a break. On a one-unit line, the values are $- 2, - 1, 0, 1, 2$ . Zero occupies a tick just like the other integers; it is not an extra gap or a missing value.

A position may be negative, but a distance is a non-negative number of units. To measure across zero, add the distances on the two sides: from $- 3$ to $4$ is three units to zero and four more.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Read A and B on the supplied line.

Worked solution

1
Read the scale from neighbouring labels.
$- 4 - (- 5) = 1$
Neighbouring ticks differ by one, so each interval represents one unit.
2
Locate A relative to zero.
$A = - 3$
A is three one-unit intervals left of zero.
3
Locate B relative to zero.
$B = 2$
B is two one-unit intervals right of zero.

Answer

A=−3; B=2.

EXAMPLE 02

Worked example 2

Consecutive ticks read −6, −3, 0, 3, 6. What is one interval worth and what comes next?

Worked solution

1
Find the change between adjacent labels.
$3 - 0 = 3$
The labels 0 and 3 are consecutive ticks, so one interval is three units.
2
Check the same scale on the negative side.
$- 6, - 3, 0$
Each step to the right adds three, including the step that reaches zero.
3
Continue one interval beyond 6.
$6 + 3 = 9$
The scale stays constant, so the next label is 9.

Answer

3 units per interval; next label 9.

03 / YOUR TURN

Try it yourself.

Check your understanding

How many units apart are −2 and 3?

Show answer & reasoning

5 units.

From $- 2$ to zero is two units, then zero to $3$ is three units. The total distance is $2 + 3 = 5$ units.

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

Read A on the supplied line.
1 mark
Fill the gaps: $- 3$ , $- 2$ , __, __, 1.
1 mark
Consecutive labels read $- 8$ , $- 4$ , 0, 4. What is each interval worth?
1 mark
Start at $- 5$ on a one-unit scale and move four ticks right. Where are you?
2 marks
How many units apart are $- 6$ and 2?
2 marks
Mia places $- 2$ halfway between $- 4$ and 4. Explain her error.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Read A on the supplied line.
1 mark
A is at the tick labelled $- 4$ .
$- 4$ .
Fill the gaps: $- 3$ , $- 2$ , __, __, 1.
1 mark
Increase by 1 each time.
$- 1$ and 0.
Consecutive labels read $- 8$ , $- 4$ , 0, 4. What is each interval worth?
1 mark
Neighbouring labels differ by 4.
4 units.
Start at $- 5$ on a one-unit scale and move four ticks right. Where are you?
2 marks
The four positions are $- 4$ , $- 3$ , $- 2$ , $- 1$ .
$- 1$ .
How many units apart are $- 6$ and 2?
2 marks
Six units to zero and two more.
8 units.
Mia places $- 2$ halfway between $- 4$ and 4. Explain her error.
2 marks
Zero is four units from each endpoint; $- 2$ is not equally far from them.
The halfway position is 0.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Positive/negative contexts; ordering; number lines; connection to coordinates.

Official curriculum source ↗

In this lesson

Understand the idea.

Read the interval

Keep the scale across zero

See the method in action.

Worked example 1

Read the scale from neighbouring labels.

Locate A relative to zero.

Locate B relative to zero.

Worked example 2

Find the change between adjacent labels.

Check the same scale on the negative side.

Continue one interval beyond 6.

Try it yourself.

Check your understanding

Keep practising