The idea, step by step
Read the interval
Each equal interval on a number line represents the same change in value. Find two labelled ticks and count the intervals between them before reading an unlabelled position.
From −4 to 2 the change is 6 units. If those labels are three equal intervals apart, each interval represents 2 units.
Keep the scale across zero
A one-unit sequence runs −3, −2, −1, 0, 1, 2, 3. Zero has its own position; do not skip it or place it between two ticks.
Distance along the line is a non-negative count of units. The positions −3 and 4 are seven units apart: three to zero, then four beyond it.
A common trap
The next whole-number position after −1 is 1.
Instead: Zero comes between −1 and 1 on a one-unit scale.
See the thinking
Worked example 1
Read A and B on the supplied line.
- Check the tick labels: each interval is 1 unit.
- A is on −3 and B is on 2.
Worked example 2
Consecutive ticks read −6, −3, 0, 3, 6. What is one interval worth and what comes next?
- The labels increase by 3 each time.
- One more interval after 6 gives 9.
Check your understanding
How many units apart are −2 and 3?
Show answer
5 units.
Two units to zero and three more give five.
Your turn
6 questions · 9 marks · Work at your own pace.
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.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Positive/negative contexts; ordering; number lines; connection to coordinates.
Official curriculum source ↗