The idea, step by step
Position and movement are different
A point gives a position on the number line. A movement gives a number of units and a direction. Positive changes move right; negative changes move left. Start at the given point before counting any steps.
From −5, moving 8 units right first travels 5 units to zero, then 3 more to +3. Counting the starting point as the first step would put the finish one unit too close.
Distance does not have a negative sign
Distance describes how many units separate two positions, so it is non-negative. Signed change also records the direction from the first position to the second.
From −7 to −2, the distance is 5 units and the signed change is +5. Reverse the journey: the distance stays 5 units, but the signed change becomes −5.
A common trap
A negative change means a negative distance.
Instead: Distance is a non-negative size; the sign belongs to the direction.
See the thinking
Move right through zero
Start at −5 and move 8 units right. Where do you finish?
- Five units right reaches zero.
- Three units of the move remain.
- Finish at 3.
Move left through zero
Start at 4 and move 9 units left. Where do you finish?
- Four units left reaches zero.
- Five units remain to move left.
- Finish at −5.
Check your understanding
Find the signed change from −4 to 2.
Show answer
+6
Move 4 units right to zero, then 2 more units right.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- Start at −3 and move 5 units right. Find the finish.2 marks
- Start at 6 and move 10 units left. Find the finish.2 marks
- Find the signed change from −7 to −2.2 marks
- A move of 6 units left ends at −1. Where did it start?2 marks
- Find the distance between −2 and 3.2 marks
- Start at −8 and move 11 units right. Give the finish and the signed change.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Start at −3 and move 5 units right. Find the finish.2 marks
Three units reach zero.
Two more units reach 2.
2 - Start at 6 and move 10 units left. Find the finish.2 marks
Six units reach zero.
Four more units reach −4.
−4 - Find the signed change from −7 to −2.2 marks
−2 is five units right of −7.
Right is the positive direction.
+5 - A move of 6 units left ends at −1. Where did it start?2 marks
Undo the move by travelling 6 units right from −1.
The start was 5.
5 - Find the distance between −2 and 3.2 marks
Two units reach zero.
Three further units reach 3.
.
5 units - Start at −8 and move 11 units right. Give the finish and the signed change.3 marks
Eight units right reach zero; three more reach 3.
The entire movement was +11.
Finish 3; change +11.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum
Positive and negative numbers in context; comparing and ordering integers; number lines and directed change; adding integers; subtracting integers; mixed addition/subtraction problems. Multiplication/division of negative integers is a labelled preview, not the Year 7 core endpoint.
Official curriculum source ↗