Understand the idea.
Position and movement are different
A position is where you start; a directed change tells how far and which way to move. Positive change moves right and negative change moves left. Count intervals travelled, rather than counting the starting point as a step.
When a journey crosses zero, split it there. This turns one long movement into two manageable distances. Keep track of how much movement has already been used, then apply only the amount remaining.
Distance does not have a negative sign
Distance measures separation and is always non-negative. Signed change also records direction: the change from to is , but reversing the journey gives . Both journeys cover a distance of 5 units.
For a directed journey, calculate change as final position minus starting position. Check it by adding the proposed change to the start. You should reach the given finish, with the direction matching your number-line movement.
See the method in action.
Move right through zero
Start at −5 and move 8 units right. Where do you finish?
Worked solution
- 1
Reach zero from the starting point.
Five units of the rightward movement take the position from −5 to zero.
- 2
Find the unused movement.
Only five of the eight required units have been travelled.
- 3
Continue right from zero.
The remaining three rightward units give the final position 3.
3
Move left through zero
Start at 4 and move 9 units left. Where do you finish?
Worked solution
- 1
Reach zero by moving left.
Four leftward units remove the positive starting distance from zero.
- 2
Find the unused movement.
Five of the nine leftward units still need to be travelled.
- 3
Continue left from zero.
Five units to the left of zero gives the final position −5.
−5
Try it yourself.
Check your understanding
Find the signed change from −4 to 2.
Show answer & reasoning
+6
From , move four units right to zero and two more right to 2. The total signed change is .
Keep practising
6 worksheet questions · 13 marks
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 ↗