The idea, step by step
Break a route into steps
A clear route gives a start, a direction and a distance, then states each change of direction. From Home at A1, go three cells east to Park at D1, then three north to School at D4. Say whether you are counting moves between cells or counting the cells themselves.
More than one route can work
If no obstacles or road restrictions are shown, different routes may reach the same place. Compare the total steps rather than judging a route by how many instructions it uses. Do not claim real metres from this map: no ground-distance scale is supplied.
A common trap
Counting the starting cell as the first move.
Instead: A move crosses from one cell to the next. Starting in A1 does not count as a move.
See the thinking
Follow a route
Start at Home A1. Move two cells east and one north. Where are you?
- Two east moves take A1 to B1, then C1.
- One north move takes C1 to C2.
- The named place in C2 is Shop.
Compare routes
Compare A1 to D4 by east-then-north with north-then-east.
- First route: 3 east + 3 north = 6 steps.
- Second route: 3 north + 3 east = 6 steps.
- Both reach the same cell without an obstacle.
Check your understanding
Start at C2 and move one cell west. Which cell do you reach?
Show answer
B2.
West decreases the column by one and keeps the row.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Start at A1. Move three cells east. Give the destination.1 mark
- Start at D4. Move three cells south. Give the destination.1 mark
- Start at A1. Move one east and two north. Give the destination.1 mark
- Write a route from Shop C2 to School D4 using only east and north moves.2 marks
- Find the fewest north/south/east/west cell steps from Library B3 to Park D1, with no obstacles.2 marks
- Can this map alone tell the walking distance from Home to School in metres? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Start at A1. Move three cells east. Give the destination.1 mark
A1 → B1 → C1 → D1.
D1, Park. - Start at D4. Move three cells south. Give the destination.1 mark
D4 → D3 → D2 → D1.
D1, Park. - Start at A1. Move one east and two north. Give the destination.1 mark
A1 → B1 → B2 → B3.
B3, Library. - Write a route from Shop C2 to School D4 using only east and north moves.2 marks
C2 → D2 → D3 → D4. North-then-east is also valid.
One cell east, then two cells north. - Find the fewest north/south/east/west cell steps from Library B3 to Park D1, with no obstacles.2 marks
Two east and two south are needed.
Four steps. - Can this map alone tell the walking distance from Home to School in metres? Explain.2 marks
A real-distance scale would be needed.
No; it gives cells but no distance scale or paths in metres.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Letter–number references; positions; directions; pathways.
Official curriculum source ↗