The idea, step by step
Change the coordinate matching the direction
Moving right or left changes x; moving up or down changes y. From (2, 1), moving 3 units right gives (5, 1). The height stays 1.
To move from (2, 1) to (3, 4), travel 1 unit right and 3 up. The order of those two moves does not change the endpoint, provided both can be made.
Check a longer route
For several instructions, record a position after every move. Do not add a horizontal change to the y-coordinate. Check that each position lies inside the stated grid.
To undo a route, reverse both its order and its directions. Undo “right 2, up 1” by moving “down 1, left 2”. Route lengths in this lesson follow horizontal and vertical grid lines; they are not diagonal distances.
A common trap
Moving up changes the first coordinate.
Instead: The first coordinate measures horizontally. Up and down change the second coordinate.
See the thinking
Follow two moves
Start at (1, 2). Move 4 right, then 3 up. Find the endpoint.
- Right 4 changes the position to (5, 2).
- Up 3 gives (5, 5).
Work backwards
A robot ends at (4, 3) after moving 2 left and 1 up. Where did it start?
- Undo up 1: (4, 2).
- Undo left 2 by going right 2: (6, 2).
Check your understanding
Start at (5, 4) and move 3 left. Where do you finish?
Show answer
(2, 4)
Only x changes: 5 − 3 = 2.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- Start at (2, 3). Move 2 right. Give the new coordinates.1 mark
- Start at (4, 5). Move 3 down. Give the new coordinates.1 mark
- Start at (1, 1). Move right 3, up 4, then left 2. Find the endpoint.2 marks
- Give horizontal and vertical directions from A(2, 5) to B(6, 2).2 marks
- A robot moves right 2 and down 3, finishing at (5, 1). Find its start.2 marks
- Two routes go from (1, 1) to (4, 3). A goes right 3 then up 2; B goes up 2 then right 3. Compare their lengths along grid lines.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Start at (2, 3). Move 2 right. Give the new coordinates.1 mark
x becomes 2 + 2 = 4; y stays 3.
(4, 3) - Start at (4, 5). Move 3 down. Give the new coordinates.1 mark
y becomes 5 − 3 = 2; x stays 4.
(4, 2) - Start at (1, 1). Move right 3, up 4, then left 2. Find the endpoint.2 marks
(1,1) → (4,1) → (4,5) → (2,5).
(2, 5) - Give horizontal and vertical directions from A(2, 5) to B(6, 2).2 marks
6 − 2 = 4 right; 5 − 2 = 3 down.
4 right and 3 down, in either order. - A robot moves right 2 and down 3, finishing at (5, 1). Find its start.2 marks
Undo down 3 by going up 3, then undo right 2 by going left 2.
(3, 4) - Two routes go from (1, 1) to (4, 3). A goes right 3 then up 2; B goes up 2 then right 3. Compare their lengths along grid lines.2 marks
Each uses 3 horizontal steps and 2 vertical steps: 3 + 2 = 5.
Both routes are 5 units long.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.
Official curriculum source ↗