Movement on coordinate grids | Year 5

01 / LEARN

Understand the idea.

Change the coordinate matching the direction

Horizontal movement changes $x$ ; vertical movement changes $y$ . Moving right adds to $x$ , and moving left subtracts from it. Moving up adds to $y$ , and moving down subtracts from it.

Keep the unchanged coordinate visible. From $(2, 1)$ , moving three right gives $(5, 1)$ : the height remains one. For a longer route, record the new ordered pair after each move to avoid changing the wrong number.

An equal-unit coordinate grid labelled from zero to six on both axes. A sage path runs one unit right from Start at (2, 1) to (3, 1), then three units up to Finish at (3, 4).

Check a longer route

Check each stop against the grid limits. A valid instruction can lead beyond a small drawn grid, so do not force the endpoint onto the nearest edge. Use the stated units, not just a count of squares.

To undo a route, reverse the order of its moves and change each direction to its opposite. Undoing “right two, then up one” means “down one, then left two”. Grid route lengths follow the horizontal and vertical moves.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Follow two moves

Start at (1, 2). Move 4 right, then 3 up. Find the endpoint.

Worked solution

1
Move four units right.
$\begin{aligned} x & = 1 + 4 = 5 \\ (x, y) & = (5, 2) \end{aligned}$
A rightward move changes only the horizontal coordinate.
2
Move three units up.
$\begin{aligned} y & = 2 + 3 = 5 \\ (x, y) & = (5, 5) \end{aligned}$
An upward move changes only the vertical coordinate.
3
State the endpoint.
$(5, 5)$
Both instructions have been applied in order to the starting point.

Answer

(5, 5)

EXAMPLE 02

Work backwards

A robot ends at (4, 3) after moving 2 left and 1 up. Where did it start?

Worked solution

1
Undo the last move first.
$\begin{aligned} y & = 3 - 1 = 2 \\ (x, y) & = (4, 2) \end{aligned}$
The last move was up one, so its reverse is down one.
2
Undo the earlier left move.
$\begin{aligned} x & = 4 + 2 = 6 \\ (x, y) & = (6, 2) \end{aligned}$
Reversing a move two left requires moving two right.
3
Check the original route forwards.
$\begin{aligned} (6, 2) & \to (4, 2) \\ (4, 2) & \to (4, 3) \end{aligned}$
Left two and up one return to the given endpoint, confirming the start.

Answer

(6, 2)

03 / YOUR TURN

Try it yourself.

Check your understanding

Start at (5, 4) and move 3 left. Where do you finish?

Show answer & reasoning

(2, 4)

Moving left subtracts from $x$ while keeping $y$ fixed. Thus $(5, 4)$ becomes $(5 - 3, 4) = (2, 4)$ .

Keep practising

6 worksheet questions · 10 marks

Open worksheet Worked solutions

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
$(1, 1) \to (4, 1) \to (4, 5) \to (2, 5)$ .
$(2, 5)$
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.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics 2026

Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.

Official curriculum source ↗

In this lesson

Understand the idea.

Change the coordinate matching the direction

Check a longer route

See the method in action.

Follow two moves

Move four units right.

Move three units up.

State the endpoint.

Work backwards

Undo the last move first.

Undo the earlier left move.

Check the original route forwards.

Try it yourself.

Check your understanding

Keep practising