Mathematics • Year 8 • Unit 2 • Lesson 2

Plotting in the Wild

Use plotted points in real settings: a pirate treasure map with two chests, a netball court diagram, a hiking GPS, a video game mini-map, and a soccer free-kick. Then explain how you'd describe a point's position in your own words.

Apply · Real-World Maths

1. Word problems

Each problem is about placing or reading a point on a grid that represents a real space. Write the (x, y) pair, and where asked, the quadrant. Show your reasoning.

1.1 — Two-chest treasure map. The lighthouse is the origin (0, 0). Chest A is at (4, 3) and Chest B is at (−3, 2).

(a) Describe in plain English how you would walk from the lighthouse to Chest A (use "east/west" and "north/south").
(b) Describe how you would walk from the lighthouse to Chest B.
(c) State the quadrant of each chest. 3 marks

Stuck? Positive x = east, positive y = north, negative x = west, negative y = south.

1.2 — Netball court. A coach draws a coordinate grid on the netball court with the centre circle as the origin. Player W is at (−2, 4), Player C is at (0, 0), Player GS is at (1, −5).

(a) Which player is standing AT the origin? What does that mean about their position?
(b) State which quadrant W and GS are in.
(c) Which two players are on the same SIDE of the y-axis (left vs right)? 3 marks

Stuck? The "side" of the y-axis is decided by the sign of x: positive = right, negative = left.

1.3 — Hiking GPS (decimal coordinates). A hiker's GPS uses the trail entrance as the origin. After 30 minutes the screen reads (2.5, 1.5) — meaning kilometres east and north.

(a) Describe how to plot (2.5, 1.5) on a grid where each square is 1 km.
(b) The hiker turns back and walks to (1, 1.5). On the grid, did she move left, right, up or down — and by how much? 3 marks

Stuck? Same y-value means the move is purely horizontal. Compare the x-values.

1.4 — Video game mini-map. In a game, the player spawns at (0, 0). Enemy spawn points are at (−4, 0), (4, 0), (0, 4) and (0, −4) — one in each of the four cardinal directions.

(a) For each enemy, state which axis they sit on.
(b) None of the enemies is in a quadrant — explain why in one sentence. 3 marks

Stuck? A point with one coordinate equal to 0 sits ON an axis, not inside a quadrant.

1.5 — Free-kick on the pitch. A soccer pitch uses the centre spot as the origin. The ball is placed at the free-kick mark (−3, −4). The goalkeeper stands at (0, −10) on the goal line.

(a) Write each position as a coordinate pair, and state the quadrant or axis it sits on.
(b) The ball is "3 left and 4 down" from the centre spot — describe a similarly-placed free kick that would land on the opposite (mirror) side of both axes. 3 marks

Stuck? Mirror across BOTH axes = flip the sign of x AND of y.

2. Explain your thinking

This question is about communication. Use full sentences. 4 marks

2.1 A friend has a blank coordinate grid. You want them to mark the point (−2.5, 3). Write a clear set of instructions they could follow without seeing the page. Your instructions must use the words "origin", "left/right" and "up/down", and must mention that 2.5 is halfway between two grid lines. End with a sentence about which quadrant they have just plotted into.

Stuck? Revisit lesson § "Step-by-step plotting" and § Key Terms — "Decimal coordinates" sit between integer grid intersections.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Two-chest treasure map

(a) Chest A(4, 3): walk 4 paces east, then 3 paces north.
(b) Chest B(−3, 2): walk 3 paces west, then 2 paces north.
(c) A → Quadrant I (+, +); B → Quadrant II (−, +).

1.2 — Netball court

(a) Player C stands at the origin (0, 0) — directly on the centre circle.
(b) W(−2, 4) → Quadrant II; GS(1, −5) → Quadrant IV.
(c) The right side of the y-axis has positive x. C (x = 0) is on the y-axis itself; GS (x = 1) is on the right. W has x = −2, so she is on the left. So GS is the only player strictly on the right; C and W are both "not on the right" (C is on the line, W is left). The pair with the SAME side is therefore C and W (both have x ≤ 0).

1.3 — Hiking GPS

(a) Start at the trail entrance (origin). Move 2.5 km east (halfway between the 2 km and 3 km gridlines on the x-axis). Then move 1.5 km north (halfway between the 1 km and 2 km gridlines on the y-axis). Mark a dot midway between grid intersections.
(b) Same y (1.5), so the move is purely horizontal. x went from 2.5 to 1.0, so she moved 1.5 km west (left).

1.4 — Video game mini-map

(a) (−4, 0) and (4, 0) lie on the x-axis. (0, 4) and (0, −4) lie on the y-axis.
(b) Each enemy has at least one coordinate equal to 0, so each one sits ON an axis. Quadrants are the regions BETWEEN axes — they don't include the axes themselves.

1.5 — Free-kick

(a) Ball (−3, −4) → Quadrant III. Keeper (0, −10) → on the y-axis.
(b) Mirror "3 left, 4 down" across BOTH axes by flipping both signs: (3, 4) — that's "3 right, 4 up" from the centre spot, placing the ball in Quadrant I.

2.1 — Explain your thinking (sample response)

Start at the origin — the (0, 0) point where the two axes cross. Move 2.5 units to the LEFT along the x-axis; because 2.5 is halfway between 2 and 3, stop your pencil exactly halfway between the −2 and −3 grid lines. From there, move 3 units UP, finishing at the third gridline above the x-axis. Mark and label the dot. You have just plotted the point in the top-left region — Quadrant II.

Marking: 1 mark for starting at the origin and going x first; 1 mark for "2.5 to the left" with the halfway language; 1 mark for "3 up"; 1 mark for correctly naming Quadrant II.