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.
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
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
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
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
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
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.
How did this worksheet feel?
What I'll revisit before next class:
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.