Mathematics • Year 8 • Unit 2 • Lesson 1
Treasure Maps, Phones & City Streets
Use the Cartesian plane where it really lives: pirate treasure maps, the pixels on a phone screen, chess boards, and the city grid. Then explain how you'd give a friend your location using two numbers.
1. Word problems
Each problem uses an ordered pair (x, y) where the FIRST number is horizontal and the SECOND is vertical. Show your reasoning — a final answer with no working only earns half marks.
1.1 — Treasure map. Captain Grid buried treasure 4 paces east and 3 paces north of the old oak. East is positive x, north is positive y, and the oak is the origin.
(a) Write the treasure's coordinates.
(b) State which quadrant the treasure lies in.
(c) A decoy chest is at (−4, 3) — same y, opposite x. In one sentence, describe how its position differs from the treasure's. 3 marks
1.2 — Phone screen pixels. A phone screen treats the bottom-left corner as the origin (0, 0). The "tap" icon you want is 120 pixels right and 250 pixels up.
(a) Write the icon's pixel coordinates as an ordered pair.
(b) Could the y-value ever be negative on this screen? Explain in one sentence. 2 marks
1.3 — Chess board addresses. A chess board labels columns a–h (left to right) and rows 1–8 (bottom to top). Treat column "a" as x = 1, "b" as x = 2, … and the row number as y.
(a) What ordered pair (x, y) describes the square c5?
(b) Which chess square is at (8, 8)? 2 marks
1.4 — Meeting up in town. Three friends choose the town clock as the origin (0, 0). Mia is 2 blocks east and 5 blocks north. Jay is 3 blocks west and 4 blocks south. Sam is right at the clock.
(a) Write coordinates for Mia, Jay and Sam.
(b) State which quadrant Mia and Jay are in (Sam isn't in any — explain why in one phrase). 3 marks
1.5 — Drone delivery. A drone leaves base at (0, 0). It first flies to a customer at (5, 0), then to another at (0, 5).
(a) Which axis is each customer on?
(b) Are either of these customers in a quadrant? Explain in one sentence. 2 marks
2. Explain your thinking
This question is about communication. Use full sentences. 4 marks
2.1 A classmate looks at the point (5, 2) and says: "That's the same as (2, 5) because it uses the same numbers." In your own words, explain (i) why they are wrong, (ii) where each of those two points actually sits on the plane, and (iii) what quadrant — if any — each one belongs to. Use the phrase "x first, y second" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Treasure map
(a) (4, 3).
(b) Both positive → Quadrant I.
(c) The decoy is the mirror image of the treasure across the y-axis — same height (y = 3) but 4 paces west of the oak instead of east, putting it in Quadrant II.
1.2 — Phone screen pixels
(a) (120, 250).
(b) No — the bottom-left corner is the origin, so every pixel on the screen has x ≥ 0 and y ≥ 0. The whole screen lives in Quadrant I (or on its axes).
1.3 — Chess board addresses
(a) c5 → column 3, row 5 → (3, 5).
(b) (8, 8) → column 8 (h), row 8 → square h8 (top-right corner).
1.4 — Meeting up in town
(a) Mia (2, 5); Jay (−3, −4); Sam (0, 0).
(b) Mia is in Quadrant I (+, +). Jay is in Quadrant III (−, −). Sam is at the origin — and the origin sits on BOTH axes, so it isn't in any quadrant.
1.5 — Drone delivery
(a) (5, 0) lies on the x-axis; (0, 5) lies on the y-axis.
(b) No — both points have one coordinate equal to 0, so they sit on an axis, not inside any quadrant.
2.1 — Explain your thinking (sample response)
The classmate is wrong because coordinates are ORDERED. The rule is x first, y second, so (5, 2) means "go 5 right, 2 up" while (2, 5) means "go 2 right, 5 up". Those land on completely different points: (5, 2) is far to the right and only a little above the x-axis, while (2, 5) is close to the y-axis and much higher up. Both points have a positive x and positive y, so they BOTH live in Quadrant I — but at different addresses inside it. Swapping the order of the numbers changes the location even though it doesn't change the quadrant this time.
Marking: 1 mark for stating order matters / "x first, y second"; 1 mark for describing the position of (5, 2); 1 mark for describing the position of (2, 5); 1 mark for correctly placing both in Quadrant I.