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Day 5 — Straight-line distance is not a route lengthYear 9 Maths · T1 W1–2 · Day 5 lesson

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Year 9 / Mathematics / Term 1 / Weeks 01 02

Part of the full two-week lesson sequence. Check the pack guide and taught point before teaching.

Open for this lesson: Pack guide.

Teacher copy: This page may include teaching prompts or answer keys. Answer keys in this public library can be viewed by anyone. Give learners a clean prompt, use checks as formative evidence, and change a case locally when prior access matters.

Goal/materials: use Pythagoras for coordinate distance; grid, Cards 7–9, calculator/square table available.

Notice, 3: On Card 7 (0,0)→(6,8), mark horizontal 6 and vertical 8. Ask whether their sum 14 is the straight shortcut. Key: no, 14 is the two-leg path.
Model, 5: “The right triangle gives d²=6²+8²=36+64=100, so d=10 grid units.” Do not call this a travel time, accessible route or device measurement.
Together, 8: Card 8 (-2,1)→(1,5): legs 3 and 4, d=5. Card 9 (1,-2)→(7,6): legs 6 and 8, d=10. Check the distance is positive and unchanged if point order swaps.
Try, 6: Fresh park-plan sketch (-1,-1)→(2,3). Key: Δx=3, Δy=4, d=5 grid units. Learner shows squared legs or a right triangle.
Check, 3: “Distance between (3,2) and (3,-5)?” Key: 7 units. If learner squares the vertical difference unnecessarily, show direct axis interval and compare the general formula. Assessment Items 1–4 may be collected across Days 4–6.

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