Learning intention and success evidence
We are learning to calculate straight-line distance between coordinate points and use it as one piece of planning evidence.
- I show horizontal and vertical changes before substituting.
- I report distance in metres, not coordinate units.
- I separate “shortest” from “best” when another constraint matters.
Exact Phase 4 curriculum anchor
- Using Pythagoras’ theorem to:find the length of an unknown side in a right-angled trianglecheck if a triangle has a right anglecalculate the distance between two points in the coordinate plane, yielding the distance formula d = √(x2 − x1)2 + (y2 − y1)2 - find the length of an unknown side in a right-angled triangle - check if a triangle has a right angle - calculate the distance between two points in the coordinate plane, yielding the distance formula d = √(x2 − x1)2 + (y2 − y1)2
Preparation
Print: learner pack page L2. Retain the fictional scale from Lesson 1: 1 unit = 10 m. Calculators are useful; no internet or real zoo data is required.
60-minute runsheet
- Whakaoho — estimate first (5 min): without calculating, rank O(0,0)→W(4,8), O→C(8,−4) and O→H(−6,5) from shortest to longest.
- Derive the method (12 min): draw the right triangle from O to W. Label horizontal change 4 and vertical change 8, then connect Pythagoras: d = √(4²+8²) = √80 units.
- Guided calculation (15 min): pairs calculate O→C and O→H. Each line must show Δx, Δy, substitution, coordinate-unit result and metre result.
- Route decision (18 min): compare direct O→W with O→R₂→W, where R₂=(6,2). The direct path is restricted in the fictional brief; decide whether the detour remains under 130 m.
- Error clinic (7 min): diagnose: d = √[(8−4)+(−4−8)] for C(8,−4) to W(4,8). Rewrite it correctly and explain both errors.
- Exit evidence (3 min): write one sentence beginning “The shortest route is not automatically the selected route because…”
Worked checkpoints
- O→C = √80 units ≈ 8.94 units = 89.4 m.
- O→H = √61 units ≈ 7.81 units = 78.1 m.
- O→W = 89.4 m. O→R₂→W ≈ 63.2 m + 63.2 m = 126.4 m, so the fictional 130 m constraint is met.
Assessment note: accept correct exact radical forms before rounding. Require units at the final step.