Learning intention and success evidence
We are learning to use perimeter and area calculations to test options against a fictional planning brief.
- I calculate with correct dimensions and square units.
- I distinguish a hard constraint from a preference.
- I defend a feasible option and name its trade-off.
Exact Phase 4 curriculum anchor
- Finding:the perimeter of 2D shapesthe circumference of circlesthe area of parallelograms, trapeziums, and kites, relating the formulae used to the formula for a rectangle - the perimeter of 2D shapes - the circumference of circles - the area of parallelograms, trapeziums, and kites, relating the formulae used to the formula for a rectangle - Deriving the formulae for the perimeter of half and quarter circles from the formula for a full circle - Calculating the perimeter of half circles and quarter circles
Fictional decision brief
A learning habitat footprint must have area at least 1,000 m², perimeter no more than 150 m, a straight-line route from O shorter than 110 m, and estimated barrier cost no more than $90,000 at the fictional rate of $600 per metre. These are classroom constraints, not animal-welfare or zoo-design standards.
60-minute runsheet
- Whakaoho — units audit (5 min): sort m, m² and dollars beside length, area and cost. Explain why a 40 m by 30 m rectangle is not “1,200 m”.
- Model one option (10 min): Option A is a 40 m by 30 m rectangle whose centre is 80 m from O. Calculate area, perimeter and barrier cost.
- Pair calculations (15 min): Option B is a 50 m by 22 m rectangle, centre distance 95 m. Option C is a parallelogram with base 45 m, perpendicular height 25 m, side length 28 m and centre distance 105 m.
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Constraint matrix (20 min): two more options are on
the table. Option D is a 60 m by 18 m rectangle, centre distance 100 m.
Option E is a 35 m by 30 m rectangle, centre distance 115 m. Mark
pass/fail for all four constraints across all five options. Reject the
infeasible ones before applying any preference, then choose between the
options that survive using one declared preference.
Watch for: Option E is the cheapest of the five and passes every constraint that depends on the shape itself. It is still infeasible. A pair that screens only area, perimeter and cost will accept it — the distance from O is the constraint they forgot to check, and it is the one this unit is actually about. - Trade-off conference (7 min): pairs exchange decisions. The listener must identify which calculation, constraint and preference drove the recommendation.
- Exit evidence (3 min): write: “Option ___ is feasible because ___. I still cannot claim it is best because ___.”
Worked checkpoints
| Option | Area | Perimeter | Cost | Feasible? |
|---|---|---|---|---|
| A | 1,200 m² | 140 m | $84,000 | Yes |
| B | 1,100 m² | 144 m | $86,400 | Yes |
| C | 1,125 m² | 146 m | $87,600 | Yes |
| D | 1,080 m² | 156 m | $93,600 | No — perimeter and cost |
| E | 1,050 m² | 130 m | $78,000 | No — 115 m from O |
A, B and C all satisfy the hard constraints supplied in this fictional scenario. That is deliberate: once the infeasible options are gone, arithmetic cannot finish the job, and learners must make their preference explicit instead of treating calculation as an automatic decision.
D and E exist so that the rejection step is real rather than rehearsed. D is the longest shape: its area clears the minimum, but stretching a rectangle to 60 m drives the perimeter past 150 m, and because barrier cost is charged per metre the same failure appears twice. Ask pairs why those two constraints cannot fail independently. E fails on nothing you can see in its dimensions — it is the cheapest option and the second-smallest perimeter — and is rejected only on where it sits relative to O.