Justice pitch: model against real constraints
Ākonga design against cost, materials, climate and consent constraints, state their assumptions, and test how sensitive the design is to one assumption being wrong.
- Years 9–10 move: Model with assumptions stated and tested
- Evidence it produces: A design plus what breaks if one assumption fails
Before you plan from this: the justice pitch below is now authored into the lesson body. The other route's body still overlaps strongly with this one but differs in emphasis — choose either route on topic and year band.
Whare Iti: Geometry of Design
Big living in small spaces
Ako | Learning Intentions
- Know: The formulas for area and perimeter of composite shapes.
- Do: Create a scale floor plan for a tiny home that maximises utility within a fixed area.
- Understand: How geometry is used to solve design problems like housing affordability.
He Kōrero Tīmatanga - Introduction
Housing is expensive. One solution gaining popularity in Aotearoa is the "Tiny Home" movement. But designing a small space requires clever mathematics. Every square centimetre counts.
Discussion Starter
"What is the minimum space a person needs to live comfortably? Why?"
Consider: Sleeping, cooking, washing, relaxing.
Part 1: The Design Challenge
Your Client: A young couple looking for their first home.
Constraints:
- Maximum Floor Area: 30m² (excluding loft).
- Must include: Kitchen, Bathroom, Living Area, Sleeping Area (can be loft).
- Max Trailer Width: 2.5m (Legal road limit).
Part 2: Geometry in Action
Students draw a floor plan on grid paper (Scale 1:50).
📐 Calculation Station
Calculate the Area of each "zone" in your house.
Bathroom Area = 1.2m x 2.0m = 2.4m²
Total Footprint = Length x Width
Must be ≤ 30m²
Part 3: Cost Estimation (Surface Area)
To estimate the cost of cladding, we need the Surface Area of the exterior walls.
Task: Calculate the total wall area (minus windows/doors) to determine how many timber-boards are needed.
Part 4: Plan Critique — Defend Your Square Metres (15 minutes)
No video for this part. In pairs, swap whare iti plans and audit each other's numbers rather than each other's taste.
- Recalculate, don't trust: Take your partner's floor plan and work out the total footprint yourself from their dimensions. Do you get the same answer? Is it still ≤ 30 m²?
- Find the dead space: Identify one area on their plan that is used for nothing — a corner you cannot stand in, a corridor wider than it needs to be. Give it in square metres.
- Spend it: Propose one change that gives those square metres to a zone that needs them. Your partner has to be able to redo the area calculation from your proposal alone.
- Cost it: Does your change alter the exterior wall area from Part 3? If so, by how much, and what does that do to the cladding estimate?
Share back: Each pair reports one change and the number that justifies it. The number is the argument — "it looks better" does not count.
Kaiako Notes
Encourage students to research real Tiny House plans online for inspiration. This connects abstract geometry to tangible, desirable outcomes.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students design a whare iti to a brief, using scale drawing, perimeter, area, and volume to model real constraints — then defend their square metres: what the design gives, what it costs, and who it serves. Geometry is the tool; the critique is the goal.
Ngā Paearu Angitū — Success Criteria
- ✅ Can apply scale resizing and justify its effect on perimeter, area, or volume in a design brief
- ✅ Can calculate perimeters, areas of composite shapes, and volumes of prisms for a whare iti plan
- ✅ Can critique a design against its constraints — cost, space, sustainability — using their own calculations as evidence
Differentiation & Inclusion
Scaffold support: Provide grid templates and a worked Calculation Station example as an entry point. Extension tasks include modelling papakainga land-use scenarios or optimising the plan for a tighter budget.
ELL / ESOL: Pre-teach geometry vocabulary alongside contextual terms (whare iti, toitū); label diagrams in both languages and use floor plans or physical models to ground abstract measures.
Inclusion: Offer manipulatives and digital tools alongside written tasks; neurodiverse learners benefit from step-by-step data investigation guides and reduced open-ended prompts.
Mātauranga Māori lens: Whare design embodies geometric knowledge — area, perimeter and scale decisions are cultural as well as mathematical. Kaitiakitanga frames the sustainability constraint: a whare iti that wastes space or materials fails both the brief and the value.
Prior knowledge: Perimeter and area formulas; comfort with scale drawings and unit conversions.
Curriculum alignment
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 4 (Years 9–10) · Measurement (Knowledge): “- Resizing (enlarging or reducing) a shape changes its perimeter, area, or volume proportionally according to the dimensions of the units; linear metric conversions must be squared to convert area and cubed to convert volume.”
- NZC (2007) · Mathematics and Statistics · Level 5: “Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.”