Numeracy pitch: measure and build the design
Ākonga apply area, volume and scale to a whare iti design and check that the numbers are consistent.
- Numeracy move: Geometry applied and checked
- Evidence it produces: A dimensioned design whose measurements agree
Before you plan from this: the lesson body below is currently near-identical to the other route's. This panel describes the intended difference, which is not authored yet — so choose either route on topic and year band, not on this pitch. Both routes are kept and will be differentiated; neither is being retired.
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 centimeter 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 apply mathematical skills (statistics, geometry, data analysis) to real Aotearoa housing and sustainability contexts — connecting mātauranga Māori principles of kāinga, papakainga, and whanaungatanga to contemporary housing challenges and design.
Ngā Paearu Angitū — Success Criteria
- ✅ Can collect, display, and interpret data about Aotearoa housing using appropriate statistical representations
- ✅ Applies geometric reasoning to evaluate sustainable design principles in whare design
- ✅ Connects mathematical findings to social justice questions about housing equity and Māori land rights
Differentiation & Inclusion
Scaffold support: Provide pre-structured data tables as an entry point for statistical analysis; use visual floor-plan templates for geometry tasks. Extension tasks include calculating comparative housing density statistics or modelling papakainga land-use scenarios.
ELL / ESOL: Pre-teach mathematical vocabulary alongside contextual terms (papakainga, whanaungatanga, toitū); use diagrams and real photographs of Aotearoa housing to ground abstract data.
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: Kāinga and papakainga as living mathematical contexts — whare design embodies geometric knowledge. Whanaungatanga shapes community housing decisions. Kaitiakitanga frames sustainability calculations. Māori land statistics connect tūhuratanga (inquiry) to tino rangatiratanga.
Prior knowledge: Basic statistics (mean, median, graphs); introductory geometry (area, perimeter, scale).
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.”