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 maximizes utility within a fixed area.
- Understand: How geometry is used to solve design problems like housing affordability.
He Kōrero Timatanga - 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.
🎬 Media Anchor
Use this clip to reinforce geometric reasoning and transformation language before floor-plan refinement.
- Pause and discuss: Which transformation idea helps optimize space in your whare iti plan?
- Transfer task: Revise one zone in your design and annotate the geometric reasoning.
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
- Mathematics — Level 4 Statistics: Plan and conduct investigations using the statistical enquiry cycle; interpret findings in context.
- Mathematics — Level 4 Geometry: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles.