Numeracy first: read the data, then conclude
Every lesson in this edition starts from the housing and sustainability data itself. Ākonga read the tables, compute the measures, and only then draw conclusions they can defend with figures.
- Approach: Data-reading and calculation ladder, lesson by lesson
- Evidence it produces: Conclusions that cite a computed figure, not an impression
Unit 60: Mathematics in Aotearoa
Housing, Sustainability, and Data
This unit is designed for the new NCEA Level 1 Mathematics and Statistics supervision. It focuses on AS 91945 (1.2) : "Use mathematical methods to explore problems that relate to life in Aotearoa New Zealand".
Whakatūwhera - Unit Opening
We face a housing crisis and a climate crisis. How can mathematics help us understand these problems and design solutions? By analysing data on housing affordability and using geometry to design efficient, sustainable "tiny homes", students see math as a tool for social and environmental justice.
📋 Kaiako Planning Snapshot
Ngā Whāinga Akoranga — Learning Intentions
- Ākonga will apply mathematical thinking — statistics, geometry, and data analysis — to real-world housing and sustainability challenges.
- Ākonga will understand how housing unaffordability and environmental degradation reflect systemic inequities, including impacts on Māori whānau.
- Ākonga will draw on tikanga Māori and the concept of kaitiakitanga to evaluate sustainable design solutions.
- Ākonga will design a mathematically-informed solution to a housing or sustainability problem in their community.
Paearu Angitu — Success Criteria
- I can collect and analyse housing data using statistical methods and explain what it shows about equity.
- I can apply geometric principles to design an efficient and sustainable living space.
- I can explain how whanaungatanga and manaakitanga inform community-centred housing design.
- I can present a mathematically justified solution to a real housing or sustainability challenge.
Entry / On-Level / Extension
- Entry: Guided data tasks with visual scaffolds; pre-built graph templates; step-by-step geometry investigations with annotations.
- On-level: Independent data collection and analysis; design a tiny home using specified mathematical constraints; community survey task.
- Extension: Cost-benefit analysis of sustainable housing materials; design a community development proposal integrating mātauranga Māori principles.
Inclusion Guidance
- ESOL / ELL learners: Pre-teach vocabulary for data and geometry. Use visual diagrams and worked examples. Partner tasks encourage language development through collaboration.
- Neurodiverse learners / ADHD: Chunked investigations with clear milestones. UDL principle: graph paper, digital tools, and physical models as alternative representations. Choice of final format.
- Dyslexia: Emphasis on visual and spatial tasks where possible; oral explanation of reasoning accepted alongside written work.
Part 1: The Numbers Behind the Housing Crisis
Learning Focus
Using statistical inquiry to understand trends in house prices, rent, and inflation over the last 20 years. Students will analyse multivariate data to tell a story about equity in Aotearoa.
Key Methods
- Time Series Data: Plotting trends over time.
- Percentages & Ratios: Comparing income vs housing costs.
- Interpretation: What does "median" mean in this context?
Core Activities
- Lesson 1: Data Detective - Exploring the Stats NZ dataset.
Part 2: Tiny Home Geometry
Learning Focus
Applying measurement and geometric reasoning to design a sustainable "Tiny Home" or "Whare Iti". Maximising space and minimising waste.
Key Methods
- Area & Perimeter: Optimising floor plans.
- Volume: Calculating air flow and materials.
- Scale Drawings: Creating accurate plans (1:50).
Core Activities
- Lesson 2: Whare Iti Design - The geometry of optimisation.
Part 3: Community & Culture
Learning Focus
Exploring data related to Te Reo Māori speakers, iwi demographics, and community wellbeing.
Core Activities
- Lesson 3: Our People, Our Numbers - Demographic analysis.
Curriculum alignment
- Number — Practices: - Applying a proportional increase or decrease to a number - Calculating the percentage increase or decrease between two numbers (e.g. What is the percentage increase between …
- Measurement — Practices: - Applying a proportional increase or decrease to a number - Calculating the percentage increase or decrease between two numbers (e.g. What is the percentage increase between …
- Statistics — Practices: - Applying a proportional increase or decrease to a number - Calculating the percentage increase or decrease between two numbers (e.g. What is the percentage increase between …
- Algebra — Practices: - Applying a proportional increase or decrease to a number - Calculating the percentage increase or decrease between two numbers (e.g. What is the percentage increase between …
- Geometry — Practices: - Applying a proportional increase or decrease to a number - Calculating the percentage increase or decrease between two numbers (e.g. What is the percentage increase between …
🔗 Unit Progression & Next Steps
Three lessons that use real mathematics to understand housing and people in Aotearoa:
- 📖 Lesson 1: Data Detective — Housing in Aotearoa — Collect, display, and interpret real housing data.
- 📖 Lesson 2: Whare Iti Design — Sustainable Geometry — Apply geometry and measurement to design a sustainable small dwelling.
- 📖 Lesson 3: Statistics of Our People — Analyse demographic statistics and explain what the numbers reveal about Aotearoa's communities.
The unit connects mathematics to social justice: using numbers and design to understand — and argue about — real housing issues.
📋 Teacher Planning Snapshot
Ngā Paearu Angitū — Success Criteria
- ✅ I can collect, display, and interpret real data about housing in Aotearoa.
- ✅ I can apply geometry and measurement to design a sustainable small dwelling (whare iti).
- ✅ I can analyse demographic statistics and explain what they reveal about communities in Aotearoa.
Differentiation & Inclusion
Entry-level learners: Provide pre-formatted data tables and calculation templates; use fully worked examples for the geometry before independent work.
ELL / ESOL: Pre-teach statistical and geometric vocabulary (mean, median, area, perimeter, scale); pair data with visuals; allow home-language discussion of what the numbers mean.
Accelerated learners: Source and clean their own dataset; justify design trade-offs in the whare iti with supporting calculation; critique how statistics can mislead.
Neurodiverse / Inclusion: Break multi-step calculations into visible steps; provide graph paper or digital geometry tools; keep the task structure predictable.