Unit 4: Economic Justice & Rangatiratanga

Alternative Economic Models & Community Prosperity

U Unit Overview
1 Economic Foundations
2 Environmental Kaitiakitanga
3 Cultural Mathematics
4 Technology & Innovation
5 Community Science

šŸŒ… Karakia & Cultural Opening (10 mins)

Gather ākonga in a circle and open with ā€œE Rongoā€. Invite students to share one kupu that connects mathematics to their whānau or community (e.g., budgeting, kapa haka formations, gaming). Capture responses on a collaborative board or large butcher paper to revisit later.

WhakataukÄ« Focus: ā€œMā te huruhuru ka rere te manu.ā€ ā€” With the right resources, the bird will soar. Anchor the lesson in the notion that mathematics provides those feathers for our communities.

šŸ“– Lesson Overview

This lesson reveals the mathematics embedded inside Māori economic practices and artistry. Ākonga explore tukutuku and kōwhaiwhai geometry, analyse a marae kai budget using ratios and percentages, and model probability through the traditional game rūrū. They finish by designing a maths-rich artefact that could serve their hapori.

Enrichment Challenge: How do ratios shift when a marae doubles its hauora kai budget for a tangihanga? Use the calculator below to model sustainable decisions that still honour tikanga.

Learning intentions:

  • Analyse kotahitanga-driven budgeting data using ratios, fractions, and percentages.
  • Describe and construct geometric transforms that underpin tukutuku and kōwhaiwhai designs.
  • Model probability situations drawn from Māori games and compare theoretical vs experimental results.

Success criteria (students canā€¦):

  • Explain the cultural story behind a mathematical pattern or decision.
  • Visualise data using digital tools and justify recommendations for whānau wellbeing.
  • Record experimental results, calculate relative frequency, and reflect on fairness.

šŸ§­ Learning Journey

šŸŽ„ Media Anchor

Video: Mātauranga and Patterned Knowledge

  • How can cultural pattern systems strengthen mathematical reasoning?
  • What does this reveal about economics as a values-driven system?
  1. Phase 1 ā€“ Pattern Literacy: Decode tukutuku panels and kōwhaiwhai using transformations and symmetry.
  2. Phase 2 ā€“ Whānau Economics: Investigate a marae kai budget, calculate ratios/percentages, and adjust allocations to reflect tikanga priorities.
  3. Phase 3 ā€“ Probability in Play: Simulate rÅ«rÅ« with a digital + physical experiment, comparing theoretical and empirical results.
  4. Phase 4 ā€“ Reflection & Sharing: Capture insights in My Kete and draft a whānau pānui or student-designed visual that celebrates mathematical storytelling.

šŸ” Phase 1: Toi Māori Geometry Lab (25 mins)

Station Rotations (3 x 7 mins + 4 min debrief)

Set up three stations. Ākonga rotate in small groups, recording findings on the Geometric Patterns in Māori Art handout and sketching ideas on the Kōwhaiwhai Pattern Template.

  • Station A ā€“ Tukutuku Symmetry: Identify translations, reflections, and dilations. Students annotate using transparent overlays.
  • Station B ā€“ Ratio of Colours: Use the interactive calculator below to model colour distribution and create pie charts (extension: compare to the Pie Chart Builder).
  • Station C ā€“ Koruru Coordinates: Plot a koruru outline on grid paper, labelling key coordinates and angles that preserve the integrity of the design.

Interactive Tukutuku Ratio Explorer

Students adjust the number of coloured squares to instantly view simplified ratios, percentages, and a proportional bar. Encourage them to model real tukutuku stories (e.g., Poutama, Roimata Toroa) and justify why certain proportions matter.

šŸ’¹ Phase 2: Marae Kai Budget Modelling (30 mins)

Data Story ā€“ Te Puna Reo Marae

Share the narrative: the marae feeds 120 whānau during kaupapa, with current budget allocations shown below. Ask ākonga to spot trends and areas to uplift manaakitanga.

Marae Kai Expenditure (per hui)
Category Current Spend ($) Proposed Manaaki Boost (%)
Fresh Produce (hua whenua) 480 +15%
Protein (ika, kai ā te whenua) 620 +5%
Pantry Staples 280 0%
Manaakitanga Extras (desserts, gifts) 160 +25%
Utilities & Cleaning 140 0%

Small-Group Modelling

  1. Convert each spend into percentages of the total budget. Compare with the boost column to see how priorities shift.
  2. Use spreadsheets (or the Budget Scenario Sheet in Google Classroom) to test two scenarios: Healthy Kai First vs Manaakitanga Tangihanga.
  3. Make recommendations in a short pitch: ā€œTo honour mana whenua and hauora, we proposeā€¦ā€ referencing data visualisations (bar/pie charts).

Differentiation: Provide colour-coded scaffolds for percentages or extension prompts asking students to calculate cost per whānau member.

šŸŽ² Phase 3: Probability Through RÅ«rÅ« (20 mins)

Hands-On Simulation

Introduce rūrū and demonstrate scoring. Ākonga record 20 throws in pairs, tally results, and compute experimental probability. Compare with theoretical probabilities derived from the number of scoring combinations.

Digital Comparison

Use a quick spreadsheet or digital spinner (e.g., NRICH probability tools) to simulate 200 throws. Discuss variance, sample size, and fairness. Encourage students to relate outcomes back to marae decision-making: how does data support tikanga when outcomes vary?

šŸ§ŗ Reflection, My Kete & Whānau Pānui (10 mins)

  • Exit Ticket: Add one insight to My Kete: ā€œMaths helped our hapori today byā€¦ā€ with an uploaded screenshot/photo.
  • Whānau Connection: Draft a short pānui paragraph outlining how kai budgeting and tukutuku maths support hauora. Encourage sharing with whānau before the next hui.
  • Next Lesson Bridge: Preview how digital innovation (Lesson 4) will build on todayā€™s data stories.

šŸ“‹ Curriculum Connections & Assessment

Te Mātaiaho Phases: Mathematics & Statistics Phase 3 (patterns & relationships, modelling & problem solving) | Social Sciences Phase 3 (economies and resources).

NZC Links: Mathematics Levels 4ā€“5 (number strategies, geometry & measurement, statistics) integrated with Social Sciences (economic decisions).

Assessment Opportunities:

  • Formative: Station recording sheets, ratio calculator reflections, probability tables.
  • Summative (optional): Mini-report summarising budget recommendations plus designed kōwhaiwhai panel annotated with transformations.
  • Student voice: Audio reflection uploaded to My Kete explaining one mathematical idea that strengthened rangatiratanga.

Resources Recap: