📚 Unit Plans → 🌍 Unit 3: STEM Through Mātauranga Māori → 📖 Unit 3 Lesson 3: Mathematics in Cultural Context | Mangakōtukutuku College
Years 9–10Pūtaiao / Science

Unit 3, Lesson 3: Mathematics in Cultural Context

Unit 3 Lesson 3: Mathematics in Cultural Context | Mangakōtukutuku College - Educational resource from Te Kete Ako

Pattern Detective Questions

Toi Māori: Mathematics Made Visible (20 minutes)

Art as Mathematical Expression

Traditional Māori art forms like kōwhaiwhai, tukutuku, and tāniko are sophisticated mathematical systems. They demonstrate geometric principles through cultural expression, embedding mathematical concepts in meaningful cultural contexts that tell stories and connect people to their whakapapa.

Key Mathematical Concepts in Action

Geometric Transformations
  • Translation: Sliding patterns along rafters (kōwhaiwhai)
  • Rotation: Turning motifs around central points (pātiki)
  • Reflection: Mirroring patterns across lines (tāniko borders)
  • Tessellation: Filling space without gaps (tukutuku panels)
Cultural Mathematics
  • Whakapapa Patterns: Family relationships as geometric sequences
  • Seasonal Cycles: Circular and spiral mathematical concepts
  • Resource Algorithms: Mathematical rules for sustainable harvesting
  • Navigation Geometry: Angles, directions, and spatial relationships

Activity: Pattern Analysis

Using the Māori Geometric Patterns handout, work in pairs to identify and describe the mathematical transformations in each art form. Create your own pattern using these principles and explain the mathematical rules you followed.

Algorithmic Thinking: Tāniko & Code

Weaving is Coding

Long before computers, Māori weavers were using binary code and algorithms to create complex Tāniko patterns. Tāniko is a system of finger weaving where threads are either visible (on top) or hidden (behind) - just like the 1s and 0s of computer code.

The Tāniko Algorithm

  • Binary System: Two states - 'Up' (visible) or 'Down' (hidden).
  • Grid Based: Patterns are built on a strict coordinate grid, exactly like pixels on a screen.
  • Iterative Rules: "Repeat this sequence 4 times, then shift right by 1." This is a coding loop.
  • Debugging: If one thread is out of place, the pattern breaks - weavers must find the 'bug' and fix it.

Modern Computer Science

  • Pixels: Images made of tiny coloured squares on a grid.
  • Binary Code: Computers store data as 1s (on) and 0s (off).
  • Loops: Code instructions to repeat tasks efficiently.
  • Encryption: Complex patterns can store or hide information.

Activity: Decode the Pattern

Use the grid paper provided to 'execute' this weaving algorithm:

  1. Row 1: [Black, White, Black, White] (Repeat x 4)
  2. Row 2: [White, Black, White, Black] (Repeat x 4)
  3. Row 3: Same as Row 1
  4. Row 4: Same as Row 2

What pattern emerges? (Checkerboard)

Hands-on Pattern Exploration (20 minutes)

Creating with Mathematical Principles

Now you'll apply geometric transformations to create your own culturally-inspired mathematical art. This hands-on exploration helps you understand how mathematical concepts work in practice.

Kōwhaiwhai Challenge

  1. Design a basic motif (simple shape or symbol)
  2. Apply translation to create a repeating border
  3. Add reflection to create symmetrical variations
  4. Consider: What story does your pattern tell?
  5. Calculate: How many times does your motif repeat in 50cm?

Tukutuku Mathematics

  1. Create a basic geometric unit (triangle, diamond, cross)
  2. Apply rotation to create rotational symmetry
  3. Test tessellation - does it fill space without gaps?
  4. Analyse: What angle rotations create different effects?
  5. Calculate: How many units fit in a 30cm x 30cm panel?

Mathematical Reflection

After creating your patterns, reflect: How do mathematical rules help create beauty? How might these same principles apply to other areas of science and life? What cultural meanings could your mathematical patterns represent?

Traditional Games & Probability (15 minutes)

Mathematics in Play: Traditional Games

Traditional Māori games involved sophisticated understanding of probability, strategy, and mathematical thinking. These games weren't just entertainment - they were ways to develop mathematical reasoning, strategic thinking, and decision-making skills.

Pōtaka (Spinning Top)

Players spin carved tops and predict outcomes based on how they land. This involves:

  • Probability calculation: Likelihood of different landing positions
  • Physics understanding: How weight distribution affects spin
  • Strategic thinking: Predicting an outcome before the spin, then checking it

Mu Tōrere (Strategic Board Game)

An eight-pointed star game requiring mathematical strategy:

  • Combinatorics: Calculating possible moves and positions
  • Pattern recognition: Identifying winning configurations
  • Logical reasoning: Planning multi-step strategies

Probability Challenge

Let's explore probability using traditional game principles:

  1. Create a simple four-sided spinner: push a pencil through the centre of a square of card and number the four edges
  2. Predict: What's the probability of landing on each side?
  3. Test: Spin 20 times and record results
  4. Analyse: How do your results compare to your predictions?
  5. Reflect: How did traditional players use this mathematical knowledge?

Integration Activity: Mathematics Across Cultures (10 minutes)

Universal Principles, Cultural Expression

Mathematics is a universal language, but every culture expresses it differently. Compare how mathematical concepts appear across cultures and consider what this tells us about human thinking and cultural values.

Māori Examples

  • Geometric patterns in art
  • Probability in games
  • Cycles in lunar calendar
  • Ratios in navigation

Other Cultural Examples

  • Islamic geometric art
  • African fractal designs
  • European perspective art
  • Asian numerical systems

Modern Applications

  • Computer graphics algorithms
  • Game theory in economics
  • Pattern recognition in AI
  • Architectural design

Reflection Questions

Whakaata - Reflection & Assessment (10 minutes)

Mathematical & Cultural Understanding

Complete this reflection to demonstrate your understanding of mathematics as culturally embedded knowledge:

  1. Pattern Recognition: Identify and describe three geometric transformations you discovered in traditional Māori art. Explain how these relate to mathematical concepts you've learned in other contexts.
  2. Probability Understanding: Using a traditional game example, explain how probability concepts were understood and applied by Māori before formal mathematical education. How does this change your understanding of mathematical knowledge?
  3. Cultural Mathematics: Give an example of how mathematical thinking in Māori culture served purposes beyond calculation (storytelling, spiritual connection, community building, etc.). What does this tell you about the nature of mathematics?
  4. Personal Application: How will understanding mathematics through cultural contexts change the way you approach mathematical problems? How might this perspective help you in STEM fields?
  5. Integration Thinking: Design a modern application (technology, art, or science) that combines traditional Māori mathematical principles with contemporary mathematical or scientific concepts.

Assessment Criteria

Extension Activities

Digital Art Project

Use computer software to create digital kōwhaiwhai or tukutuku patterns. Explore how programming loops and functions relate to traditional pattern-making rules.

Game Theory Research

Research traditional games from different cultures and analyse their mathematical properties. Create a presentation comparing strategic thinking across cultures.

Community Math Project

Interview community elders about traditional mathematical knowledge. Document and present their insights about patterns, measurements, and calculations in traditional practices.

Architecture Challenge

Design a modern building that incorporates traditional Māori mathematical patterns. Calculate the geometry needed and explain how cultural principles inform your mathematical choices.

Whakakapi - Closing Reflection

"He atahua te tapatapa o ngā mātauranga" - Beautiful is the pattern of knowledge. Today we have discovered that mathematics is not cold numbers and abstract concepts, but living patterns that connect us to our ancestors, our culture, and each other.

The geometric principles in our art, the probability wisdom in our games, the mathematical thinking in our traditions - these show us that our tīpuna were sophisticated mathematicians who embedded their knowledge in beauty and meaning. We carry this understanding forward as we continue to explore the mathematical patterns that shape our world.

Kia kaha ki ngā tapatapa - be strong in the patterns!

🎬 Media Anchor

Khan Academy names the three moves formally — translation, reflection, rotation (7m22). It is a generic maths explainer with no Māori content; that is the point. Watch it for the vocabulary, then bring the vocabulary back to the tukutuku and kōwhaiwhai your ākonga have been working with, where those same three moves have been in use far longer than the words for them.

Real source: Khan Academy, Introduction to transformations. Runtime 7m22. Replaces a Corbettmaths sequences clip that was previously mislabelled here and had no transformation content.

Curriculum alignment