Unit 3, Lesson 3: Mathematics in Cultural Context
Discovering Geometry in Māori Art and Traditional Probability in Games
Students explore how mathematical concepts are embedded in Māori cultural practices, from the geometric patterns in traditional art to the probability principles in ancestral games, understanding mathematics as a universal language expressed through cultural context.
Lesson Overview
Duration
75 minutes
Year Level
Years 8-10
Curriculum Areas
Mathematics, Arts, Te Reo Māori
Karakia & Cultural Opening (5 minutes)
Opening Karakia
"Tiaho mai rā ngā tapatapa o neherā
Ngā taonga mātauranga o ō mātou tīpuna
Kia kite ai mātou i ngā raina me ngā tapatapa
O te taiao, o te tangata hoki"
Shine forth the patterns of the past
The treasured knowledge of our ancestors
So that we may see the lines and patterns
Of the environment and of people too
Setting Mathematical & Cultural Intent
Today we discover that mathematics is not separate from culture but deeply woven into it. The patterns in our art, the strategies in our games, the rhythms of our lives - all contain mathematical principles that our tīpuna understood and used. We honor this knowledge by learning to see mathematics through Māori eyes.
Ngā Whāinga Ako - Learning Objectives
Knowledge & Understanding
- Identify geometric principles in traditional Māori art forms
- Understand probability concepts through traditional games
- Recognize mathematics as culturally embedded knowledge
- Explain how patterns reflect whakapapa and relationships
- Connect mathematical concepts to spiritual and cultural meanings
Skills & Application
- Create geometric patterns using traditional principles
- Calculate probabilities in traditional games
- Analyze symmetry, translation, and rotation in cultural artifacts
- Design mathematically informed cultural expressions
- Apply pattern recognition to solve problems
Hook Activity: Pattern Detective Challenge (10 minutes)
Mathematics Hide-and-Seek
Challenge: Look at these traditional Māori designs and find the hidden mathematics. What geometric principles can you spot?
Kōwhaiwhai Pattern
∞∞∞∞∞
What mathematical operations created this?
Tukutuku Pattern
◊+◊+◊
+◊+◊+
What symmetries do you see?
Tāniko Border
▼▲▼▲▼
How would you continue this pattern?
Pattern Detective Questions
- What mathematical transformations (flip, slide, turn) do you recognize?
- Which patterns could be created by following a mathematical rule?
- How might these patterns relate to stories or whakapapa?
- What happens if you imagine these patterns extending infinitely?
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.
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
- Design a basic motif (simple shape or symbol)
- Apply translation to create a repeating border
- Add reflection to create symmetrical variations
- Consider: What story does your pattern tell?
- Calculate: How many times does your motif repeat in 50cm?
Tukutuku Mathematics
- Create a basic geometric unit (triangle, diamond, cross)
- Apply rotation to create rotational symmetry
- Test tessellation - does it fill space without gaps?
- Analyze: What angle rotations create different effects?
- 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.
Kōruru (Spinning Game)
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: Betting and risk assessment
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:
- Create a simple four-sided "kōruru" using a pencil and paper cube
- Predict: What's the probability of landing on each side?
- Test: Spin 20 times and record results
- Analyze: How do your results compare to your predictions?
- 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
- How does cultural context change the way we understand mathematics?
- What advantages might different cultural approaches to mathematics offer?
- How can understanding mathematics through multiple cultural lenses make us better mathematicians?
- What mathematical concepts from your own cultural background could you explore?
Whakaata - Reflection & Assessment (10 minutes)
Mathematical & Cultural Understanding
Complete this reflection to demonstrate your understanding of mathematics as culturally embedded knowledge:
- 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.
- 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?
- 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?
- 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?
- Integration Thinking: Design a modern application (technology, art, or science) that combines traditional Māori mathematical principles with contemporary mathematical or scientific concepts.
Assessment Criteria
- Mathematical Understanding: Correctly identifies and applies geometric and probability concepts
- Cultural Appreciation: Demonstrates respect for and understanding of Māori mathematical knowledge
- Integration Thinking: Shows ability to connect cultural and formal mathematical concepts
- Critical Analysis: Reflects thoughtfully on the nature of mathematical knowledge
- Creative Application: Develops innovative connections between traditional and contemporary mathematics
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 analyze 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!