Art, Ancestors, and Algorithms
Traditional Māori art is more than just decoration; it is a visual language rich with meaning, history, and mathematics. The intricate patterns found in kōwhaiwhai (painted rafters), tukutuku (woven panels), and tāniko (weaving) are beautiful examples of geometric principles like translation, rotation, reflection, and symmetry. These patterns were carefully constructed, following rules and algorithms passed down through generations of artists and mathematicians.
Core Geometric Patterns
Kōwhaiwhai: Translation and Reflection
Kōwhaiwhai patterns, often seen on the rafters of a marae, are a perfect example of translation (sliding a pattern along a line) and reflection (flipping a pattern). The repeating patterns often represent the genealogy of the iwi, with each element flowing from the last.
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Translation
Tukutuku: Symmetry and Tessellation
Tukutuku panels are woven with flax and other materials to create geometric patterns that often have rotational symmetry. The patterns, such as pātiki (flounder) or kaokao (armpit), are tessellated (repeated to fill a space without gaps or overlaps) across the panel.
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Tessellation
Deconstructing a Pattern: The Pātiki
The pātiki (flounder) pattern is a common design in tukutuku panels. It represents hospitality and abundance. Mathematically, it is a simple yet elegant example of rotational symmetry. The basic diamond shape is rotated around a central point to create the final design.
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Critical Thinking & Design Challenge
1. Choose one of the geometric principles (translation, rotation, reflection, symmetry). Where do you see examples of this principle in your everyday life?
2. On the grid below, use the principles of translation and reflection to create your own simple kōwhaiwhai-inspired pattern.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to explore the intersection of STEM disciplines and mātauranga Māori — understanding how Indigenous knowledge systems and Western science share complementary ways of knowing the world.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify connections between mātauranga Māori and STEM concepts in this resource.
- ✅ Students can explain how dual knowledge systems strengthen understanding of natural phenomena.
Differentiation & Inclusion
Scaffold support: Provide concept maps or sentence frames to scaffold access for students at the entry level. Offer extension tasks exploring specific mātauranga Māori knowledge domains (e.g., tohu āhua rangi, rongoā, whakapapa o te taiao) in greater depth.
ELL / ESOL: Pre-teach key vocabulary in both te reo Māori and English — including domain-specific STEM terms. Bilingual glossaries and visual anchors support comprehension. Allow students to demonstrate understanding in their preferred language.
Inclusion: Tasks are designed for a range of readiness levels. Neurodiverse learners benefit from structured, chunked activities with clear success criteria. Use hands-on, inquiry-based formats where possible. Affirm the value of different ways of knowing.
Mātauranga Māori lens: Mātauranga Māori encompasses astronomy, ecology, navigation, agriculture, and medicine — systems of knowledge developed over centuries. This unit treats mātauranga Māori as epistemically equal to Western science, not supplementary. Bring kaitiakitanga as a guiding ethic: knowledge is held in relationship, not extracted.
Prior knowledge: Students benefit from baseline understanding of the relevant STEM domain. No specialist te reo Māori knowledge required — glossaries provided. Best used after introductory lessons or as a standalone exploration.
Curriculum alignment
- Nature of Science — Knowledge: Science is a way of investigating, understanding, and explaining our natural, physical world; mātauranga Māori offers complementary systems of knowledge that enrich scientific understanding.
- Identity, Culture, and Organisation: Understand how different knowledge systems — including mātauranga Māori — shape how communities relate to the natural world.