Tukutuku Patterns & Mathematics
Ngā Tauira Tukutuku • Geometry in Māori Art
🎨 What is Tukutuku?
Tukutuku are decorative lattice panels found inside wharenui (meeting houses). They are made by weaving colored strips through a wooden frame to create geometric patterns. Each pattern has a name and meaning.
Tukutuku demonstrates that Māori have always used sophisticated mathematics — symmetry, tessellation, and geometric patterns!
📐 Traditional Tukutuku Patterns
Poutama
Stairway pattern — represents growth, learning, and achievement
Kaokao
Rib pattern — represents strength and protection
🔢 Mathematics in Tukutuku
Symmetry
Many tukutuku patterns have line symmetry (reflective) and rotational symmetry.
Tessellation
Patterns tessellate — they repeat without gaps or overlaps to fill a space.
Transformation
Patterns use translation (sliding), reflection (flipping), and rotation (turning).
Coordinates
Each colored piece can be located using a grid reference (row, column).
📝 Activity 1: Identify Symmetry
Look at the Poutama pattern above.
a) Does it have line symmetry? If yes, draw the line(s) of symmetry.
b) Does it have rotational symmetry? What order?
📝 Activity 2: Poutama Counting
In the Poutama (stairway) pattern:
a) How many red squares are in the bottom row?
b) How many red squares are in the second row from the bottom?
c) What pattern do you notice? Write a rule.
d) If the pattern continued for 10 rows, how many red squares would be in the top row?
📝 Activity 3: Design Your Own Pattern
Use the grid below to design your own tukutuku-inspired pattern. Use at least 2 colors and include symmetry.
Describe the symmetry in your pattern:
📚 Kupu Māori — Vocabulary
Pattern
Symmetry
Meeting house
Stairway pattern
Rib/armpit pattern
Weaving
👩🏫 Teacher Notes
Curriculum: NZC Level 3-4 Geometry — Transformation, Symmetry, Patterns
Cultural Considerations:
- Consider visiting a local marae to see real tukutuku
- Each pattern has deep cultural significance — treat with respect
- Invite a local weaver to share their knowledge if possible
Extension: Research other patterns (Niho Taniwha, Patiki) and their mathematical properties.