Activity: Tukutuku Tile Challenge

Use tiles to build patterns and discover their algebraic rules.

Materials

Coloured tiles or squares of paper (e.g., red and yellow)
Graph paper

Challenge 1: A stepped growing pattern

You are building a mathematical pattern out of tiles. You are not making a tukutuku panel — tukutuku are made for a wharenui by people who hold that knowledge, and that is not what this task is.

Poutama is a stepped pattern found in tukutuku and in raranga. It is widely associated with ascending stages of learning and attainment. The rule below is a mathematical rule we have chosen because it grows in even steps; it is not the structure of poutama, and the maths does not explain the pattern's meaning.

Rule: Your pattern is based on the rule 2n + 1.
Build Stage 1: Let n=1. The number of tiles is 2(1) + 1 = 3. Build it.
Build Stage 2: Let n=2. The number of tiles is 2(2) + 1 = 5. Build it next to Stage 1.
Build Stage 3: Let n=3. The number of tiles is 2(3) + 1 = 7. Build it.
Record: Draw your first three stages on graph paper.
Predict: How many tiles will be in Stage 5? And Stage 10?

🪶 Kaiako note. Do not assess ākonga on cultural interpretation here. If your kura has a relationship with local carvers, weavers or a wharenui, that is the right place for the meaning of poutama to come from — not from this sheet.

Challenge 2: Create Your Own

Now it's your turn to be the designer.

Create your own algebraic rule for a growing pattern (e.g., 3n, n + 5, 3n - 2).
Write down your rule.
Build the first three stages of your pattern using the tiles.
Swap your pattern with another group. Can you figure out their rule?

🔑 Kaiako answer key

Challenge 1 — predictions

Stage 5: 2(5) + 1 = 11 tiles.
Stage 10: 2(10) + 1 = 21 tiles.

Challenge 2 has no single answer — ākonga invent the rule. What you are marking is whether the built pattern, the rule they wrote and the tile count all agree. Ask the group who received the swapped pattern to state the rule they recovered; if it differs from the rule the designers wrote, one of the three (build, rule, count) is out of step, and finding which is the real assessment.

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

A Lesson 3 tiling activity. Ākonga build a stepped design stage by stage and find the rule for how the tile count grows.

Ngā Paearu Angitū — Success Criteria

✅ I can build the stages of a pattern from a given rule.
✅ I can predict a later stage without building it.
✅ I can invent a rule and build a pattern where the tiles, the table and the rule all agree.

Differentiation & Inclusion

Physical tiles matter here; graph paper alone is harder for ākonga who need to see the growth. Challenge 2 is open-ended, so a simple rule such as 3n is a complete answer. Pair ākonga who invent complex rules with those who need to read a rule off a picture.

🌿 Mātauranga Māori Lens

Poutama is a stepped pattern. The maths on this sheet is about how a stepped pattern grows, stage by stage, and nothing on this sheet explains what poutama means. Those are two different kinds of knowledge and the sheet keeps them apart on purpose. If you want ākonga to meet the second kind, the people who hold it are the right source — not this page.