Summative Task: Design a Tukutuku Panel
Use your algebra skills to design a beautiful and meaningful pattern.
The Project
Your task is to build a growing pattern that can be described by an algebraic rule, and to present it as a stepped panel design on graph paper. You are designing a mathematical pattern, 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.
Part 1: Poutama — a stepped growing pattern
Poutama is a stepped pattern found in tukutuku and in raranga. It is widely associated with ascending stages of learning and attainment. What follows is a mathematical study of how a stepped pattern grows; the fuller meaning of poutama, and the tikanga around tukutuku, belong to the people who hold them — see the note at the foot of this page.
🪶 Kaiako note. This task uses a stepped pattern because it is mathematically rich, not because the maths explains the pattern's meaning. Do not assess ākonga on cultural interpretation. 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.
Your task is to create a rule for a stepped growing pattern.
- Choose a rule: Create an algebraic rule for a growing pattern (e.g., 4n + 2). It must be your own rule.
- Show the first 3 stages: On graph paper, draw the first three stages of your pattern.
- Create a table: Make a table showing the stage number (n) and the number of squares for the first 5 stages.
- Explain your rule: Write a sentence explaining how your pattern grows and what your algebraic rule is.
Part 2: Your Design
On a new piece of graph paper, draw a panel design built from your stepped pattern. It should show at least 5 stages of the pattern's growth, and someone looking at it should be able to work out your rule from the picture alone.
Assessment Rubric
| Criteria | Achieved | Merit | Excellence |
|---|---|---|---|
| Algebraic Rule | Correctly writes a one-step algebraic rule. | Correctly writes a two-step algebraic rule. | Creates a complex and original multi-step rule. |
| Pattern Representation | Draws the pattern and completes the table with some accuracy. | Accurately draws the pattern and completes the table, showing clear growth. | Flawlessly represents the pattern, table, and rule, showing a deep understanding of the connection. |
| Panel Design | Design is clear and uses the pattern. | Design is well presented and clearly shows the pattern's growth across stages. | Design makes the algebraic rule visible in the layout itself — a reader can recover the rule from the picture. |
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
The summative task asks ākonga to invent their own growing pattern, express it as an algebraic rule, and prove the rule and the picture agree — pulling together the pattern work of L1 and L3 and the rule-writing of L2.
Ngā Paearu Angitū — Success Criteria
- ✅ I can invent a growing pattern of my own and write its rule algebraically.
- ✅ I can draw the first stages and tabulate them so the table, the drawing and the rule all agree.
- ✅ I can explain in a sentence how my pattern grows, and predict a stage I have not drawn.
Differentiation & Inclusion
The task is deliberately open: a one-step rule such as 3n is a complete Achieved response, so no ākonga is locked out. Graph paper and tiles should both be available. Assess the agreement between rule, table and drawing — not the neatness of the design, and not cultural interpretation.
Ākonga are designing a mathematical pattern and presenting it as a stepped panel. They are not making tukutuku. The task borrows a shape, not a practice, and the rubric marks algebra: does the rule, the table and the drawing agree? Cultural interpretation is not assessed anywhere in this task.