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: The Poutama Pattern
The Poutama (stairway) pattern often shows steps. Let's build one.
- 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?
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?
Curriculum alignment
- Statistics — Knowledge: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
- Algebra — Knowledge: - A coordinate plane extends to 4 quadrants that meet at the origin (0, 0). - Linear patterns have a constant increase or decrease, can be described by the rule t = a × n + d,…
- Algebra — Practices: - Identifying and plotting points in the four quadrants of the coordinate plane, using ordered pairs and values from a table - Using tables, graphs in the coordinate plane, an…
- Algebra — Knowledge: - The distributive, commutative, and associative laws are true for all real numbers. - Algebraic expressions can be presented in many different ways including fully factorised…
- Number — Knowledge: - Finding equivalent fractions and representing fractions in their simplest form - Adding and subtracting fractions, including improper fractions and mixed numbers, and repres…
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will develop algebraic thinking and pattern recognition (tātai tauira) through te ao Māori contexts, connecting mathematical reasoning to cultural and real-world problem-solving in Aotearoa.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify, describe, and extend patterns using algebraic notation.
- ✅ Students can explain their mathematical reasoning and connect it to real-world contexts.
Differentiation & Inclusion
Scaffold support: Provide concrete materials and visual representations before moving to abstract notation. Offer entry-level tasks using number patterns, and extension challenges involving proof or generalisation for capable learners.
ELL / ESOL: Pre-teach key mathematical vocabulary (variable, expression, equation, pattern). Allow diagrams and tables as alternate representations. Bilingual glossaries recommended.
Inclusion: Neurodiverse learners benefit from structured step-by-step templates and multiple representations (visual, numeric, algebraic). Avoid time pressure on procedural tasks.
Tātai (to reckon, count, calculate) reflects the deep mathematical tradition within te ao Māori — from whakapapa genealogy structures to wharenui proportional geometry, navigation, and seasonal calendars. Mātauranga Māori holds rich pattern-based thinking: tukutuku panel sequences, kōwhaiwhai scroll patterns, and fishing seasonal cycles all encode algebraic relationships. Algebra taught through these lenses makes abstract thinking visible and culturally grounded.