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 ā Knowledge: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
- Algebra ā 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 Ć n + d,ā¦
- Algebra ā 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, anā¦
- Algebra ā Knowledge: - The distributive, commutative, and associative laws are true for all real numbers. - Algebraic expressions can be presented in many different ways including fully factorisedā¦
- Number ā Knowledge: - Finding equivalent fractions and representing fractions in their simplest form - Adding and subtracting fractions, including improper fractions and mixed numbers, and represā¦
š Teacher Planning Snapshot
NgÄ WhÄinga Ako ā Learning Intentions
Students will develop algebraic thinking and pattern recognition (tÄtai tauira) through te ao MÄori contexts, connecting mathematical reasoning to cultural and real-world problem-solving in Aotearoa.
NgÄ Paearu AngitÅ« ā Success Criteria
- ā Students can identify, describe, and extend patterns using algebraic notation.
- ā 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.
TÄtai (to reckon, count, calculate) reflects the deep mathematical tradition within te ao MÄori ā from whakapapa genealogy structures to wharenui proportional geometry, navigation, and seasonal calendars. MÄtauranga MÄori holds rich pattern-based thinking: tukutuku panel sequences, kÅwhaiwhai scroll patterns, and fishing seasonal cycles all encode algebraic relationships. Algebra taught through these lenses makes abstract thinking visible and culturally grounded.