šŸ“š Unit Plans ā†’ šŸŒ Year 9 Algebra ā€” Te Tātai Tauira ā†’ šŸ“„ Activity: Tukutuku Tile Challenge
Years 9ā€“10 Pāngarau / Mathematics

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.

  1. Rule: Your pattern is based on the rule 2n + 1.
  2. Build Stage 1: Let n=1. The number of tiles is 2(1) + 1 = 3. Build it.
  3. Build Stage 2: Let n=2. The number of tiles is 2(2) + 1 = 5. Build it next to Stage 1.
  4. Build Stage 3: Let n=3. The number of tiles is 2(3) + 1 = 7. Build it.
  5. Record: Draw your first three stages on graph paper.
  6. 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.

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

šŸ“‹ Teacher Planning Snapshot

Ngā Whāinga Ako ā€” 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 AngitÅ« ā€” Success Criteria

  • āœ… Students can identify, describe, and extend patterns using algebraic notation.
  • āœ… 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.

šŸŒæ Mātauranga Māori Lens

Tātai (to reckon, count, calculate) reflects the deep mathematical tradition within te ao Māori ā€” 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.

Curriculum alignment

  • Mathematics ā€” Algebra: Use graphs, tables, and rules to describe linear relationships and solve problems.
  • Mathematics ā€” Algebra: Form and solve simple linear equations and represent the rules for pattern sequences algebraically.