📚 Unit Plans → 🌍 Y7/8 Introduction to Algebra — Te Tātai Tauira → 📄 Activity: Tukutuku Tile Challenge
Years 7–10 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?

📋 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.

🌿 Mātauranga Māori Lens

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.

Curriculum alignment

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