Handout: Kōwhaiwhai Patterns

Finding the algebra in Māori art.

Pattern 1: The Koru Swirl

This pattern starts with one swirl and adds another one each time.

Stage 1: (

Stage 2: ( (

Stage 3: ( ( (

1. Draw Stage 4.

2. Complete the table:

Stage (n)	1	2	3	4	10
Swirls	1	2	3	?	?

3. What is the algebraic rule for this pattern? Rule: n

Pattern 2: The Pitau Branch

This pattern grows by adding two branches each time.

Stage 1: /\

Stage 2: /\_/\

Stage 3: /\_/\_/\

1. Draw Stage 4.

2. Complete the table:

Stage (n)	1	2	3	4	10
Branches	2	4	6	?	?

3. What is the algebraic rule for this pattern? Rule: _________

Challenge: The Rafter Pattern

This pattern starts with 3 lines and adds 2 more each time.

Stage 1: |||

Stage 2: |||||

Stage 3: |||||||

Can you find the algebraic rule for the number of lines in stage 'n'?

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.

Hononga Marautanga · Curriculum Alignment

Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.