Starter (10 mins)
Matchstick Patterns
Create a simple growing pattern with matchsticks (or draw it). For example, a sequence of squares. Stage 1 has 4 sticks, Stage 2 has 7, Stage 3 has 10. Ask students to build or draw Stage 4 and predict how many sticks are needed for Stage 10.
Main Activity (25 mins)
Kōwhaiwhai Patterns
Introduce kōwhaiwhai as a real-world example of repeating and growing patterns. Use the "Kōwhaiwhai Patterns" handout. Students analyse simple kōwhaiwhai-inspired designs to determine the 'rule' for the pattern's growth.
Task: Students must write an algebraic expression for the number of elements in the nth stage of the pattern. For example, if a pattern starts with 2 scrolls and adds 3 more each time, the rule is 3n - 1.
View HandoutPlenary (15 mins)
Design Your Own Rule
In pairs, students create their own simple algebraic rule (e.g., 2n + 1). They then draw the first three stages of the geometric pattern that their rule describes. Pairs can swap patterns and try to guess the rule.
This activity prepares them for the final summative assessment where they will design a tukutuku panel based on algebraic rules.
Media Anchor (8-10 mins)
Video anchor: Pattern rules to algebraic expressions
Use this clip before kōwhaiwhai analysis to connect visual growth to symbolic notation.
Pause and discuss: How would you express this visual growth pattern using n?
Transfer task: Students capture one method from the video and apply it to the first question in the next activity.
Resources Needed
- "Kōwhaiwhai Patterns" Handout
- Matchsticks or counters
- Images of real kōwhaiwhai from a local marae (if possible)
📋 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.
Curriculum alignment
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 3 (Years 7–8) · 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, partially factorised, and fully expanded forms.”
- NZC (2007) · Mathematics and Statistics · Level 4: “Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.”