Lesson 3: Building with Algebra
Learning Intention: We Are Learning To use algebraic rules to create and describe geometric patterns.
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)
KÅwhaiwhai Patterns
Introduce kÅwhaiwhai as a real-world example of repeating and growing patterns. Use the "KÅwhaiwhai Patterns" handout. Students analyze simple kÅwhaiwhai-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 kÅwhaiwhai analysis to connect visual growth to symbolic notation.
Pause and discuss: How would you express this visual growth pattern using n?
Transfer task: Students apply one method from the clip to the first equation in the next task set.
Resources Needed
- "KÅwhaiwhai Patterns" Handout
- Matchsticks or counters
- Images of real kÅwhaiwhai from a local marae (if possible)
Curriculum alignment
- Statistics ā Knowledge: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
- 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: - Each composite number can be represented as a unique product of prime factors and summarised with exponent notation.
- Measurement ā Knowledge: - Each composite number can be represented as a unique product of prime factors and summarised with exponent notation.
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.