Practice: Rule-Finder
Look at the geometric patterns and find the algebraic rule that describes them.
Pattern A: Growing Squares
Stage 1: □
Stage 2: □□
Stage 3: □□□
1. Complete the table:
| Stage (n) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Squares | 1 | 2 | 3 | ? | ? |
2. What is the rule? Rule: _________
Pattern B: L-Shapes
Stage 1: □
Stage 2: □□
□
Stage 3: □□□
□
□
1. Complete the table:
| Stage (n) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Squares | 1 | 3 | 5 | ? | ? |
2. What is the rule? Rule: _________
Curriculum alignment
- 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¦
- Statistics ā Knowledge: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
- Algebra ā Knowledge: - A coordinate plane extends to 4 quadrants that meet at the origin (0, 0). - Linear patterns have a constant increase or decrease, can be described by the rule t = a Ć n + d,ā¦
- Algebra ā Practices: - Investigating the patterns of triangular numbers, square numbers, and cube numbers, extending the patterns, creating tables of values, and plotting the values on the coordinā¦
- Statistics ā Knowledge: - associative - benchmark - brackets - commutative - discount - distributive - divisibility rule - evaluating expressions - expanded form - exponent, power
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.