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 — 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, an…
- Statistics — Knowledge: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
- Algebra — 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 × n + d,…
- Algebra — 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 coordin…
- Statistics — Knowledge: - associative - benchmark - brackets - commutative - discount - distributive - divisibility rule - evaluating expressions - expanded form - exponent, power
📋 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.