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)12345
Squares123??

2. What is the rule? Rule: _________

Pattern B: L-Shapes

Stage 1:

Stage 2: □□
    □

Stage 3: □□□
        □
        □

1. Complete the table:

Stage (n)12345
Squares135??

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 Ɨ 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

šŸ“‹ 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 AngitÅ« — Success Criteria

  • āœ… Students can identify, describe, and extend patterns using algebraic notation.
  • āœ… 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.