Activity: The Pattern Machine
The machine has a secret rule. Figure it out by looking at what goes in and what comes out!
Machine #1
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 5 |
| 2 | 6 |
| 3 | 7 |
| 4 | ? |
| 10 | ? |
Machine #2
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | ? |
| 10 | ? |
Machine #3
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 9 |
| 2 | 8 |
| 3 | 7 |
| 4 | ? |
| 10 | ? |
Challenge Machine
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | ? |
| 10 | ? |
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: - associative - benchmark - brackets - commutative - discount - distributive - divisibility rule - evaluating expressions - expanded form - exponent, power
- 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,…
- Geometry — Practices: - Proving that the interior angle sum of a triangle is 180°, and generalising a rule for the interior angle sum and exterior angles for any polygon - Reasoning about unknown a…
📋 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.