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 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: - associative - benchmark - brackets - commutative - discount - distributive - divisibility rule - evaluating expressions - expanded form - exponent, power
- 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¦
- Geometry ā Practices: - Proving that the interior angle sum of a triangle is 180Ā°, and generalising a rule for the interior angle sum and exterior angles for any polygon - Reasoning about unknown aā¦
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.