Year 9: generalise to the nth term
Ākonga express the general term algebraically and justify WHY the rule holds, not merely that it works so far.
- Year 9 move: General term derived and justified
- Evidence it produces: An nth-term rule with an argument for why it must hold
Starter (10 mins)
What's Next?
Show students a simple sequence of numbers (e.g., 2, 4, 6, 8, __) and shapes (e.g., triangle, square, pentagon, __). In pairs, students discuss what comes next and what the "rule" is. Share ideas as a class.
Main Activity (25 mins)
Pattern Detective Agency
Hand out the "Pattern Detectives" worksheet. Students work in small groups (their "agencies") to solve the pattern mysteries. Each case presents a different type of pattern (arithmetic, geometric, repeating, etc.).
Differentiation: The "Extra Challenge" case involves a two-step rule for gifted learners. Provide number lines or blocks for students needing more support.
View HandoutPlenary (15 mins)
Connecting to Our World
Discuss: Where do we see patterns in the real world? (e.g., seasons, tides, music, art). Introduce the concept of tukutuku panels and how they are built on repeating patterns. Show examples and discuss the mathematical rules they might follow.
Connection to Te Ao Māori: This links mathematical patterns to cultural design and storytelling, showing that algebra is a way of describing the world around us.
Resources Needed
- "Pattern Detectives" Handout
- Whiteboard or projector
- Counters or blocks (for support)
- Images of tukutuku panels
📺 Related Videos
Curriculum alignment
- 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…
- Geometry — Knowledge: - The sum of the exterior angles of a polygon is 360°. - In a regular polygon, all exterior angles are the same; an exterior angle can be found by subtracting the interior ang…
- Number — Practices: - Using exponents and identifying square roots for square numbers up to at least 144 - Using radicals (√) to represent square roots - Using divisibility rules to identify numb…
- Number — Knowledge: - Locating integers on a number line - Ordering whole negative and positive numbers using a number line - Identifying the additive inverse of any number - Representing additio…
- Measurement — Practices: - Using exponents and identifying square roots for square numbers up to at least 144 - Using radicals (√) to represent square roots - Using divisibility rules to identify numb…
📋 Teacher Planning Snapshot
📐 Year 9 — From “what comes next” to the general rule
Extending a pattern is the Year 7–8 job. Year 9 asks for the nth term: not the 20th figure but the rule that gives ANY figure. Ākonga build a table (position → value), find the constant difference, and write the rule as an expression — then test it on a term they have not drawn. The check that matters: substitute position 1 back in. If the rule does not reproduce the start of the pattern, the rule is wrong, not the pattern.
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.