Years 7–8 · Lesson 3: Building with Algebra | Te Kete Ako

Years 7–8 pitch · Lesson 3

Years 7–8: write the expression

Ākonga turn a described situation into a simple algebraic expression and check it on one case.

Years 7–8 move: Situation translated to an expression
Evidence it produces: An expression that gives the right answer for a tested value

Same topic at the other level: Year 9 pitch →

Starter (10 mins)

Matchstick Patterns

Create a simple growing pattern with matchsticks (or draw it). For example, a sequence of squares. Stage 1 has 4 sticks, Stage 2 has 7, Stage 3 has 10. Ask students to build or draw Stage 4 and predict how many sticks are needed for Stage 10. (Stage 4 needs 13 sticks; the rule is 3n + 1, so Stage 10 needs 31.)

Main Activity (25 mins)

Kōwhaiwhai Patterns

Introduce kōwhaiwhai as a real-world example of repeating and growing patterns. Use the "Kōwhaiwhai Patterns" handout. Students analyse simple kōwhaiwhai-inspired designs to determine the 'rule' for the pattern's growth.

Task: Students must write an algebraic expression for the number of elements in the nth stage of the pattern. For example, if a pattern starts with 2 scrolls and adds 3 more each time, the rule is 3n - 1.

Plenary (15 mins)

Design Your Own Rule

In pairs, students create their own simple algebraic rule (e.g., 2n + 1). They then draw the first three stages of the geometric pattern that their rule describes. Pairs can swap patterns and try to guess the rule.

This activity prepares them for the final summative assessment where they will design a tukutuku panel based on algebraic rules.

Media Anchor (8-10 mins)

Video anchor: Pattern rules to algebraic expressions

Use this clip before kōwhaiwhai analysis to connect visual growth to symbolic notation.

Pause and discuss: How would you express this visual growth pattern using n?

Transfer task: Students apply one method from the clip to the first equation in the next task set.

Resources Needed

"Kōwhaiwhai Patterns" Handout
Matchsticks or counters
Images of real kōwhaiwhai from a local marae (if possible)

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

Ākonga learn to turn a growing pattern into a rule written with letters, working from matchstick stages and from the growth structure of kōwhaiwhai designs.

Ngā Paearu Angitū — Success Criteria

✅ I can build the next stage of a growing pattern and predict a much later stage without drawing every step.
✅ I can write the rule for a growing pattern as an expression, such as 3n + 1.
✅ I can work backwards: given a rule, I can draw the pattern it describes.

Differentiation & Inclusion

Matchsticks or counters should stay available all lesson; ākonga who go straight to symbols and get stuck can usually unstick themselves by building Stage 4. The nth-term step is the hard one — accept "add 3 each time" as a first answer and then ask for Stage 100, which is what forces the expression.

🌿 Mātauranga Māori Lens

This lesson uses kōwhaiwhai-inspired designs because repetition and growth are visible in them, and visible growth is exactly what an algebraic rule describes. Images of real kōwhaiwhai from a local marae, if you can get them, will show ākonga how much more is going on in the real thing than the growth rule captures — which is the honest version of this connection.