Starter (10 mins)
The Covered Number
Write a simple equation on the board like "5 + ? = 12". Cover the question mark with a card. Ask students what number is hidden. Repeat with different operations (e.g., "10 - ? = 3", "3 x ? = 15"). Explain that in algebra, we use letters instead of a question mark or a box.
Main Activity (25 mins)
Translating to Algebra
Introduce the term 'variable'. Use the "Variable Vocabulary" handout to define key terms. Work through the first few examples together as a class. Students then work in pairs to translate word problems into simple algebraic expressions.
Example: "I have some apples, and my friend gives me 3 more. Now I have 8." How can we write this using algebra? (a + 3 = 8).
View HandoutPlenary (15 mins)
Algebra in Real Life
Brainstorm situations where we might not know a value. Examples: the cost of an item before you see the price tag, the number of people who will come to a party, the temperature tomorrow. Discuss how we could use a variable to represent these unknown quantities in planning or discussion.
Media Anchor (8-10 mins)
Video anchor: Recognising arithmetic and geometric patterns
This is the same clip ākonga watched in Lesson 1 — it is about patterns, not about variables. Replay it here for one purpose only: every rule in it names a quantity that changes. Ask ākonga to say each rule aloud and then write the changing quantity as a letter. If your class does not need the replay, skip this card; the lesson does not depend on it.
Pause and discuss: Why is using a variable more powerful than writing a blank box?
Transfer task: Students capture one method from the video and apply it to the first question in the next activity.
Resources Needed
- "Variable Vocabulary" Handout
- Whiteboard or projector
- Mini-whiteboards for students
📋 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.
Curriculum alignment
- NZC (2007) · Mathematics and Statistics · Level 4: “Form and solve simple linear equations.”