Years 7–8: x as the unknown number
Ākonga meet x as a specific number they can find, and solve one-step equations by undoing.
- Years 7–8 move: One-step equations solved by inverse
- Evidence it produces: A solved equation with the undoing step shown
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 × ? = 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: Take one rule from the clip and rewrite it with a letter for the quantity that changes.
Resources Needed
- "Variable Vocabulary" Handout
- Whiteboard or projector
- Mini-whiteboards for students
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Ākonga learn that a letter stands for a number we do not know yet, and how to write a word problem using one. The lesson moves from a covered number on the board to naming that unknown as a variable.
Ngā Paearu Angitū — Success Criteria
- ✅ I can work out the hidden number in a sentence like 5 + ? = 12.
- ✅ I can explain what a variable is and why we write a letter instead of a gap.
- ✅ I can turn a short word problem into an algebraic expression.
Differentiation & Inclusion
The covered-number starter is the scaffold: ākonga who cannot yet write x + 3 = 8 can still say what is under the card, and that is the same thinking. Let them answer orally before writing. Mini-whiteboards matter here because they make a wrong first attempt cheap to erase.