Activity: Real-World Algebra Stations
Create and solve a two-step equation for each scenario.
Station 1: Mobile Phone Plan
A mobile phone plan costs $20 per month, plus $2 for every gigabyte of data used. This month, the bill was $32.
Task: Write and solve an equation to find out how many gigabytes (g) were used.
Equation: _________________
Solution: g = ___
Station 2: Taxi Fare
A taxi ride has a flat fee of $5, plus $3 for every kilometre driven. The total fare was $23.
Task: Write and solve an equation to find out how many kilometres (k) were driven.
Equation: _________________
Solution: k = ___
Station 3: Savings Goal
You have $50 saved already. You save an extra $10 each week. Your goal is to save $150 for a new bike.
Task: Write and solve an equation to find out how many weeks (w) it will take to reach your goal.
Equation: _________________
Solution: w = ___
🔑 Kaiako answer key
Station 1 — Mobile Phone Plan
- Equation: 20 + 2g = 32
- 2g = 12, so g = 6 gigabytes.
Station 2 — Taxi Fare
- Equation: 5 + 3k = 23
- 3k = 18, so k = 6 kilometres.
Station 3 — Savings Goal
- Equation: 50 + 10w = 150
- 10w = 100, so w = 10 weeks.
Watch for: the flat fee is the number on its own and the per-unit rate is the number attached to the letter. Ākonga who swap them get 2 + 20g = 32 and an answer of 1.5, which is not a whole number of gigabytes — that non-whole answer is a useful signal that the equation, not the arithmetic, is wrong. Accept equivalent forms such as 2g + 20 = 32.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
A Lesson 5 station activity. Ākonga build and solve a two-step equation from each real-world scenario.
Ngā Paearu Angitū — Success Criteria
- ✅ I can turn a real situation into a two-step equation.
- ✅ I can identify which number is the flat fee and which is the rate.
- ✅ I can solve it and say what the answer means in the situation.
Differentiation & Inclusion
Each station is independent, so ākonga can start anywhere and do as many as they manage. Ākonga who cannot form the equation can still be asked "how much of the $32 is the flat fee?" and work numerically first. Extension: ask them to write a fourth station for the class.
Hononga Marautanga · Curriculum Alignment
Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.