Years 7–8: two steps, whole numbers
Ākonga solve two-step equations with whole numbers and check the answer by substitution.
- Years 7–8 move: Two-step solution plus a substitution check
- Evidence it produces: A solution verified by putting it back in
Starter (10 mins)
Inverse Operations Review
Quick-fire questions for the class: What is the inverse of adding? Subtracting? Multiplying? Dividing? Emphasise that to solve equations, we undo them in the reverse order of operations (reverse BEDMAS).
Main Activity (25 mins)
Solving Two-Step Equations
Model solving a two-step equation like 2x + 3 = 11. Explain that we undo the addition/subtraction first, then the multiplication/division. "We want to get 'x' on its own, so we first move the constant, then the coefficient."
Students work through the "Two-Step Equation Marathon" practice sheet, starting with the first level. Circulate and provide support.
View Practice SheetPlenary (15 mins)
Real-World Algebra Stations
Set up the "Real-World Algebra" station cards around the room. In small groups, students rotate through the stations, creating and solving a two-step equation for each real-world scenario. This demonstrates the practical application of their new skills.
View Station CardsMedia Anchor (8-10 mins)
Video anchor: Solving two-step equations clearly
Use this clip to reinforce reverse-order operations before station rotation work begins.
Pause and discuss: How do you check a two-step solution efficiently for accuracy?
Transfer task: Students apply one method from the clip to the first equation in the next task set.
Resources Needed
- "Two-Step Equation Marathon" Practice Sheet
- "Real-World Algebra" Station Cards
- Mini-whiteboards
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Ākonga learn to solve two-step equations by undoing them in reverse order — constant first, then coefficient — and to build such an equation from a real situation.
Ngā Paearu Angitū — Success Criteria
- ✅ I can name the inverse of each of the four operations.
- ✅ I can solve a two-step equation such as 2x + 3 = 11 and show every step of my working.
- ✅ I can create and solve a two-step equation from a real-world scenario.
Differentiation & Inclusion
Ākonga who can solve one-step equations but not two-step usually have an ordering problem, not an arithmetic one; have them write the two undo-steps as a plan before touching the equation. The station rotation at the end lets ākonga work at their own pace and can be shortened to two stations without losing the point.