Years 7–8: keep it balanced
Ākonga keep an equation balanced through one operation applied to both sides.
- Years 7–8 move: Balance maintained across one operation
- Evidence it produces: An equation solved with both sides shown at each step
Starter (10 mins)
Think of a Number
Play a "think of a number" game. "I'm thinking of a number. I add 5, and the answer is 13. What's my number?" Students work backwards. Explain that this is what we do when we solve equations: we perform the "inverse operation".
Main Activity (25 mins)
The Equation Balancer
Introduce the idea of an equation as a balanced scale. What you do to one side, you must do to the other. Use physical balance scales with weights if available, or draw them.
Use the "Equation Balancer" handout. Students work through a series of one-step equations, showing their working by applying the inverse operation to both sides.
View HandoutPlenary (15 mins)
Create Your Own Problem
Students write their own simple word problem that can be solved with a one-step equation. They translate it into algebra and solve it. For example: "There were some birds on a wire. 5 flew away, and now there are 8 left. How many were there to start with?" (b - 5 = 8).
Students can share their problems with a partner to solve.
Media Anchor (8-10 mins)
Video anchor: Solving two-step equations clearly
Read this before you play it. This clip works two-step equations, which is Lesson 5, not this lesson. It is the same clip Lesson 5 uses. Two ways to use it honestly: hold it back and let Lesson 5 have it, or play it here as a look-ahead for ākonga who have finished the one-step set and want to see where this is going. Do not use it as the worked example for this lesson's practice — the method it shows has a step your ākonga have not met yet.
Pause and discuss: The clip undoes two operations. Which one does it undo first, and why that one?
Transfer task: None from this clip in Lesson 4. The one-step practice set is worked from the "Equation Balancer" handout above.
Resources Needed
- "Equation Balancer" Handout
- Balance scales and weights (optional)
- Mini-whiteboards
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Ākonga learn that both sides of a whārite (equation) are held in balance, and solve one-step equations by doing the same thing to each side. Inverse operations are named as the tool for undoing.
Ngā Paearu Angitū — Success Criteria
- ✅ I can explain why an equation behaves like a balance scale.
- ✅ I can solve a one-step equation using the inverse operation, and check my answer.
- ✅ I can write my own word problem and solve it with a one-step equation.
Differentiation & Inclusion
Physical balance scales are worth setting up for this lesson specifically; the image is the whole idea. Ākonga who reverse the inverse operation should substitute their answer back in — the check finds the error without you having to name it. Do not put this lesson under time pressure.