Today is rung 1 of 9 on this topic
Solving equations by balancing
Can do: Solves one- and two-step equations by doing the same thing to both sides, and checks the answer.
Why it matters
Balance is the idea that makes all equation solving coherent. Children taught "move it over and change the sign" have a rule that fails as soon as it's applied twice.
What it looks like when it's wobbly
Moves terms across the equals sign by memorised rules and can't tell when they've broken the equation.
⏱️ Two-minute check
"Solve 3x + 4 = 19. Now check your answer."
Solid looks like: x = 5, and they substitute back to verify.
The full activity for this topic · 20 minutes
Keep the Scales Level
- 1Model the equation with a cup (the unknown) and coins on two sides of a drawn balance.
- 2Whatever you remove, remove from both sides. Say it every time.
- 3Then divide both sides equally to find one cup's worth.
- 4Write the algebra alongside each physical move.
- 5Always substitute the answer back in. Checking is a habit, not an extra.
If it's too hard
One-step equations only, modelled physically.
If it's too easy
Variables on both sides, and equations with brackets.
Say this
"Whatever you do to one side, you do to the other. Otherwise the scales tip and it's not true any more."