Handout: The Equation Balancer

Keep the scales balanced by doing the same thing to both sides!

Example:

Solve for x:

x + 6 = 14

To get 'x' by itself, we do the opposite of '+ 6', which is '- 6'. We must do it to both sides.

x + 6 - 6 = 14 - 6

x = 8

Your Turn: Solve for the variable

a + 10 = 22

a = ___
b - 5 = 11

b = ___
3c = 18 (Remember, 3c means 3 × c)

c = ___
d / 4 = 5 (d divided by 4)

d = ___

Challenge Zone

Can you solve this two-step equation?

2x + 3 = 15

Hint: Get rid of the '+ 3' first!

x = ___

🔑 Kaiako answer key

Your Turn

a + 10 = 22 → a = 12 (subtract 10 from both sides)
b − 5 = 11 → b = 16 (add 5 to both sides)
3c = 18 → c = 6 (divide both sides by 3)
d ÷ 4 = 5 → d = 20 (multiply both sides by 4)

Challenge Zone

2x + 3 = 15 → 2x = 12 → x = 6. Undo the + 3 first, then the × 2. Check: 2(6) + 3 = 15 ✓.

Watch for: insist on both sides being written at every step, not just the answer. The whole point of the balance image is that the working shows the balance being kept.

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

A worksheet for Lesson 4, solving one-step equations by keeping both sides of the whārite balanced.

Ngā Paearu Angitū — Success Criteria

✅ I can keep an equation balanced by doing the same thing to both sides.
✅ I can solve a one-step equation and write both sides at every step.
✅ I can undo the constant first in a two-step equation.

Differentiation & Inclusion

Physical balance scales make the idea concrete and are worth the setup for ākonga who find the symbols abstract. Insist on both sides being written at every step — that habit is what makes Lesson 5 possible. The Challenge Zone is optional at this stage.