Preserving
equality.

1. Launch (5 minutes): compare 8 = 8 with 8 − 3 = 8 − 3. Ask what maintains equality.
2. Model (10 minutes): solve 3x + 5 = 20, naming the operation on both sides.
3. Discuss (10 minutes): examine the illustrative error 3x = 25 and explain how to repair it.
4. Guided rehearsal (10 minutes): solve 4x + 3 = 19 and justify each step.
5. Close (5 minutes): ask why substituting the solution checks the original equation. Keep any classroom responses outside this platform.

1. Subtract 5 from both sides: 3x + 5 − 5 = 20 − 5. Equal quantities remain equal under the same subtraction.
2. Divide both sides by nonzero 3: 3x ÷ 3 = 15 ÷ 3. This reverses multiplication by 3.
3. Check: 3(5) + 5 = 20. The value satisfies the original equation.

“Move the 5 and change its sign”

Response: write the subtraction on both sides first. Connect any shortcut to the operation that preserves equality.

“The equals sign means the answer”

Response: compare 12 = 7 + 5 and 7 + 5 = 12. Both express the same equality.

“3x means 3 + x”

Response: describe three equal groups of x and connect that representation to multiplication.

• What changes on each side? What stays equal?
• Could we divide by 3 first? Explain why that is valid but requires dividing every term.
• How would you show that x = 5 works?

These are constructed examples, not uploaded student work. No standards alignment or completed expert review is claimed.