Free Grade 3 Forming Equations Lessons
Free Grade 3 lessons for Forming Equations: 12 real questions with a full answer key and worked solutions. An equation is a balance. Do the same thing to both sides until the letter is on its own, then check by substituting back.
Free
Stretch
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain forming equations
Explain forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate forming equations
Calculate forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare forming equations
Compare forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify forming equations
Justify forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Forming Equations works
An equation is a balance. Do the same thing to both sides until the letter is on its own, then check by substituting back.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Solve x + 5 = 14.[1]
- 2.Solve x + 6 = 17.[1]
- 3.Solve x + 4 = 15.[1]
- 4.Solve x + 6 = 7.[1]
- 5.Solve 5x + 13 = -12.[2]
- 6.Solve 7x + 16 = 72.[2]
- 7.Solve 8x + 2 = 26.[2]
- 8.Solve 5x + 18 = 58.[2]
- 9.Solve 2x + 11 = 1x + 4.[3]
- 10.Solve 8x + 6 = 1x + -43.[3]
- 11.Solve 9x + 11 = 8x + 20.[3]
- 12.Solve 6x + 14 = 5x + 8.[3]
Show answers and working
1. x = 9
Subtract 5 from both sides: x = 9. Check: 1 × 9 + 5 = 14.
2. x = 11
Subtract 6 from both sides: x = 11. Check: 1 × 11 + 6 = 17.
3. x = 11
Subtract 4 from both sides: x = 11. Check: 1 × 11 + 4 = 15.
4. x = 1
Subtract 6 from both sides: x = 1. Check: 1 × 1 + 6 = 7.
5. x = -5
Subtract 13 from both sides: 5x = -25. Divide by 5: x = -5. Check: 5 × -5 + 13 = -12.
6. x = 8
Subtract 16 from both sides: 7x = 56. Divide by 7: x = 8. Check: 7 × 8 + 16 = 72.
7. x = 3
Subtract 2 from both sides: 8x = 24. Divide by 8: x = 3. Check: 8 × 3 + 2 = 26.
8. x = 8
Subtract 18 from both sides: 5x = 40. Divide by 5: x = 8. Check: 5 × 8 + 18 = 58.
9. x = -7
Subtract 1x from both sides: 1x + 11 = 4. Subtract 11: 1x = -7. Divide by 1: x = -7.
10. x = -7
Subtract 1x from both sides: 7x + 6 = -43. Subtract 6: 7x = -49. Divide by 7: x = -7.
11. x = 9
Subtract 8x from both sides: 1x + 11 = 20. Subtract 11: 1x = 9. Divide by 1: x = 9.
12. x = -6
Subtract 5x from both sides: 1x + 14 = 8. Subtract 14: 1x = -6. Divide by 1: x = -6.
Worked examples
Solve x + 18 = 21.
- Subtract 18 from both sides: x = 3.
- Check: 1 × 3 + 18 = 21.
- Answer: x = 3
Solve 4x + 16 = 24.
- Subtract 16 from both sides: 4x = 8.
- Divide by 4: x = 2.
- Check: 4 × 2 + 16 = 24.
- Answer: x = 2
Solve 8x + 13 = 7x + 11.
- Subtract 7x from both sides: 1x + 13 = 11.
- Subtract 13: 1x = -2.
- Divide by 1: x = -2.
- Answer: x = -2
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Does an operation to only one side.
Correction: Keep the balance — both sides, every time.
Uses the wrong inverse (subtracts to undo multiplying).
Correction: Undo × with ÷ and + with −.
Teacher tips
- · Always ask pupils to substitute their answer back in.
Parent tips
- · 'I think of a number' puzzles at dinner.
Real-life applications
- · Working out an unknown price or time from a total.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Forming Equations
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Frequently asked
- Is this Grade 3 Forming Equations lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Equations with Unknowns Both Sides, Equations with Brackets, Algebraic Expressions. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Forming Equations?
- Move on to Algebraic Expressions, Inequalities, Sequences, Quadratics, which build directly on this idea.
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