Free Grade 3 Working with Forming Equations Worksheets
Free Grade 3 worksheets for Working with 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with forming equations
Explain working with forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with forming equations
Calculate working with forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with forming equations
Compare working with forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with forming equations
Justify working with 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 Working with 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 + 4 = 15.[1]
- 2.Solve x + 12 = 23.[1]
- 3.Solve x + 10 = 21.[1]
- 4.Solve x + 19 = 24.[1]
- 5.Solve 8x + 17 = 49.[2]
- 6.Solve 4x + 12 = 48.[2]
- 7.Solve 3x + 11 = 35.[2]
- 8.Solve 2x + 14 = 22.[2]
- 9.Solve 3x + 14 = 1x + 12.[3]
- 10.Solve 7x + 7 = 4x + 4.[3]
- 11.Solve 2x + 11 = 1x + 9.[3]
- 12.Solve 4x + 3 = 3x + 12.[3]
Show answers and working
1. x = 11
Subtract 4 from both sides: x = 11. Check: 1 × 11 + 4 = 15.
2. x = 11
Subtract 12 from both sides: x = 11. Check: 1 × 11 + 12 = 23.
3. x = 11
Subtract 10 from both sides: x = 11. Check: 1 × 11 + 10 = 21.
4. x = 5
Subtract 19 from both sides: x = 5. Check: 1 × 5 + 19 = 24.
5. x = 4
Subtract 17 from both sides: 8x = 32. Divide by 8: x = 4. Check: 8 × 4 + 17 = 49.
6. x = 9
Subtract 12 from both sides: 4x = 36. Divide by 4: x = 9. Check: 4 × 9 + 12 = 48.
7. x = 8
Subtract 11 from both sides: 3x = 24. Divide by 3: x = 8. Check: 3 × 8 + 11 = 35.
8. x = 4
Subtract 14 from both sides: 2x = 8. Divide by 2: x = 4. Check: 2 × 4 + 14 = 22.
9. x = -1
Subtract 1x from both sides: 2x + 14 = 12. Subtract 14: 2x = -2. Divide by 2: x = -1.
10. x = -1
Subtract 4x from both sides: 3x + 7 = 4. Subtract 7: 3x = -3. Divide by 3: x = -1.
11. x = -2
Subtract 1x from both sides: 1x + 11 = 9. Subtract 11: 1x = -2. Divide by 1: x = -2.
12. x = 9
Subtract 3x from both sides: 1x + 3 = 12. Subtract 3: 1x = 9. Divide by 1: x = 9.
Worked examples
Solve x + 15 = 20.
- Subtract 15 from both sides: x = 5.
- Check: 1 × 5 + 15 = 20.
- Answer: x = 5
Solve 5x + 9 = 19.
- Subtract 9 from both sides: 5x = 10.
- Divide by 5: x = 2.
- Check: 5 × 2 + 9 = 19.
- Answer: x = 2
Solve 6x + 18 = 3x + -9.
- Subtract 3x from both sides: 3x + 18 = -9.
- Subtract 18: 3x = -27.
- Divide by 3: x = -9.
- Answer: x = -9
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 Working with Forming Equations
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Frequently asked
- Is this Grade 3 Working with Forming Equations worksheet really free?
- Yes. Every worksheets 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 Introducing Forming Equations, Equations with Unknowns Both Sides. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Working with Forming Equations?
- Move on to Forming Equations in Context, One-step Equations, Two-step Equations, Equations with Brackets, which build directly on this idea.
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