Free Grade 3 Working with Equations with Brackets Lessons
Free Grade 3 lessons for Working with Equations with Brackets: 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with equations with brackets
Explain working with equations with brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with equations with brackets
Calculate working with equations with brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with equations with brackets
Compare working with equations with brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with equations with brackets
Justify working with equations with brackets 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 Equations with Brackets 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 + 16 = 21.[1]
- 2.Solve x + 6 = 18.[1]
- 3.Solve x + 14 = 14.[1]
- 4.Solve x + 2 = 7.[1]
- 5.Solve 2x + 17 = 9.[2]
- 6.Solve 8x + 13 = 101.[2]
- 7.Solve 5x + 12 = 42.[2]
- 8.Solve 7x + 3 = 38.[2]
- 9.Solve 8x + 16 = 3x + -14.[3]
- 10.Solve 7x + 4 = 2x + -41.[3]
- 11.Solve 4x + 2 = 2x + -14.[3]
- 12.Solve 6x + 17 = 1x + -3.[3]
Show answers and working
1. x = 5
Subtract 16 from both sides: x = 5. Check: 1 × 5 + 16 = 21.
2. x = 12
Subtract 6 from both sides: x = 12. Check: 1 × 12 + 6 = 18.
3. x = 0
Subtract 14 from both sides: x = 0. Check: 1 × 0 + 14 = 14.
4. x = 5
Subtract 2 from both sides: x = 5. Check: 1 × 5 + 2 = 7.
5. x = -4
Subtract 17 from both sides: 2x = -8. Divide by 2: x = -4. Check: 2 × -4 + 17 = 9.
6. x = 11
Subtract 13 from both sides: 8x = 88. Divide by 8: x = 11. Check: 8 × 11 + 13 = 101.
7. x = 6
Subtract 12 from both sides: 5x = 30. Divide by 5: x = 6. Check: 5 × 6 + 12 = 42.
8. x = 5
Subtract 3 from both sides: 7x = 35. Divide by 7: x = 5. Check: 7 × 5 + 3 = 38.
9. x = -6
Subtract 3x from both sides: 5x + 16 = -14. Subtract 16: 5x = -30. Divide by 5: x = -6.
10. x = -9
Subtract 2x from both sides: 5x + 4 = -41. Subtract 4: 5x = -45. Divide by 5: x = -9.
11. x = -8
Subtract 2x from both sides: 2x + 2 = -14. Subtract 2: 2x = -16. Divide by 2: x = -8.
12. x = -4
Subtract 1x from both sides: 5x + 17 = -3. Subtract 17: 5x = -20. Divide by 5: x = -4.
Worked examples
Solve x + 8 = 14.
- Subtract 8 from both sides: x = 6.
- Check: 1 × 6 + 8 = 14.
- Answer: x = 6
Solve 5x + 15 = 60.
- Subtract 15 from both sides: 5x = 45.
- Divide by 5: x = 9.
- Check: 5 × 9 + 15 = 60.
- Answer: x = 9
Solve 4x + 11 = 3x + 8.
- Subtract 3x from both sides: 1x + 11 = 8.
- Subtract 11: 1x = -3.
- Divide by 1: x = -3.
- Answer: x = -3
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 Equations with Brackets
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Frequently asked
- Is this Grade 3 Working with Equations with Brackets 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 Introducing Equations with Brackets, Two-step Equations. 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 Working with Equations with Brackets?
- Move on to Equations with Brackets in Context, One-step Equations, Two-step Equations, Equations with Unknowns Both Sides, which build directly on this idea.
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