Free Grade 3 Introducing Equations with Brackets Techniques Lessons
Free Grade 3 lessons for Introducing Equations with Brackets Techniques: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing equations with brackets techniques
Explain introducing equations with brackets techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing equations with brackets techniques
Calculate introducing equations with brackets techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing equations with brackets techniques
Compare introducing equations with brackets techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing equations with brackets techniques
Justify introducing equations with brackets techniques 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 Introducing Equations with Brackets Techniques 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 = 16.[1]
- 2.Solve x + 12 = 19.[1]
- 3.Solve x + 17 = 23.[1]
- 4.Solve x + 6 = 7.[1]
- 5.Solve 5x + 12 = 42.[2]
- 6.Solve 3x + 17 = 20.[2]
- 7.Solve 6x + 15 = 3.[2]
- 8.Solve 6x + 2 = 32.[2]
- 9.Solve 8x + 16 = 2x + 58.[3]
- 10.Solve 7x + 7 = 6x + 2.[3]
- 11.Solve 4x + 6 = 1x + 21.[3]
- 12.Solve 7x + 12 = 5x + 24.[3]
Show answers and working
1. x = 12
Subtract 4 from both sides: x = 12. Check: 1 × 12 + 4 = 16.
2. x = 7
Subtract 12 from both sides: x = 7. Check: 1 × 7 + 12 = 19.
3. x = 6
Subtract 17 from both sides: x = 6. Check: 1 × 6 + 17 = 23.
4. x = 1
Subtract 6 from both sides: x = 1. Check: 1 × 1 + 6 = 7.
5. x = 6
Subtract 12 from both sides: 5x = 30. Divide by 5: x = 6. Check: 5 × 6 + 12 = 42.
6. x = 1
Subtract 17 from both sides: 3x = 3. Divide by 3: x = 1. Check: 3 × 1 + 17 = 20.
7. x = -2
Subtract 15 from both sides: 6x = -12. Divide by 6: x = -2. Check: 6 × -2 + 15 = 3.
8. x = 5
Subtract 2 from both sides: 6x = 30. Divide by 6: x = 5. Check: 6 × 5 + 2 = 32.
9. x = 7
Subtract 2x from both sides: 6x + 16 = 58. Subtract 16: 6x = 42. Divide by 6: x = 7.
10. x = -5
Subtract 6x from both sides: 1x + 7 = 2. Subtract 7: 1x = -5. Divide by 1: x = -5.
11. x = 5
Subtract 1x from both sides: 3x + 6 = 21. Subtract 6: 3x = 15. Divide by 3: x = 5.
12. x = 6
Subtract 5x from both sides: 2x + 12 = 24. Subtract 12: 2x = 12. Divide by 2: x = 6.
Worked examples
Solve x + 8 = 13.
- Subtract 8 from both sides: x = 5.
- Check: 1 × 5 + 8 = 13.
- Answer: x = 5
Solve 8x + 18 = -6.
- Subtract 18 from both sides: 8x = -24.
- Divide by 8: x = -3.
- Check: 8 × -3 + 18 = -6.
- Answer: x = -3
Solve 9x + 3 = 7x + 25.
- Subtract 7x from both sides: 2x + 3 = 25.
- Subtract 3: 2x = 22.
- Divide by 2: x = 11.
- Answer: x = 11
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.
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Frequently asked
- Is this Grade 3 Introducing Equations with Brackets Techniques 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 Essentials, 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 Introducing Equations with Brackets Techniques?
- Move on to Introducing Equations with Brackets Word Problems, Introducing Equations with Brackets Common Errors, Working with Equations with Brackets, Equations with Brackets in Context, which build directly on this idea.
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