Free Grade 3 Introduction to Working with Two-step Equations Techniques Quizzes
Free Grade 3 quizzes for Introduction to Working with Two-step Equations 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
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introduction to working with two-step equations techniques
Identify introduction to working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introduction to working with two-step equations techniques
Explain introduction to working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to working with two-step equations techniques
Calculate introduction to working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to working with two-step equations techniques
Compare introduction to working with two-step equations 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 Introduction to Working with Two-step Equations 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 + 3 = 4.[1]
- 2.Solve x + 10 = 21.[1]
- 3.Solve x + 20 = 24.[1]
- 4.Solve x + 17 = 27.[1]
- 5.Solve 3x + 8 = 17.[2]
- 6.Solve 5x + 1 = 1.[2]
- 7.Solve 4x + 4 = 12.[2]
- 8.Solve 4x + 1 = 33.[2]
- 9.Solve 8x + 12 = 6x + 14.[3]
- 10.Solve 5x + 2 = 2x + -16.[3]
- 11.Solve 7x + 12 = 6x + 16.[3]
- 12.Solve 8x + 8 = 4x + -4.[3]
Show answers and working
1. x = 1
Subtract 3 from both sides: x = 1. Check: 1 × 1 + 3 = 4.
2. x = 11
Subtract 10 from both sides: x = 11. Check: 1 × 11 + 10 = 21.
3. x = 4
Subtract 20 from both sides: x = 4. Check: 1 × 4 + 20 = 24.
4. x = 10
Subtract 17 from both sides: x = 10. Check: 1 × 10 + 17 = 27.
5. x = 3
Subtract 8 from both sides: 3x = 9. Divide by 3: x = 3. Check: 3 × 3 + 8 = 17.
6. x = 0
Subtract 1 from both sides: 5x = 0. Divide by 5: x = 0. Check: 5 × 0 + 1 = 1.
7. x = 2
Subtract 4 from both sides: 4x = 8. Divide by 4: x = 2. Check: 4 × 2 + 4 = 12.
8. x = 8
Subtract 1 from both sides: 4x = 32. Divide by 4: x = 8. Check: 4 × 8 + 1 = 33.
9. x = 1
Subtract 6x from both sides: 2x + 12 = 14. Subtract 12: 2x = 2. Divide by 2: x = 1.
10. x = -6
Subtract 2x from both sides: 3x + 2 = -16. Subtract 2: 3x = -18. Divide by 3: x = -6.
11. x = 4
Subtract 6x from both sides: 1x + 12 = 16. Subtract 12: 1x = 4. Divide by 1: x = 4.
12. x = -3
Subtract 4x from both sides: 4x + 8 = -4. Subtract 8: 4x = -12. Divide by 4: x = -3.
Worked examples
Solve x + 6 = 9.
- Subtract 6 from both sides: x = 3.
- Check: 1 × 3 + 6 = 9.
- Answer: x = 3
Solve 4x + 10 = 14.
- Subtract 10 from both sides: 4x = 4.
- Divide by 4: x = 1.
- Check: 4 × 1 + 10 = 14.
- Answer: x = 1
Solve 3x + 12 = 2x + 19.
- Subtract 2x from both sides: 1x + 12 = 19.
- Subtract 12: 1x = 7.
- Divide by 1: x = 7.
- Answer: x = 7
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 Introduction to Working with Two-step Equations Techniques quiz really free?
- Yes. Every quizzes 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 Working with Two-step Equations Essentials. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Introduction to Working with Two-step Equations Techniques?
- Move on to Key Vocabulary of Working with Two-step Equations Techniques, Rules and Methods in Working with Two-step Equations Techniques, Working with Working with Two-step Equations Techniques, Working with Two-step Equations Techniques in Examinations, which build directly on this idea.
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