Free Grade 3 Introduction to Working with Two-step Equations Essentials Quizzes
Free Grade 3 quizzes for Introduction to Working with Two-step Equations Essentials: 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
25 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 essentials
Identify introduction to working with two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introduction to working with two-step equations essentials
Explain introduction to working with two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to working with two-step equations essentials
Calculate introduction to working with two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to working with two-step equations essentials
Compare introduction to working with two-step equations essentials 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 Essentials 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 + 2 = 8.[1]
- 2.Solve x + 7 = 16.[1]
- 3.Solve x + 3 = 14.[1]
- 4.Solve x + 9 = 9.[1]
- 5.Solve 5x + 11 = 16.[2]
- 6.Solve 4x + 15 = 47.[2]
- 7.Solve 6x + 11 = 77.[2]
- 8.Solve 2x + 4 = 28.[2]
- 9.Solve 8x + 17 = 2x + 11.[3]
- 10.Solve 8x + 20 = 5x + 11.[3]
- 11.Solve 5x + 10 = 2x + 40.[3]
- 12.Solve 3x + 8 = 1x + 12.[3]
Show answers and working
1. x = 6
Subtract 2 from both sides: x = 6. Check: 1 × 6 + 2 = 8.
2. x = 9
Subtract 7 from both sides: x = 9. Check: 1 × 9 + 7 = 16.
3. x = 11
Subtract 3 from both sides: x = 11. Check: 1 × 11 + 3 = 14.
4. x = 0
Subtract 9 from both sides: x = 0. Check: 1 × 0 + 9 = 9.
5. x = 1
Subtract 11 from both sides: 5x = 5. Divide by 5: x = 1. Check: 5 × 1 + 11 = 16.
6. x = 8
Subtract 15 from both sides: 4x = 32. Divide by 4: x = 8. Check: 4 × 8 + 15 = 47.
7. x = 11
Subtract 11 from both sides: 6x = 66. Divide by 6: x = 11. Check: 6 × 11 + 11 = 77.
8. x = 12
Subtract 4 from both sides: 2x = 24. Divide by 2: x = 12. Check: 2 × 12 + 4 = 28.
9. x = -1
Subtract 2x from both sides: 6x + 17 = 11. Subtract 17: 6x = -6. Divide by 6: x = -1.
10. x = -3
Subtract 5x from both sides: 3x + 20 = 11. Subtract 20: 3x = -9. Divide by 3: x = -3.
11. x = 10
Subtract 2x from both sides: 3x + 10 = 40. Subtract 10: 3x = 30. Divide by 3: x = 10.
12. x = 2
Subtract 1x from both sides: 2x + 8 = 12. Subtract 8: 2x = 4. Divide by 2: x = 2.
Worked examples
Solve x + 9 = 14.
- Subtract 9 from both sides: x = 5.
- Check: 1 × 5 + 9 = 14.
- Answer: x = 5
Solve 2x + 3 = -3.
- Subtract 3 from both sides: 2x = -6.
- Divide by 2: x = -3.
- Check: 2 × -3 + 3 = -3.
- Answer: x = -3
Solve 4x + 9 = 3x + -1.
- Subtract 3x from both sides: 1x + 9 = -1.
- Subtract 9: 1x = -10.
- Divide by 1: x = -10.
- Answer: x = -10
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 Essentials 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 Introducing Two-step Equations. 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 Essentials?
- Move on to Key Vocabulary of Working with Two-step Equations Essentials, Rules and Methods in Working with Two-step Equations Essentials, Working with Working with Two-step Equations Essentials, Working with Two-step Equations Essentials in Examinations, which build directly on this idea.
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