Free Grade 3 Introducing One-step Equations Quizzes
Free Grade 3 quizzes for Introducing One-step 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing one-step equations
Explain introducing one-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing one-step equations
Calculate introducing one-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing one-step equations
Compare introducing one-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing one-step equations
Justify introducing one-step 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 Introducing One-step 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 + 7 = 12.[1]
- 2.Solve x + 10 = 21.[1]
- 3.Solve x + 1 = 3.[1]
- 4.Solve x + 5 = 6.[1]
- 5.Solve 4x + 18 = 22.[2]
- 6.Solve 4x + 14 = 2.[2]
- 7.Solve 6x + 20 = 8.[2]
- 8.Solve 8x + 15 = -17.[2]
- 9.Solve 3x + 16 = 1x + 22.[3]
- 10.Solve 9x + 10 = 1x + 74.[3]
- 11.Solve 6x + 14 = 3x + 26.[3]
- 12.Solve 8x + 16 = 3x + 16.[3]
Show answers and working
1. x = 5
Subtract 7 from both sides: x = 5. Check: 1 × 5 + 7 = 12.
2. x = 11
Subtract 10 from both sides: x = 11. Check: 1 × 11 + 10 = 21.
3. x = 2
Subtract 1 from both sides: x = 2. Check: 1 × 2 + 1 = 3.
4. x = 1
Subtract 5 from both sides: x = 1. Check: 1 × 1 + 5 = 6.
5. x = 1
Subtract 18 from both sides: 4x = 4. Divide by 4: x = 1. Check: 4 × 1 + 18 = 22.
6. x = -3
Subtract 14 from both sides: 4x = -12. Divide by 4: x = -3. Check: 4 × -3 + 14 = 2.
7. x = -2
Subtract 20 from both sides: 6x = -12. Divide by 6: x = -2. Check: 6 × -2 + 20 = 8.
8. x = -4
Subtract 15 from both sides: 8x = -32. Divide by 8: x = -4. Check: 8 × -4 + 15 = -17.
9. x = 3
Subtract 1x from both sides: 2x + 16 = 22. Subtract 16: 2x = 6. Divide by 2: x = 3.
10. x = 8
Subtract 1x from both sides: 8x + 10 = 74. Subtract 10: 8x = 64. Divide by 8: x = 8.
11. x = 4
Subtract 3x from both sides: 3x + 14 = 26. Subtract 14: 3x = 12. Divide by 3: x = 4.
12. x = 0
Subtract 3x from both sides: 5x + 16 = 16. Subtract 16: 5x = 0. Divide by 5: x = 0.
Worked examples
Solve x + 5 = 16.
- Subtract 5 from both sides: x = 11.
- Check: 1 × 11 + 5 = 16.
- Answer: x = 11
Solve 8x + 18 = 114.
- Subtract 18 from both sides: 8x = 96.
- Divide by 8: x = 12.
- Check: 8 × 12 + 18 = 114.
- Answer: x = 12
Solve 3x + 14 = 1x + 38.
- Subtract 1x from both sides: 2x + 14 = 38.
- Subtract 14: 2x = 24.
- Divide by 2: x = 12.
- Answer: x = 12
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 Introducing One-step Equations
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Frequently asked
- Is this Grade 3 Introducing One-step Equations 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 Algebraic Expressions. 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 Introducing One-step Equations?
- Move on to Working with One-step Equations, One-step Equations in Context, Two-step Equations, Equations with Brackets, which build directly on this idea.
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