Free Grade 3 Introducing Two-step Equations Worksheets
Free Grade 3 worksheets for Introducing Two-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
Stretch
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing two-step equations
Explain introducing two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing two-step equations
Calculate introducing two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing two-step equations
Compare introducing two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing two-step equations
Justify introducing two-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 Two-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 + 20 = 21.[1]
- 2.Solve x + 7 = 19.[1]
- 3.Solve x + 19 = 31.[1]
- 4.Solve x + 4 = 6.[1]
- 5.Solve 6x + 16 = 16.[2]
- 6.Solve 6x + 19 = 55.[2]
- 7.Solve 5x + 13 = 13.[2]
- 8.Solve 2x + 4 = 22.[2]
- 9.Solve 8x + 20 = 7x + 13.[3]
- 10.Solve 5x + 16 = 1x + -20.[3]
- 11.Solve 5x + 19 = 3x + 9.[3]
- 12.Solve 7x + 8 = 2x + 48.[3]
Show answers and working
1. x = 1
Subtract 20 from both sides: x = 1. Check: 1 × 1 + 20 = 21.
2. x = 12
Subtract 7 from both sides: x = 12. Check: 1 × 12 + 7 = 19.
3. x = 12
Subtract 19 from both sides: x = 12. Check: 1 × 12 + 19 = 31.
4. x = 2
Subtract 4 from both sides: x = 2. Check: 1 × 2 + 4 = 6.
5. x = 0
Subtract 16 from both sides: 6x = 0. Divide by 6: x = 0. Check: 6 × 0 + 16 = 16.
6. x = 6
Subtract 19 from both sides: 6x = 36. Divide by 6: x = 6. Check: 6 × 6 + 19 = 55.
7. x = 0
Subtract 13 from both sides: 5x = 0. Divide by 5: x = 0. Check: 5 × 0 + 13 = 13.
8. x = 9
Subtract 4 from both sides: 2x = 18. Divide by 2: x = 9. Check: 2 × 9 + 4 = 22.
9. x = -7
Subtract 7x from both sides: 1x + 20 = 13. Subtract 20: 1x = -7. Divide by 1: x = -7.
10. x = -9
Subtract 1x from both sides: 4x + 16 = -20. Subtract 16: 4x = -36. Divide by 4: x = -9.
11. x = -5
Subtract 3x from both sides: 2x + 19 = 9. Subtract 19: 2x = -10. Divide by 2: x = -5.
12. x = 8
Subtract 2x from both sides: 5x + 8 = 48. Subtract 8: 5x = 40. Divide by 5: x = 8.
Worked examples
Solve x + 16 = 18.
- Subtract 16 from both sides: x = 2.
- Check: 1 × 2 + 16 = 18.
- Answer: x = 2
Solve 8x + 14 = 22.
- Subtract 14 from both sides: 8x = 8.
- Divide by 8: x = 1.
- Check: 8 × 1 + 14 = 22.
- Answer: x = 1
Solve 6x + 3 = 5x + 5.
- Subtract 5x from both sides: 1x + 3 = 5.
- Subtract 3: 1x = 2.
- Divide by 1: x = 2.
- Answer: x = 2
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 Two-step Equations
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 Introducing Two-step Equations worksheet really free?
- Yes. Every worksheets 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 One-step Equations. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Two-step Equations?
- Move on to Working with Two-step Equations, Two-step Equations in Context, One-step Equations, Equations with Brackets, which build directly on this idea.
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