Free Grade 3 Introducing Two-step Equations Essentials Worksheets
Free Grade 3 worksheets for Introducing 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
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing two-step equations essentials
Identify introducing two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing two-step equations essentials
Explain introducing two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing two-step equations essentials
Calculate introducing two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing two-step equations essentials
Compare introducing 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 Introducing 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 + 14 = 16.[1]
- 2.Solve x + 11 = 12.[1]
- 3.Solve x + 7 = 16.[1]
- 4.Solve x + 13 = 14.[1]
- 5.Solve 6x + 1 = 43.[2]
- 6.Solve 4x + 7 = -1.[2]
- 7.Solve 2x + 9 = 9.[2]
- 8.Solve 9x + 4 = 103.[2]
- 9.Solve 4x + 18 = 3x + 9.[3]
- 10.Solve 2x + 2 = 1x + 9.[3]
- 11.Solve 7x + 12 = 5x + 30.[3]
- 12.Solve 2x + 10 = 1x + 10.[3]
Show answers and working
1. x = 2
Subtract 14 from both sides: x = 2. Check: 1 × 2 + 14 = 16.
2. x = 1
Subtract 11 from both sides: x = 1. Check: 1 × 1 + 11 = 12.
3. x = 9
Subtract 7 from both sides: x = 9. Check: 1 × 9 + 7 = 16.
4. x = 1
Subtract 13 from both sides: x = 1. Check: 1 × 1 + 13 = 14.
5. x = 7
Subtract 1 from both sides: 6x = 42. Divide by 6: x = 7. Check: 6 × 7 + 1 = 43.
6. x = -2
Subtract 7 from both sides: 4x = -8. Divide by 4: x = -2. Check: 4 × -2 + 7 = -1.
7. x = 0
Subtract 9 from both sides: 2x = 0. Divide by 2: x = 0. Check: 2 × 0 + 9 = 9.
8. x = 11
Subtract 4 from both sides: 9x = 99. Divide by 9: x = 11. Check: 9 × 11 + 4 = 103.
9. x = -9
Subtract 3x from both sides: 1x + 18 = 9. Subtract 18: 1x = -9. Divide by 1: x = -9.
10. x = 7
Subtract 1x from both sides: 1x + 2 = 9. Subtract 2: 1x = 7. Divide by 1: x = 7.
11. x = 9
Subtract 5x from both sides: 2x + 12 = 30. Subtract 12: 2x = 18. Divide by 2: x = 9.
12. x = 0
Subtract 1x from both sides: 1x + 10 = 10. Subtract 10: 1x = 0. Divide by 1: x = 0.
Worked examples
Solve x + 10 = 21.
- Subtract 10 from both sides: x = 11.
- Check: 1 × 11 + 10 = 21.
- Answer: x = 11
Solve 9x + 19 = -8.
- Subtract 19 from both sides: 9x = -27.
- Divide by 9: x = -3.
- Check: 9 × -3 + 19 = -8.
- Answer: x = -3
Solve 5x + 20 = 3x + 36.
- Subtract 3x from both sides: 2x + 20 = 36.
- Subtract 20: 2x = 16.
- Divide by 2: x = 8.
- Answer: x = 8
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 Two-step Equations Essentials 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 Essentials?
- Move on to Introducing Two-step Equations Techniques, Introducing Two-step Equations Word Problems, Introducing Two-step Equations Common Errors, Working with Two-step Equations, which build directly on this idea.
Related resources
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