Free Grade 3 Working with Two-step Equations Word Problems Lessons
Free Grade 3 lessons for Working with Two-step Equations Word Problems: 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.
- RememberIdentify working with two-step equations word problems
Identify working with two-step equations word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with two-step equations word problems
Explain working with two-step equations word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with two-step equations word problems
Calculate working with two-step equations word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with two-step equations word problems
Compare working with two-step equations word problems 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 Working with Two-step Equations Word Problems 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 + 4 = 6.[1]
- 2.Solve x + 2 = 5.[1]
- 3.Solve x + 11 = 17.[1]
- 4.Solve x + 8 = 9.[1]
- 5.Solve 8x + 15 = 95.[2]
- 6.Solve 2x + 16 = 16.[2]
- 7.Solve 2x + 11 = 25.[2]
- 8.Solve 7x + 20 = 83.[2]
- 9.Solve 8x + 5 = 1x + -37.[3]
- 10.Solve 3x + 12 = 1x + 8.[3]
- 11.Solve 8x + 17 = 5x + -10.[3]
- 12.Solve 4x + 14 = 1x + 29.[3]
Show answers and working
1. x = 2
Subtract 4 from both sides: x = 2. Check: 1 × 2 + 4 = 6.
2. x = 3
Subtract 2 from both sides: x = 3. Check: 1 × 3 + 2 = 5.
3. x = 6
Subtract 11 from both sides: x = 6. Check: 1 × 6 + 11 = 17.
4. x = 1
Subtract 8 from both sides: x = 1. Check: 1 × 1 + 8 = 9.
5. x = 10
Subtract 15 from both sides: 8x = 80. Divide by 8: x = 10. Check: 8 × 10 + 15 = 95.
6. x = 0
Subtract 16 from both sides: 2x = 0. Divide by 2: x = 0. Check: 2 × 0 + 16 = 16.
7. x = 7
Subtract 11 from both sides: 2x = 14. Divide by 2: x = 7. Check: 2 × 7 + 11 = 25.
8. x = 9
Subtract 20 from both sides: 7x = 63. Divide by 7: x = 9. Check: 7 × 9 + 20 = 83.
9. x = -6
Subtract 1x from both sides: 7x + 5 = -37. Subtract 5: 7x = -42. Divide by 7: x = -6.
10. x = -2
Subtract 1x from both sides: 2x + 12 = 8. Subtract 12: 2x = -4. Divide by 2: x = -2.
11. x = -9
Subtract 5x from both sides: 3x + 17 = -10. Subtract 17: 3x = -27. Divide by 3: x = -9.
12. x = 5
Subtract 1x from both sides: 3x + 14 = 29. Subtract 14: 3x = 15. Divide by 3: x = 5.
Worked examples
Solve x + 20 = 22.
- Subtract 20 from both sides: x = 2.
- Check: 1 × 2 + 20 = 22.
- Answer: x = 2
Solve 5x + 8 = 3.
- Subtract 8 from both sides: 5x = -5.
- Divide by 5: x = -1.
- Check: 5 × -1 + 8 = 3.
- Answer: x = -1
Solve 7x + 16 = 6x + 25.
- Subtract 6x from both sides: 1x + 16 = 25.
- Subtract 16: 1x = 9.
- Divide by 1: x = 9.
- Answer: x = 9
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 Working with Two-step Equations Word Problems lesson really free?
- Yes. Every lessons 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 Techniques, Working with Two-step Equations Essentials, Introducing Two-step Equations. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Working with Two-step Equations Word Problems?
- Move on to Working with Two-step Equations Common Errors, Introducing Two-step Equations, Two-step Equations in Context, which build directly on this idea.
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