Free Grade 3 Introducing Two-step Equations Techniques Lessons
Free Grade 3 lessons for Introducing Two-step Equations Techniques: 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 introducing two-step equations techniques
Identify introducing two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing two-step equations techniques
Explain introducing two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing two-step equations techniques
Calculate introducing two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing two-step equations techniques
Compare introducing two-step equations techniques 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 Techniques 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 + 19 = 25.[1]
- 2.Solve x + 20 = 29.[1]
- 3.Solve x + 10 = 13.[1]
- 4.Solve x + 5 = 15.[1]
- 5.Solve 4x + 12 = -8.[2]
- 6.Solve 4x + 17 = 25.[2]
- 7.Solve 5x + 8 = 3.[2]
- 8.Solve 7x + 5 = 89.[2]
- 9.Solve 3x + 14 = 2x + 23.[3]
- 10.Solve 8x + 11 = 7x + 14.[3]
- 11.Solve 8x + 18 = 5x + 33.[3]
- 12.Solve 2x + 8 = 1x + 4.[3]
Show answers and working
1. x = 6
Subtract 19 from both sides: x = 6. Check: 1 × 6 + 19 = 25.
2. x = 9
Subtract 20 from both sides: x = 9. Check: 1 × 9 + 20 = 29.
3. x = 3
Subtract 10 from both sides: x = 3. Check: 1 × 3 + 10 = 13.
4. x = 10
Subtract 5 from both sides: x = 10. Check: 1 × 10 + 5 = 15.
5. x = -5
Subtract 12 from both sides: 4x = -20. Divide by 4: x = -5. Check: 4 × -5 + 12 = -8.
6. x = 2
Subtract 17 from both sides: 4x = 8. Divide by 4: x = 2. Check: 4 × 2 + 17 = 25.
7. x = -1
Subtract 8 from both sides: 5x = -5. Divide by 5: x = -1. Check: 5 × -1 + 8 = 3.
8. x = 12
Subtract 5 from both sides: 7x = 84. Divide by 7: x = 12. Check: 7 × 12 + 5 = 89.
9. x = 9
Subtract 2x from both sides: 1x + 14 = 23. Subtract 14: 1x = 9. Divide by 1: x = 9.
10. x = 3
Subtract 7x from both sides: 1x + 11 = 14. Subtract 11: 1x = 3. Divide by 1: x = 3.
11. x = 5
Subtract 5x from both sides: 3x + 18 = 33. Subtract 18: 3x = 15. Divide by 3: x = 5.
12. x = -4
Subtract 1x from both sides: 1x + 8 = 4. Subtract 8: 1x = -4. Divide by 1: x = -4.
Worked examples
Solve x + 13 = 18.
- Subtract 13 from both sides: x = 5.
- Check: 1 × 5 + 13 = 18.
- Answer: x = 5
Solve 7x + 4 = 32.
- Subtract 4 from both sides: 7x = 28.
- Divide by 7: x = 4.
- Check: 7 × 4 + 4 = 32.
- Answer: x = 4
Solve 7x + 18 = 4x + 36.
- Subtract 4x from both sides: 3x + 18 = 36.
- Subtract 18: 3x = 18.
- Divide by 3: x = 6.
- Answer: x = 6
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 Techniques 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 Introducing Two-step Equations Essentials, One-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 Introducing Two-step Equations Techniques?
- Move on to Introducing Two-step Equations Word Problems, Introducing Two-step Equations Common Errors, Working with Two-step Equations, Two-step Equations in Context, which build directly on this idea.
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