Free Grade 3 Introducing Equations with Unknowns Both Sides Lesson Plans
Free Grade 3 lesson plans for Introducing Equations with Unknowns Both Sides: 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing equations with unknowns both sides
Explain introducing equations with unknowns both sides accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing equations with unknowns both sides
Calculate introducing equations with unknowns both sides accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing equations with unknowns both sides
Compare introducing equations with unknowns both sides accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing equations with unknowns both sides
Justify introducing equations with unknowns both sides 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 Equations with Unknowns Both Sides 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 + 18 = 18.[1]
- 2.Solve x + 4 = 10.[1]
- 3.Solve x + 14 = 24.[1]
- 4.Solve x + 3 = 9.[1]
- 5.Solve 3x + 14 = 35.[2]
- 6.Solve 8x + 17 = 113.[2]
- 7.Solve 4x + 9 = 33.[2]
- 8.Solve 5x + 20 = 15.[2]
- 9.Solve 6x + 5 = 3x + 23.[3]
- 10.Solve 6x + 7 = 3x + -20.[3]
- 11.Solve 2x + 16 = 1x + 24.[3]
- 12.Solve 8x + 7 = 3x + 42.[3]
Show answers and working
1. x = 0
Subtract 18 from both sides: x = 0. Check: 1 × 0 + 18 = 18.
2. x = 6
Subtract 4 from both sides: x = 6. Check: 1 × 6 + 4 = 10.
3. x = 10
Subtract 14 from both sides: x = 10. Check: 1 × 10 + 14 = 24.
4. x = 6
Subtract 3 from both sides: x = 6. Check: 1 × 6 + 3 = 9.
5. x = 7
Subtract 14 from both sides: 3x = 21. Divide by 3: x = 7. Check: 3 × 7 + 14 = 35.
6. x = 12
Subtract 17 from both sides: 8x = 96. Divide by 8: x = 12. Check: 8 × 12 + 17 = 113.
7. x = 6
Subtract 9 from both sides: 4x = 24. Divide by 4: x = 6. Check: 4 × 6 + 9 = 33.
8. x = -1
Subtract 20 from both sides: 5x = -5. Divide by 5: x = -1. Check: 5 × -1 + 20 = 15.
9. x = 6
Subtract 3x from both sides: 3x + 5 = 23. Subtract 5: 3x = 18. Divide by 3: x = 6.
10. x = -9
Subtract 3x from both sides: 3x + 7 = -20. Subtract 7: 3x = -27. Divide by 3: x = -9.
11. x = 8
Subtract 1x from both sides: 1x + 16 = 24. Subtract 16: 1x = 8. Divide by 1: x = 8.
12. x = 7
Subtract 3x from both sides: 5x + 7 = 42. Subtract 7: 5x = 35. Divide by 5: x = 7.
Worked examples
Solve x + 13 = 23.
- Subtract 13 from both sides: x = 10.
- Check: 1 × 10 + 13 = 23.
- Answer: x = 10
Solve 2x + 13 = 19.
- Subtract 13 from both sides: 2x = 6.
- Divide by 2: x = 3.
- Check: 2 × 3 + 13 = 19.
- Answer: x = 3
Solve 4x + 19 = 2x + 5.
- Subtract 2x from both sides: 2x + 19 = 5.
- Subtract 19: 2x = -14.
- Divide by 2: x = -7.
- Answer: x = -7
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 Equations with Unknowns Both Sides lesson plan really free?
- Yes. Every lesson plans 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 Equations with Brackets. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Equations with Unknowns Both Sides?
- Move on to Working with Equations with Unknowns Both Sides, Equations with Unknowns Both Sides in Context, One-step Equations, Two-step Equations, which build directly on this idea.
Related resources
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