Free Grade 3 Equations with Unknowns Both Sides in Context Lessons
Free Grade 3 lessons for Equations with Unknowns Both Sides in Context: 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 equations with unknowns both sides in context
Identify equations with unknowns both sides in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain equations with unknowns both sides in context
Explain equations with unknowns both sides in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate equations with unknowns both sides in context
Calculate equations with unknowns both sides in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare equations with unknowns both sides in context
Compare equations with unknowns both sides in context 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 Equations with Unknowns Both Sides in Context 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 + 9 = 18.[1]
- 2.Solve x + 11 = 21.[1]
- 3.Solve x + 14 = 25.[1]
- 4.Solve x + 1 = 10.[1]
- 5.Solve 6x + 2 = -22.[2]
- 6.Solve 4x + 19 = 15.[2]
- 7.Solve 2x + 7 = 7.[2]
- 8.Solve 3x + 5 = -1.[2]
- 9.Solve 6x + 2 = 1x + -23.[3]
- 10.Solve 7x + 2 = 6x + -1.[3]
- 11.Solve 2x + 2 = 1x + -6.[3]
- 12.Solve 9x + 1 = 6x + 31.[3]
Show answers and working
1. x = 9
Subtract 9 from both sides: x = 9. Check: 1 × 9 + 9 = 18.
2. x = 10
Subtract 11 from both sides: x = 10. Check: 1 × 10 + 11 = 21.
3. x = 11
Subtract 14 from both sides: x = 11. Check: 1 × 11 + 14 = 25.
4. x = 9
Subtract 1 from both sides: x = 9. Check: 1 × 9 + 1 = 10.
5. x = -4
Subtract 2 from both sides: 6x = -24. Divide by 6: x = -4. Check: 6 × -4 + 2 = -22.
6. x = -1
Subtract 19 from both sides: 4x = -4. Divide by 4: x = -1. Check: 4 × -1 + 19 = 15.
7. x = 0
Subtract 7 from both sides: 2x = 0. Divide by 2: x = 0. Check: 2 × 0 + 7 = 7.
8. x = -2
Subtract 5 from both sides: 3x = -6. Divide by 3: x = -2. Check: 3 × -2 + 5 = -1.
9. x = -5
Subtract 1x from both sides: 5x + 2 = -23. Subtract 2: 5x = -25. Divide by 5: x = -5.
10. x = -3
Subtract 6x from both sides: 1x + 2 = -1. Subtract 2: 1x = -3. Divide by 1: x = -3.
11. x = -8
Subtract 1x from both sides: 1x + 2 = -6. Subtract 2: 1x = -8. Divide by 1: x = -8.
12. x = 10
Subtract 6x from both sides: 3x + 1 = 31. Subtract 1: 3x = 30. Divide by 3: x = 10.
Worked examples
Solve x + 2 = 2.
- Subtract 2 from both sides: x = 0.
- Check: 1 × 0 + 2 = 2.
- Answer: x = 0
Solve 5x + 13 = 48.
- Subtract 13 from both sides: 5x = 35.
- Divide by 5: x = 7.
- Check: 5 × 7 + 13 = 48.
- Answer: x = 7
Solve 2x + 17 = 1x + 13.
- Subtract 1x from both sides: 1x + 17 = 13.
- Subtract 17: 1x = -4.
- Divide by 1: x = -4.
- Answer: x = -4
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 Equations with Unknowns Both Sides in Context 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 Equations with Unknowns Both Sides, Introducing Equations with Unknowns Both Sides, Equations with Brackets. 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 Equations with Unknowns Both Sides in Context?
- Move on to One-step Equations, Two-step Equations, Equations with Brackets, Forming Equations, which build directly on this idea.
Related resources
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