Free Grade 3 Equations Lessons
Free Grade 3 lessons for Equations: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify equations
Identify equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain equations
Explain equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate equations
Calculate equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare equations
Compare equations 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 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 + 16 = 26.[1]
- 2.Solve x + 19 = 25.[1]
- 3.Solve x + 5 = 11.[1]
- 4.Solve x + 12 = 19.[1]
- 5.Solve 3x + 13 = 37.[2]
- 6.Solve 4x + 1 = -11.[2]
- 7.Solve 2x + 12 = 28.[2]
- 8.Solve 5x + 8 = 23.[2]
- 9.Solve 3x + 5 = 1x + -15.[3]
- 10.Solve 8x + 4 = 6x + 22.[3]
- 11.Solve 4x + 6 = 3x + 3.[3]
- 12.Solve 2x + 12 = 1x + 17.[3]
Show answers and working
1. x = 10
Subtract 16 from both sides: x = 10. Check: 1 × 10 + 16 = 26.
2. x = 6
Subtract 19 from both sides: x = 6. Check: 1 × 6 + 19 = 25.
3. x = 6
Subtract 5 from both sides: x = 6. Check: 1 × 6 + 5 = 11.
4. x = 7
Subtract 12 from both sides: x = 7. Check: 1 × 7 + 12 = 19.
5. x = 8
Subtract 13 from both sides: 3x = 24. Divide by 3: x = 8. Check: 3 × 8 + 13 = 37.
6. x = -3
Subtract 1 from both sides: 4x = -12. Divide by 4: x = -3. Check: 4 × -3 + 1 = -11.
7. x = 8
Subtract 12 from both sides: 2x = 16. Divide by 2: x = 8. Check: 2 × 8 + 12 = 28.
8. x = 3
Subtract 8 from both sides: 5x = 15. Divide by 5: x = 3. Check: 5 × 3 + 8 = 23.
9. x = -10
Subtract 1x from both sides: 2x + 5 = -15. Subtract 5: 2x = -20. Divide by 2: x = -10.
10. x = 9
Subtract 6x from both sides: 2x + 4 = 22. Subtract 4: 2x = 18. Divide by 2: x = 9.
11. x = -3
Subtract 3x from both sides: 1x + 6 = 3. Subtract 6: 1x = -3. Divide by 1: x = -3.
12. x = 5
Subtract 1x from both sides: 1x + 12 = 17. Subtract 12: 1x = 5. Divide by 1: x = 5.
Worked examples
Solve x + 7 = 13.
- Subtract 7 from both sides: x = 6.
- Check: 1 × 6 + 7 = 13.
- Answer: x = 6
Solve 4x + 20 = 60.
- Subtract 20 from both sides: 4x = 40.
- Divide by 4: x = 10.
- Check: 4 × 10 + 20 = 60.
- Answer: x = 10
Solve 9x + 2 = 3x + -34.
- Subtract 3x from both sides: 6x + 2 = -34.
- Subtract 2: 6x = -36.
- Divide by 6: 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.
Every free resource for Equations
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Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
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Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Equations 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 Algebraic Expressions, Number Sense. 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?
- Move on to Inequalities, Sequences, Quadratics, Simultaneous Equations, which build directly on this idea.
Related resources
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