Free Grade 3 Introducing Forming Equations Worksheets
Free Grade 3 worksheets for Introducing Forming 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
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing forming equations
Explain introducing forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing forming equations
Calculate introducing forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing forming equations
Compare introducing forming equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing forming equations
Justify introducing forming 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 Introducing Forming 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 + 12 = 15.[1]
- 2.Solve x + 3 = 15.[1]
- 3.Solve x + 15 = 24.[1]
- 4.Solve x + 18 = 22.[1]
- 5.Solve 3x + 16 = 19.[2]
- 6.Solve 3x + 18 = 48.[2]
- 7.Solve 2x + 4 = 26.[2]
- 8.Solve 9x + 7 = 106.[2]
- 9.Solve 8x + 17 = 2x + 65.[3]
- 10.Solve 5x + 5 = 2x + -7.[3]
- 11.Solve 4x + 18 = 1x + 51.[3]
- 12.Solve 9x + 15 = 5x + 51.[3]
Show answers and working
1. x = 3
Subtract 12 from both sides: x = 3. Check: 1 × 3 + 12 = 15.
2. x = 12
Subtract 3 from both sides: x = 12. Check: 1 × 12 + 3 = 15.
3. x = 9
Subtract 15 from both sides: x = 9. Check: 1 × 9 + 15 = 24.
4. x = 4
Subtract 18 from both sides: x = 4. Check: 1 × 4 + 18 = 22.
5. x = 1
Subtract 16 from both sides: 3x = 3. Divide by 3: x = 1. Check: 3 × 1 + 16 = 19.
6. x = 10
Subtract 18 from both sides: 3x = 30. Divide by 3: x = 10. Check: 3 × 10 + 18 = 48.
7. x = 11
Subtract 4 from both sides: 2x = 22. Divide by 2: x = 11. Check: 2 × 11 + 4 = 26.
8. x = 11
Subtract 7 from both sides: 9x = 99. Divide by 9: x = 11. Check: 9 × 11 + 7 = 106.
9. x = 8
Subtract 2x from both sides: 6x + 17 = 65. Subtract 17: 6x = 48. Divide by 6: x = 8.
10. x = -4
Subtract 2x from both sides: 3x + 5 = -7. Subtract 5: 3x = -12. Divide by 3: x = -4.
11. x = 11
Subtract 1x from both sides: 3x + 18 = 51. Subtract 18: 3x = 33. Divide by 3: x = 11.
12. x = 9
Subtract 5x from both sides: 4x + 15 = 51. Subtract 15: 4x = 36. Divide by 4: x = 9.
Worked examples
Solve x + 15 = 20.
- Subtract 15 from both sides: x = 5.
- Check: 1 × 5 + 15 = 20.
- Answer: x = 5
Solve 7x + 18 = 53.
- Subtract 18 from both sides: 7x = 35.
- Divide by 7: x = 5.
- Check: 7 × 5 + 18 = 53.
- Answer: x = 5
Solve 5x + 12 = 3x + 28.
- Subtract 3x from both sides: 2x + 12 = 28.
- Subtract 12: 2x = 16.
- Divide by 2: x = 8.
- Answer: x = 8
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 Introducing Forming Equations
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 Introducing Forming Equations worksheet really free?
- Yes. Every worksheets 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 Unknowns Both Sides. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Forming Equations?
- Move on to Working with Forming Equations, Forming Equations in Context, One-step Equations, Two-step Equations, which build directly on this idea.
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