Free Grade 3 Two-step Equations Flashcards
Free Grade 3 flashcards for Two-step 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify two-step equations
Identify two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain two-step equations
Explain two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate two-step equations
Calculate two-step equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare two-step equations
Compare two-step 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 Two-step 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 + 5 = 9.[1]
- 2.Solve x + 18 = 30.[1]
- 3.Solve x + 12 = 22.[1]
- 4.Solve x + 16 = 24.[1]
- 5.Solve 3x + 15 = 27.[2]
- 6.Solve 8x + 17 = 89.[2]
- 7.Solve 4x + 8 = -8.[2]
- 8.Solve 5x + 18 = 53.[2]
- 9.Solve 8x + 8 = 6x + -12.[3]
- 10.Solve 6x + 10 = 4x + 20.[3]
- 11.Solve 7x + 2 = 5x + 8.[3]
- 12.Solve 8x + 15 = 5x + -6.[3]
Show answers and working
1. x = 4
Subtract 5 from both sides: x = 4. Check: 1 × 4 + 5 = 9.
2. x = 12
Subtract 18 from both sides: x = 12. Check: 1 × 12 + 18 = 30.
3. x = 10
Subtract 12 from both sides: x = 10. Check: 1 × 10 + 12 = 22.
4. x = 8
Subtract 16 from both sides: x = 8. Check: 1 × 8 + 16 = 24.
5. x = 4
Subtract 15 from both sides: 3x = 12. Divide by 3: x = 4. Check: 3 × 4 + 15 = 27.
6. x = 9
Subtract 17 from both sides: 8x = 72. Divide by 8: x = 9. Check: 8 × 9 + 17 = 89.
7. x = -4
Subtract 8 from both sides: 4x = -16. Divide by 4: x = -4. Check: 4 × -4 + 8 = -8.
8. x = 7
Subtract 18 from both sides: 5x = 35. Divide by 5: x = 7. Check: 5 × 7 + 18 = 53.
9. x = -10
Subtract 6x from both sides: 2x + 8 = -12. Subtract 8: 2x = -20. Divide by 2: x = -10.
10. x = 5
Subtract 4x from both sides: 2x + 10 = 20. Subtract 10: 2x = 10. Divide by 2: x = 5.
11. x = 3
Subtract 5x from both sides: 2x + 2 = 8. Subtract 2: 2x = 6. Divide by 2: x = 3.
12. x = -7
Subtract 5x from both sides: 3x + 15 = -6. Subtract 15: 3x = -21. Divide by 3: x = -7.
Worked examples
Solve x + 10 = 17.
- Subtract 10 from both sides: x = 7.
- Check: 1 × 7 + 10 = 17.
- Answer: x = 7
Solve 2x + 12 = 16.
- Subtract 12 from both sides: 2x = 4.
- Divide by 2: x = 2.
- Check: 2 × 2 + 12 = 16.
- Answer: x = 2
Solve 9x + 5 = 2x + -16.
- Subtract 2x from both sides: 7x + 5 = -16.
- Subtract 5: 7x = -21.
- Divide by 7: x = -3.
- Answer: x = -3
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 Two-step Equations
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Frequently asked
- Is this Grade 3 Two-step Equations flashcards really free?
- Yes. Every flashcards 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 One-step Equations, Algebraic Expressions. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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 Two-step Equations?
- Move on to Equations with Brackets, Equations with Unknowns Both Sides, Forming Equations, Algebraic Expressions, which build directly on this idea.
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