Free Grade 3 Working with Two-step Equations Essentials Flashcards
Free Grade 3 flashcards for Working with Two-step Equations Essentials: 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.
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20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with two-step equations essentials
Identify working with two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with two-step equations essentials
Explain working with two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with two-step equations essentials
Calculate working with two-step equations essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with two-step equations essentials
Compare working with two-step equations essentials 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 Working with Two-step Equations Essentials 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 + 3 = 11.[1]
- 2.Solve x + 11 = 15.[1]
- 3.Solve x + 11 = 16.[1]
- 4.Solve x + 7 = 13.[1]
- 5.Solve 7x + 3 = 66.[2]
- 6.Solve 3x + 19 = 55.[2]
- 7.Solve 9x + 10 = -35.[2]
- 8.Solve 5x + 18 = 18.[2]
- 9.Solve 2x + 19 = 1x + 20.[3]
- 10.Solve 9x + 3 = 2x + 45.[3]
- 11.Solve 7x + 18 = 3x + 42.[3]
- 12.Solve 4x + 19 = 2x + -1.[3]
Show answers and working
1. x = 8
Subtract 3 from both sides: x = 8. Check: 1 × 8 + 3 = 11.
2. x = 4
Subtract 11 from both sides: x = 4. Check: 1 × 4 + 11 = 15.
3. x = 5
Subtract 11 from both sides: x = 5. Check: 1 × 5 + 11 = 16.
4. x = 6
Subtract 7 from both sides: x = 6. Check: 1 × 6 + 7 = 13.
5. x = 9
Subtract 3 from both sides: 7x = 63. Divide by 7: x = 9. Check: 7 × 9 + 3 = 66.
6. x = 12
Subtract 19 from both sides: 3x = 36. Divide by 3: x = 12. Check: 3 × 12 + 19 = 55.
7. x = -5
Subtract 10 from both sides: 9x = -45. Divide by 9: x = -5. Check: 9 × -5 + 10 = -35.
8. x = 0
Subtract 18 from both sides: 5x = 0. Divide by 5: x = 0. Check: 5 × 0 + 18 = 18.
9. x = 1
Subtract 1x from both sides: 1x + 19 = 20. Subtract 19: 1x = 1. Divide by 1: x = 1.
10. x = 6
Subtract 2x from both sides: 7x + 3 = 45. Subtract 3: 7x = 42. Divide by 7: x = 6.
11. x = 6
Subtract 3x from both sides: 4x + 18 = 42. Subtract 18: 4x = 24. Divide by 4: x = 6.
12. x = -10
Subtract 2x from both sides: 2x + 19 = -1. Subtract 19: 2x = -20. Divide by 2: x = -10.
Worked examples
Solve x + 15 = 16.
- Subtract 15 from both sides: x = 1.
- Check: 1 × 1 + 15 = 16.
- Answer: x = 1
Solve 5x + 15 = 55.
- Subtract 15 from both sides: 5x = 40.
- Divide by 5: x = 8.
- Check: 5 × 8 + 15 = 55.
- Answer: x = 8
Solve 8x + 9 = 1x + 65.
- Subtract 1x from both sides: 7x + 9 = 65.
- Subtract 9: 7x = 56.
- Divide by 7: 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.
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Frequently asked
- Is this Grade 3 Working with Two-step Equations Essentials 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 Introducing Two-step Equations. 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 Working with Two-step Equations Essentials?
- Move on to Working with Two-step Equations Techniques, Working with Two-step Equations Word Problems, Working with Two-step Equations Common Errors, Introducing Two-step Equations, which build directly on this idea.
Related resources
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