Free Grade 3 Introduction to Working with Two-step Equations Techniques Worksheets
Free Grade 3 worksheets for Introduction to Working with Two-step Equations Techniques: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introduction to working with two-step equations techniques
Identify introduction to working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introduction to working with two-step equations techniques
Explain introduction to working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to working with two-step equations techniques
Calculate introduction to working with two-step equations techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to working with two-step equations techniques
Compare introduction to working with two-step equations techniques 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 Introduction to Working with Two-step Equations Techniques 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 + 18 = 29.[1]
- 2.Solve x + 19 = 28.[1]
- 3.Solve x + 10 = 18.[1]
- 4.Solve x + 13 = 24.[1]
- 5.Solve 5x + 18 = 28.[2]
- 6.Solve 5x + 15 = 10.[2]
- 7.Solve 8x + 18 = 50.[2]
- 8.Solve 4x + 3 = 35.[2]
- 9.Solve 2x + 17 = 1x + 22.[3]
- 10.Solve 3x + 5 = 2x + -2.[3]
- 11.Solve 3x + 9 = 2x + 8.[3]
- 12.Solve 7x + 15 = 3x + -17.[3]
Show answers and working
1. x = 11
Subtract 18 from both sides: x = 11. Check: 1 × 11 + 18 = 29.
2. x = 9
Subtract 19 from both sides: x = 9. Check: 1 × 9 + 19 = 28.
3. x = 8
Subtract 10 from both sides: x = 8. Check: 1 × 8 + 10 = 18.
4. x = 11
Subtract 13 from both sides: x = 11. Check: 1 × 11 + 13 = 24.
5. x = 2
Subtract 18 from both sides: 5x = 10. Divide by 5: x = 2. Check: 5 × 2 + 18 = 28.
6. x = -1
Subtract 15 from both sides: 5x = -5. Divide by 5: x = -1. Check: 5 × -1 + 15 = 10.
7. x = 4
Subtract 18 from both sides: 8x = 32. Divide by 8: x = 4. Check: 8 × 4 + 18 = 50.
8. x = 8
Subtract 3 from both sides: 4x = 32. Divide by 4: x = 8. Check: 4 × 8 + 3 = 35.
9. x = 5
Subtract 1x from both sides: 1x + 17 = 22. Subtract 17: 1x = 5. Divide by 1: x = 5.
10. x = -7
Subtract 2x from both sides: 1x + 5 = -2. Subtract 5: 1x = -7. Divide by 1: x = -7.
11. x = -1
Subtract 2x from both sides: 1x + 9 = 8. Subtract 9: 1x = -1. Divide by 1: x = -1.
12. x = -8
Subtract 3x from both sides: 4x + 15 = -17. Subtract 15: 4x = -32. Divide by 4: x = -8.
Worked examples
Solve x + 8 = 8.
- Subtract 8 from both sides: x = 0.
- Check: 1 × 0 + 8 = 8.
- Answer: x = 0
Solve 7x + 1 = 50.
- Subtract 1 from both sides: 7x = 49.
- Divide by 7: x = 7.
- Check: 7 × 7 + 1 = 50.
- Answer: x = 7
Solve 9x + 14 = 6x + 14.
- Subtract 6x from both sides: 3x + 14 = 14.
- Subtract 14: 3x = 0.
- Divide by 3: x = 0.
- Answer: x = 0
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 Introduction to Working with Two-step Equations Techniques
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
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 Introduction to Working with Two-step Equations Techniques 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 Working with Two-step Equations Essentials. 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 Introduction to Working with Two-step Equations Techniques?
- Move on to Key Vocabulary of Working with Two-step Equations Techniques, Rules and Methods in Working with Two-step Equations Techniques, Working with Working with Two-step Equations Techniques, Working with Two-step Equations Techniques in Examinations, which build directly on this idea.
Related resources
- Free Introduction to Working with Two-step Equations Techniques quizzes
- Free Introduction to Working with Two-step Equations Techniques flashcards
- Free Introduction to Working with Two-step Equations Techniques lessons
- Free Introduction to Working with Two-step Equations Techniques lesson plans
- Introduction to Working with Two-step Equations Techniques in the knowledge graph
- Free AI Tutor
Stuck on Introduction to Working with Two-step Equations Techniques? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor