Free Grade 3 Working with Collinearity Worksheets
Free Grade 3 worksheets for Working with Collinearity: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with collinearity
Identify working with collinearity accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with collinearity
Explain working with collinearity accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with collinearity
Calculate working with collinearity accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with collinearity
Compare working with collinearity 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 Collinearity 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 + 17 = 24.[1]
- 2.Solve x + 17 = 28.[1]
- 3.Solve x + 18 = 22.[1]
- 4.Solve x + 10 = 18.[1]
- 5.Solve 9x + 7 = 115.[2]
- 6.Solve 6x + 4 = 22.[2]
- 7.Solve 6x + 3 = -27.[2]
- 8.Solve 5x + 4 = 29.[2]
- 9.Solve 5x + 5 = 1x + -23.[3]
- 10.Solve 9x + 11 = 8x + 11.[3]
- 11.Solve 6x + 5 = 1x + -5.[3]
- 12.Solve 5x + 3 = 4x + -2.[3]
Show answers and working
1. x = 7
Subtract 17 from both sides: x = 7. Check: 1 × 7 + 17 = 24.
2. x = 11
Subtract 17 from both sides: x = 11. Check: 1 × 11 + 17 = 28.
3. x = 4
Subtract 18 from both sides: x = 4. Check: 1 × 4 + 18 = 22.
4. x = 8
Subtract 10 from both sides: x = 8. Check: 1 × 8 + 10 = 18.
5. x = 12
Subtract 7 from both sides: 9x = 108. Divide by 9: x = 12. Check: 9 × 12 + 7 = 115.
6. x = 3
Subtract 4 from both sides: 6x = 18. Divide by 6: x = 3. Check: 6 × 3 + 4 = 22.
7. x = -5
Subtract 3 from both sides: 6x = -30. Divide by 6: x = -5. Check: 6 × -5 + 3 = -27.
8. x = 5
Subtract 4 from both sides: 5x = 25. Divide by 5: x = 5. Check: 5 × 5 + 4 = 29.
9. x = -7
Subtract 1x from both sides: 4x + 5 = -23. Subtract 5: 4x = -28. Divide by 4: x = -7.
10. x = 0
Subtract 8x from both sides: 1x + 11 = 11. Subtract 11: 1x = 0. Divide by 1: x = 0.
11. x = -2
Subtract 1x from both sides: 5x + 5 = -5. Subtract 5: 5x = -10. Divide by 5: x = -2.
12. x = -5
Subtract 4x from both sides: 1x + 3 = -2. Subtract 3: 1x = -5. Divide by 1: x = -5.
Worked examples
Solve x + 11 = 22.
- Subtract 11 from both sides: x = 11.
- Check: 1 × 11 + 11 = 22.
- Answer: x = 11
Solve 2x + 4 = 20.
- Subtract 4 from both sides: 2x = 16.
- Divide by 2: x = 8.
- Check: 2 × 8 + 4 = 20.
- Answer: x = 8
Solve 4x + 8 = 1x + 2.
- Subtract 1x from both sides: 3x + 8 = 2.
- Subtract 8: 3x = -6.
- Divide by 3: x = -2.
- Answer: x = -2
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 Working with Collinearity
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Frequently asked
- Is this Grade 3 Working with Collinearity 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 Introducing Collinearity, Position Vectors. 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 Working with Collinearity?
- Move on to Collinearity in Context, Position Vectors, Vector Proof, which build directly on this idea.
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