Free Grade 3 Working with Substitution Method Essentials Worksheets
Free Grade 3 worksheets for Working with Substitution Method Essentials: 12 real questions with a full answer key and worked solutions. An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
Free
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with substitution method essentials
Identify working with substitution method essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with substitution method essentials
Explain working with substitution method essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with substitution method essentials
Calculate working with substitution method essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with substitution method essentials
Compare working with substitution method 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 Substitution Method Essentials works
An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Find the value of 4x + 10 when x = 5.[1]
- 2.Find the value of 9x + 17 when x = 9.[1]
- 3.Find the value of 7x + 4 when x = 4.[1]
- 4.Find the value of 2x + 17 when x = 6.[1]
- 5.Simplify 2x + 9y + 2x − 2y.[2]
- 6.Simplify 4x + 4y + 2x − 5y.[2]
- 7.Simplify 4x + 8y + 5x − 8y.[2]
- 8.Simplify 3x + 8y + 4x − 4y.[2]
- 9.Expand 2(2x + 2).[3]
- 10.Expand 4(4x + 7).[3]
- 11.Expand 5(6x + 1).[3]
- 12.Expand 3(4x + 1).[3]
Show answers and working
1. 30
Replace x with 5: 4 × 5 + 10. 20 + 10 = 30.
2. 98
Replace x with 9: 9 × 9 + 17. 81 + 17 = 98.
3. 32
Replace x with 4: 7 × 4 + 4. 28 + 4 = 32.
4. 29
Replace x with 6: 2 × 6 + 17. 12 + 17 = 29.
5. 4x + 7y
Collect x terms: 2x + 2x = 4x. Collect y terms: 9y − 2y = 7y.
6. 6x − 1y
Collect x terms: 4x + 2x = 6x. Collect y terms: 4y − 5y = -1y.
7. 9x + 0y
Collect x terms: 4x + 5x = 9x. Collect y terms: 8y − 8y = 0y.
8. 7x + 4y
Collect x terms: 3x + 4x = 7x. Collect y terms: 8y − 4y = 4y.
9. 4x + 4
Multiply each term inside by 2. 2 × 2x = 4x, 2 × 2 = 4.
10. 16x + 28
Multiply each term inside by 4. 4 × 4x = 16x, 4 × 7 = 28.
11. 30x + 5
Multiply each term inside by 5. 5 × 6x = 30x, 5 × 1 = 5.
12. 12x + 3
Multiply each term inside by 3. 3 × 4x = 12x, 3 × 1 = 3.
Worked examples
Find the value of 4x + 1 when x = 8.
- Replace x with 8: 4 × 8 + 1.
- 32 + 1 = 33.
- Answer: 33
Simplify 7x + 6y + 8x − 6y.
- Collect x terms: 7x + 8x = 15x.
- Collect y terms: 6y − 6y = 0y.
- Answer: 15x + 0y
Expand 3(3x + 4).
- Multiply each term inside by 3.
- 3 × 3x = 9x, 3 × 4 = 12.
- Answer: 9x + 12
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads 3x as 3 + x, or as 3 with x stuck on.
Correction: 3x means 3 × x.
Only multiplies the first term when expanding.
Correction: Draw arrows from the outside to every inside term.
Teacher tips
- · Use algebra tiles to show collecting like terms.
Parent tips
- · Ask what 'number of pizzas × price' is for different orders.
Real-life applications
- · Formulas for cost: total = 5n + 2 for n items plus delivery.
Assessment objectives
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Frequently asked
- Is this Grade 3 Working with Substitution Method Essentials 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 Substitution Method. 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 Substitution Method Essentials?
- Move on to Working with Substitution Method Techniques, Working with Substitution Method Word Problems, Working with Substitution Method Common Errors, Introducing Substitution Method, which build directly on this idea.
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