Free Grade 3 Substitution Method in Context Worksheets
Free Grade 3 worksheets for Substitution Method in Context: 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify substitution method in context
Identify substitution method in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain substitution method in context
Explain substitution method in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate substitution method in context
Calculate substitution method in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare substitution method in context
Compare substitution method in context 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 Substitution Method in Context 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 6x + 4 when x = 6.[1]
- 2.Find the value of 7x + 20 when x = 9.[1]
- 3.Find the value of 3x + 1 when x = 6.[1]
- 4.Find the value of 7x + 14 when x = 6.[1]
- 5.Simplify 7x + 9y + 7x − 1y.[2]
- 6.Simplify 8x + 3y + 2x − 3y.[2]
- 7.Simplify 6x + 3y + 5x − 7y.[2]
- 8.Simplify 5x + 2y + 7x − 5y.[2]
- 9.Expand 4(5x + 1).[3]
- 10.Expand 3(3x + 8).[3]
- 11.Expand 3(2x + 3).[3]
- 12.Expand 2(3x + 6).[3]
Show answers and working
1. 40
Replace x with 6: 6 × 6 + 4. 36 + 4 = 40.
2. 83
Replace x with 9: 7 × 9 + 20. 63 + 20 = 83.
3. 19
Replace x with 6: 3 × 6 + 1. 18 + 1 = 19.
4. 56
Replace x with 6: 7 × 6 + 14. 42 + 14 = 56.
5. 14x + 8y
Collect x terms: 7x + 7x = 14x. Collect y terms: 9y − 1y = 8y.
6. 10x + 0y
Collect x terms: 8x + 2x = 10x. Collect y terms: 3y − 3y = 0y.
7. 11x − 4y
Collect x terms: 6x + 5x = 11x. Collect y terms: 3y − 7y = -4y.
8. 12x − 3y
Collect x terms: 5x + 7x = 12x. Collect y terms: 2y − 5y = -3y.
9. 20x + 4
Multiply each term inside by 4. 4 × 5x = 20x, 4 × 1 = 4.
10. 9x + 24
Multiply each term inside by 3. 3 × 3x = 9x, 3 × 8 = 24.
11. 6x + 9
Multiply each term inside by 3. 3 × 2x = 6x, 3 × 3 = 9.
12. 6x + 12
Multiply each term inside by 2. 2 × 3x = 6x, 2 × 6 = 12.
Worked examples
Find the value of 7x + 2 when x = 4.
- Replace x with 4: 7 × 4 + 2.
- 28 + 2 = 30.
- Answer: 30
Simplify 6x + 3y + 8x − 5y.
- Collect x terms: 6x + 8x = 14x.
- Collect y terms: 3y − 5y = -2y.
- Answer: 14x − 2y
Expand 2(4x + 7).
- Multiply each term inside by 2.
- 2 × 4x = 8x, 2 × 7 = 14.
- Answer: 8x + 14
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 Substitution Method in Context 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 Substitution Method, Introducing Substitution Method, Elimination 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 Substitution Method in Context?
- Move on to Elimination Method, Graphical Solutions, which build directly on this idea.
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