Free Grade 3 Substitution Method Lesson Plans
Free Grade 3 lesson plans for Substitution Method: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify substitution method
Identify substitution method accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain substitution method
Explain substitution method accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate substitution method
Calculate substitution method accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare substitution method
Compare substitution method 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 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 9x + 19 when x = 7.[1]
- 2.Find the value of 9x + 9 when x = 4.[1]
- 3.Find the value of 9x + 1 when x = 4.[1]
- 4.Find the value of 8x + 10 when x = 9.[1]
- 5.Simplify 2x + 6y + 5x − 7y.[2]
- 6.Simplify 7x + 4y + 2x − 5y.[2]
- 7.Simplify 9x + 5y + 5x − 4y.[2]
- 8.Simplify 9x + 3y + 7x − 7y.[2]
- 9.Expand 5(6x + 5).[3]
- 10.Expand 2(6x + 1).[3]
- 11.Expand 3(3x + 8).[3]
- 12.Expand 2(3x + 2).[3]
Show answers and working
1. 82
Replace x with 7: 9 × 7 + 19. 63 + 19 = 82.
2. 45
Replace x with 4: 9 × 4 + 9. 36 + 9 = 45.
3. 37
Replace x with 4: 9 × 4 + 1. 36 + 1 = 37.
4. 82
Replace x with 9: 8 × 9 + 10. 72 + 10 = 82.
5. 7x − 1y
Collect x terms: 2x + 5x = 7x. Collect y terms: 6y − 7y = -1y.
6. 9x − 1y
Collect x terms: 7x + 2x = 9x. Collect y terms: 4y − 5y = -1y.
7. 14x + 1y
Collect x terms: 9x + 5x = 14x. Collect y terms: 5y − 4y = 1y.
8. 16x − 4y
Collect x terms: 9x + 7x = 16x. Collect y terms: 3y − 7y = -4y.
9. 30x + 25
Multiply each term inside by 5. 5 × 6x = 30x, 5 × 5 = 25.
10. 12x + 2
Multiply each term inside by 2. 2 × 6x = 12x, 2 × 1 = 2.
11. 9x + 24
Multiply each term inside by 3. 3 × 3x = 9x, 3 × 8 = 24.
12. 6x + 4
Multiply each term inside by 2. 2 × 3x = 6x, 2 × 2 = 4.
Worked examples
Find the value of 6x + 15 when x = 5.
- Replace x with 5: 6 × 5 + 15.
- 30 + 15 = 45.
- Answer: 45
Simplify 5x + 3y + 4x − 7y.
- Collect x terms: 5x + 4x = 9x.
- Collect y terms: 3y − 7y = -4y.
- Answer: 9x − 4y
Expand 4(6x + 5).
- Multiply each term inside by 4.
- 4 × 6x = 24x, 4 × 5 = 20.
- Answer: 24x + 20
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
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Substitution Method lesson plan really free?
- Yes. Every lesson plans 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 Elimination Method, Quadratics. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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?
- Move on to Graphical Solutions, Algebraic Expressions, Equations, Inequalities, which build directly on this idea.
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