Free Grade 3 Algebraic Proof in Context Lesson Plans
Free Grade 3 lesson plans for Algebraic Proof 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify algebraic proof in context
Identify algebraic proof in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain algebraic proof in context
Explain algebraic proof in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate algebraic proof in context
Calculate algebraic proof in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare algebraic proof in context
Compare algebraic proof 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 Algebraic Proof 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 2x + 20 when x = 9.[1]
- 2.Find the value of 6x + 11 when x = 2.[1]
- 3.Find the value of 6x + 17 when x = 7.[1]
- 4.Find the value of 6x + 5 when x = 7.[1]
- 5.Simplify 4x + 4y + 8x − 5y.[2]
- 6.Simplify 8x + 3y + 9x − 5y.[2]
- 7.Simplify 3x + 8y + 9x − 7y.[2]
- 8.Simplify 7x + 2y + 6x − 7y.[2]
- 9.Expand 5(2x + 6).[3]
- 10.Expand 3(5x + 2).[3]
- 11.Expand 3(2x + 9).[3]
- 12.Expand 5(2x + 2).[3]
Show answers and working
1. 38
Replace x with 9: 2 × 9 + 20. 18 + 20 = 38.
2. 23
Replace x with 2: 6 × 2 + 11. 12 + 11 = 23.
3. 59
Replace x with 7: 6 × 7 + 17. 42 + 17 = 59.
4. 47
Replace x with 7: 6 × 7 + 5. 42 + 5 = 47.
5. 12x − 1y
Collect x terms: 4x + 8x = 12x. Collect y terms: 4y − 5y = -1y.
6. 17x − 2y
Collect x terms: 8x + 9x = 17x. Collect y terms: 3y − 5y = -2y.
7. 12x + 1y
Collect x terms: 3x + 9x = 12x. Collect y terms: 8y − 7y = 1y.
8. 13x − 5y
Collect x terms: 7x + 6x = 13x. Collect y terms: 2y − 7y = -5y.
9. 10x + 30
Multiply each term inside by 5. 5 × 2x = 10x, 5 × 6 = 30.
10. 15x + 6
Multiply each term inside by 3. 3 × 5x = 15x, 3 × 2 = 6.
11. 6x + 27
Multiply each term inside by 3. 3 × 2x = 6x, 3 × 9 = 27.
12. 10x + 10
Multiply each term inside by 5. 5 × 2x = 10x, 5 × 2 = 10.
Worked examples
Find the value of 8x + 14 when x = 2.
- Replace x with 2: 8 × 2 + 14.
- 16 + 14 = 30.
- Answer: 30
Simplify 7x + 1y + 9x − 6y.
- Collect x terms: 7x + 9x = 16x.
- Collect y terms: 1y − 6y = -5y.
- Answer: 16x − 5y
Expand 3(4x + 4).
- Multiply each term inside by 3.
- 3 × 4x = 12x, 3 × 4 = 12.
- Answer: 12x + 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 Algebraic Proof in Context 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 Working with Algebraic Proof, Introducing Algebraic Proof, Counterexamples. 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 Algebraic Proof in Context?
- Move on to Counterexamples, Proof by Exhaustion, which build directly on this idea.
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