Free Grade 3 Algebraic Proof in Context Worksheets
Free Grade 3 worksheets 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
35 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 6x + 12 when x = 5.[1]
- 2.Find the value of 5x + 13 when x = 3.[1]
- 3.Find the value of 6x + 7 when x = 8.[1]
- 4.Find the value of 7x + 20 when x = 5.[1]
- 5.Simplify 6x + 7y + 9x − 6y.[2]
- 6.Simplify 5x + 8y + 9x − 9y.[2]
- 7.Simplify 5x + 3y + 9x − 6y.[2]
- 8.Simplify 8x + 4y + 4x − 8y.[2]
- 9.Expand 4(2x + 1).[3]
- 10.Expand 4(6x + 9).[3]
- 11.Expand 2(6x + 1).[3]
- 12.Expand 4(3x + 4).[3]
Show answers and working
1. 42
Replace x with 5: 6 × 5 + 12. 30 + 12 = 42.
2. 28
Replace x with 3: 5 × 3 + 13. 15 + 13 = 28.
3. 55
Replace x with 8: 6 × 8 + 7. 48 + 7 = 55.
4. 55
Replace x with 5: 7 × 5 + 20. 35 + 20 = 55.
5. 15x + 1y
Collect x terms: 6x + 9x = 15x. Collect y terms: 7y − 6y = 1y.
6. 14x − 1y
Collect x terms: 5x + 9x = 14x. Collect y terms: 8y − 9y = -1y.
7. 14x − 3y
Collect x terms: 5x + 9x = 14x. Collect y terms: 3y − 6y = -3y.
8. 12x − 4y
Collect x terms: 8x + 4x = 12x. Collect y terms: 4y − 8y = -4y.
9. 8x + 4
Multiply each term inside by 4. 4 × 2x = 8x, 4 × 1 = 4.
10. 24x + 36
Multiply each term inside by 4. 4 × 6x = 24x, 4 × 9 = 36.
11. 12x + 2
Multiply each term inside by 2. 2 × 6x = 12x, 2 × 1 = 2.
12. 12x + 16
Multiply each term inside by 4. 4 × 3x = 12x, 4 × 4 = 16.
Worked examples
Find the value of 5x + 20 when x = 3.
- Replace x with 3: 5 × 3 + 20.
- 15 + 20 = 35.
- Answer: 35
Simplify 5x + 5y + 7x − 3y.
- Collect x terms: 5x + 7x = 12x.
- Collect y terms: 5y − 3y = 2y.
- Answer: 12x + 2y
Expand 4(6x + 1).
- Multiply each term inside by 4.
- 4 × 6x = 24x, 4 × 1 = 4.
- Answer: 24x + 4
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 Algebraic Proof 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 Algebraic Proof, Introducing Algebraic Proof, Counterexamples. 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 Algebraic Proof in Context?
- Move on to Counterexamples, Proof by Exhaustion, which build directly on this idea.
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