Free Grade 3 Introducing Algebraic Proof Lessons
Free Grade 3 lessons for Introducing Algebraic Proof: 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
Stretch
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing algebraic proof
Explain introducing algebraic proof accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing algebraic proof
Calculate introducing algebraic proof accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing algebraic proof
Compare introducing algebraic proof accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing algebraic proof
Justify introducing algebraic proof 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 Introducing Algebraic Proof 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 7x + 7 when x = 9.[1]
- 2.Find the value of 2x + 7 when x = 7.[1]
- 3.Find the value of 5x + 10 when x = 6.[1]
- 4.Find the value of 2x + 18 when x = 2.[1]
- 5.Simplify 8x + 1y + 6x − 3y.[2]
- 6.Simplify 6x + 1y + 7x − 1y.[2]
- 7.Simplify 8x + 7y + 9x − 2y.[2]
- 8.Simplify 7x + 4y + 9x − 5y.[2]
- 9.Expand 2(2x + 9).[3]
- 10.Expand 2(4x + 4).[3]
- 11.Expand 3(2x + 7).[3]
- 12.Expand 2(6x + 6).[3]
Show answers and working
1. 70
Replace x with 9: 7 × 9 + 7. 63 + 7 = 70.
2. 21
Replace x with 7: 2 × 7 + 7. 14 + 7 = 21.
3. 40
Replace x with 6: 5 × 6 + 10. 30 + 10 = 40.
4. 22
Replace x with 2: 2 × 2 + 18. 4 + 18 = 22.
5. 14x − 2y
Collect x terms: 8x + 6x = 14x. Collect y terms: 1y − 3y = -2y.
6. 13x + 0y
Collect x terms: 6x + 7x = 13x. Collect y terms: 1y − 1y = 0y.
7. 17x + 5y
Collect x terms: 8x + 9x = 17x. Collect y terms: 7y − 2y = 5y.
8. 16x − 1y
Collect x terms: 7x + 9x = 16x. Collect y terms: 4y − 5y = -1y.
9. 4x + 18
Multiply each term inside by 2. 2 × 2x = 4x, 2 × 9 = 18.
10. 8x + 8
Multiply each term inside by 2. 2 × 4x = 8x, 2 × 4 = 8.
11. 6x + 21
Multiply each term inside by 3. 3 × 2x = 6x, 3 × 7 = 21.
12. 12x + 12
Multiply each term inside by 2. 2 × 6x = 12x, 2 × 6 = 12.
Worked examples
Find the value of 8x + 10 when x = 8.
- Replace x with 8: 8 × 8 + 10.
- 64 + 10 = 74.
- Answer: 74
Simplify 5x + 1y + 9x − 8y.
- Collect x terms: 5x + 9x = 14x.
- Collect y terms: 1y − 8y = -7y.
- Answer: 14x − 7y
Expand 3(5x + 4).
- Multiply each term inside by 3.
- 3 × 5x = 15x, 3 × 4 = 12.
- Answer: 15x + 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 Introducing Algebraic Proof lesson really free?
- Yes. Every lessons 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 Counterexamples. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Introducing Algebraic Proof?
- Move on to Working with Algebraic Proof, Algebraic Proof in Context, Counterexamples, Proof by Exhaustion, which build directly on this idea.
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