Free Grade 3 Introducing Algebraic Proof Techniques Lessons
Free Grade 3 lessons for Introducing Algebraic Proof Techniques: 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 introducing algebraic proof techniques
Identify introducing algebraic proof techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing algebraic proof techniques
Explain introducing algebraic proof techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing algebraic proof techniques
Calculate introducing algebraic proof techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing algebraic proof techniques
Compare introducing algebraic proof techniques 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 Techniques 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 5x + 10 when x = 3.[1]
- 2.Find the value of 7x + 11 when x = 7.[1]
- 3.Find the value of 4x + 7 when x = 7.[1]
- 4.Find the value of 8x + 16 when x = 7.[1]
- 5.Simplify 5x + 3y + 3x − 9y.[2]
- 6.Simplify 4x + 7y + 8x − 7y.[2]
- 7.Simplify 7x + 7y + 4x − 4y.[2]
- 8.Simplify 2x + 3y + 8x − 8y.[2]
- 9.Expand 2(5x + 9).[3]
- 10.Expand 2(5x + 2).[3]
- 11.Expand 3(6x + 8).[3]
- 12.Expand 4(5x + 6).[3]
Show answers and working
1. 25
Replace x with 3: 5 × 3 + 10. 15 + 10 = 25.
2. 60
Replace x with 7: 7 × 7 + 11. 49 + 11 = 60.
3. 35
Replace x with 7: 4 × 7 + 7. 28 + 7 = 35.
4. 72
Replace x with 7: 8 × 7 + 16. 56 + 16 = 72.
5. 8x − 6y
Collect x terms: 5x + 3x = 8x. Collect y terms: 3y − 9y = -6y.
6. 12x + 0y
Collect x terms: 4x + 8x = 12x. Collect y terms: 7y − 7y = 0y.
7. 11x + 3y
Collect x terms: 7x + 4x = 11x. Collect y terms: 7y − 4y = 3y.
8. 10x − 5y
Collect x terms: 2x + 8x = 10x. Collect y terms: 3y − 8y = -5y.
9. 10x + 18
Multiply each term inside by 2. 2 × 5x = 10x, 2 × 9 = 18.
10. 10x + 4
Multiply each term inside by 2. 2 × 5x = 10x, 2 × 2 = 4.
11. 18x + 24
Multiply each term inside by 3. 3 × 6x = 18x, 3 × 8 = 24.
12. 20x + 24
Multiply each term inside by 4. 4 × 5x = 20x, 4 × 6 = 24.
Worked examples
Find the value of 5x + 4 when x = 5.
- Replace x with 5: 5 × 5 + 4.
- 25 + 4 = 29.
- Answer: 29
Simplify 9x + 5y + 9x − 9y.
- Collect x terms: 9x + 9x = 18x.
- Collect y terms: 5y − 9y = -4y.
- Answer: 18x − 4y
Expand 4(2x + 5).
- Multiply each term inside by 4.
- 4 × 2x = 8x, 4 × 5 = 20.
- Answer: 8x + 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
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Frequently asked
- Is this Grade 3 Introducing Algebraic Proof Techniques 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 Introducing Algebraic Proof Essentials, 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 Techniques?
- Move on to Introducing Algebraic Proof Word Problems, Introducing Algebraic Proof Common Errors, Working with Algebraic Proof, Algebraic Proof in Context, which build directly on this idea.
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