Free Grade 3 Introducing Expanding Double Brackets Lesson Plans
Free Grade 3 lesson plans for Introducing Expanding Double Brackets: 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing expanding double brackets
Explain introducing expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing expanding double brackets
Calculate introducing expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing expanding double brackets
Compare introducing expanding double brackets accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing expanding double brackets
Justify introducing expanding double brackets 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 Expanding Double Brackets 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 + 6 when x = 2.[1]
- 2.Find the value of 5x + 4 when x = 6.[1]
- 3.Find the value of 6x + 5 when x = 8.[1]
- 4.Find the value of 3x + 7 when x = 5.[1]
- 5.Simplify 4x + 2y + 3x − 2y.[2]
- 6.Simplify 8x + 9y + 9x − 5y.[2]
- 7.Simplify 6x + 5y + 9x − 4y.[2]
- 8.Simplify 2x + 2y + 5x − 6y.[2]
- 9.Expand 3(2x + 6).[3]
- 10.Expand 3(6x + 6).[3]
- 11.Expand 4(4x + 1).[3]
- 12.Expand 4(3x + 7).[3]
Show answers and working
1. 20
Replace x with 2: 7 × 2 + 6. 14 + 6 = 20.
2. 34
Replace x with 6: 5 × 6 + 4. 30 + 4 = 34.
3. 53
Replace x with 8: 6 × 8 + 5. 48 + 5 = 53.
4. 22
Replace x with 5: 3 × 5 + 7. 15 + 7 = 22.
5. 7x + 0y
Collect x terms: 4x + 3x = 7x. Collect y terms: 2y − 2y = 0y.
6. 17x + 4y
Collect x terms: 8x + 9x = 17x. Collect y terms: 9y − 5y = 4y.
7. 15x + 1y
Collect x terms: 6x + 9x = 15x. Collect y terms: 5y − 4y = 1y.
8. 7x − 4y
Collect x terms: 2x + 5x = 7x. Collect y terms: 2y − 6y = -4y.
9. 6x + 18
Multiply each term inside by 3. 3 × 2x = 6x, 3 × 6 = 18.
10. 18x + 18
Multiply each term inside by 3. 3 × 6x = 18x, 3 × 6 = 18.
11. 16x + 4
Multiply each term inside by 4. 4 × 4x = 16x, 4 × 1 = 4.
12. 12x + 28
Multiply each term inside by 4. 4 × 3x = 12x, 4 × 7 = 28.
Worked examples
Find the value of 4x + 17 when x = 9.
- Replace x with 9: 4 × 9 + 17.
- 36 + 17 = 53.
- Answer: 53
Simplify 8x + 1y + 5x − 9y.
- Collect x terms: 8x + 5x = 13x.
- Collect y terms: 1y − 9y = -8y.
- Answer: 13x − 8y
Expand 2(6x + 7).
- Multiply each term inside by 2.
- 2 × 6x = 12x, 2 × 7 = 14.
- Answer: 12x + 14
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
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- What should a learner already know before this?
- Start with Sequences. 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 Introducing Expanding Double Brackets?
- Move on to Working with Expanding Double Brackets, Expanding Double Brackets in Context, Factorising Quadratics, Completing the Square, which build directly on this idea.
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