Free Grade 3 Factorising Quadratics in Context Lessons
Free Grade 3 lessons for Factorising Quadratics in Context: 12 real questions with a full answer key and worked solutions. A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
Free
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify factorising quadratics in context
Identify factorising quadratics in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain factorising quadratics in context
Explain factorising quadratics in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate factorising quadratics in context
Calculate factorising quadratics in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare factorising quadratics in context
Compare factorising quadratics 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 Factorising Quadratics in Context works
A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Factorise x² + 1x − 30.[1]
- 2.Factorise x² + 13x + 36.[1]
- 3.Factorise x² − 3x − 54.[1]
- 4.Factorise x² + 6x + 8.[1]
- 5.Solve x² − 4x − 12 = 0.[2]
- 6.Solve x² + 2x − 24 = 0.[2]
- 7.Solve x² − 2x − 15 = 0.[2]
- 8.Solve x² + 8x − 9 = 0.[2]
- 9.Solve x² − 7x − 8 = 0.[3]
- 10.Solve x² − 3x − 4 = 0.[3]
- 11.Solve x² + 8x + 15 = 0.[3]
- 12.Solve x² + 9x + 18 = 0.[3]
Show answers and working
1. (x − 5)(x + 6)
Find two numbers that multiply to -30 and add to 1: -5 and 6. So x² + 1x − 30 = (x − 5)(x + 6).
2. (x + 4)(x + 9)
Find two numbers that multiply to 36 and add to 13: 4 and 9. So x² + 13x + 36 = (x + 4)(x + 9).
3. (x − 9)(x + 6)
Find two numbers that multiply to -54 and add to -3: -9 and 6. So x² − 3x − 54 = (x − 9)(x + 6).
4. (x + 4)(x + 2)
Find two numbers that multiply to 8 and add to 6: 4 and 2. So x² + 6x + 8 = (x + 4)(x + 2).
5. x = -2 or x = 6
Factorise: (x + 2)(x − 6) = 0. One bracket must be zero: x = -2 or x = 6.
6. x = 4 or x = -6
Factorise: (x − 4)(x + 6) = 0. One bracket must be zero: x = 4 or x = -6.
7. x = 5 or x = -3
Factorise: (x − 5)(x + 3) = 0. One bracket must be zero: x = 5 or x = -3.
8. x = 1 or x = -9
Factorise: (x − 1)(x + 9) = 0. One bracket must be zero: x = 1 or x = -9.
9. x = -1 or x = 8
Factorise: (x + 1)(x − 8) = 0. One bracket must be zero: x = -1 or x = 8.
10. x = -1 or x = 4
Factorise: (x + 1)(x − 4) = 0. One bracket must be zero: x = -1 or x = 4.
11. x = -5 or x = -3
Factorise: (x + 5)(x + 3) = 0. One bracket must be zero: x = -5 or x = -3.
12. x = -6 or x = -3
Factorise: (x + 6)(x + 3) = 0. One bracket must be zero: x = -6 or x = -3.
Worked examples
Factorise x² + 2x − 24.
- Find two numbers that multiply to -24 and add to 2: -4 and 6.
- So x² + 2x − 24 = (x − 4)(x + 6).
- Answer: (x − 4)(x + 6)
Solve x² + 6x + 5 = 0.
- Factorise: (x + 1)(x + 5) = 0.
- One bracket must be zero: x = -1 or x = -5.
- Answer: x = -1 or x = -5
Solve x² − 1x − 56 = 0.
- Factorise: (x + 7)(x − 8) = 0.
- One bracket must be zero: x = -7 or x = 8.
- Answer: x = -7 or x = 8
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Gives x = 3 from (x + 3) = 0.
Correction: x + 3 = 0 means x = −3.
Gets the signs muddled when factorising.
Correction: Check by expanding the brackets.
Teacher tips
- · Use a product–sum grid for finding the pair.
Parent tips
- · Ask what two numbers multiply to 12 and add to 7.
Real-life applications
- · Projectile paths, maximising area.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Factorising Quadratics in Context 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 Working with Factorising Quadratics, Introducing Factorising Quadratics, Expanding Double Brackets. 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 Factorising Quadratics in Context?
- Move on to Expanding Double Brackets, Completing the Square, The Quadratic Formula, Quadratic Graphs, which build directly on this idea.
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