Free Grade 3 Working with Factorising Quadratics Lesson Plans
Free Grade 3 lesson plans for Working with Factorising Quadratics: 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
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with factorising quadratics
Explain working with factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with factorising quadratics
Calculate working with factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with factorising quadratics
Compare working with factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with factorising quadratics
Justify working with factorising quadratics 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 Working with Factorising Quadratics 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 + 4x − 45.[1]
- 2.Factorise x² − 3x − 18.[1]
- 3.Factorise x² + 1x − 30.[1]
- 4.Factorise x² − 8x + 15.[1]
- 5.Solve x² + 3x − 40 = 0.[2]
- 6.Solve x² − 2x − 3 = 0.[2]
- 7.Solve x² − 1x − 20 = 0.[2]
- 8.Solve x² − 11x + 18 = 0.[2]
- 9.Solve x² − 9x + 14 = 0.[3]
- 10.Solve x² − 6x − 27 = 0.[3]
- 11.Solve x² + 17x + 72 = 0.[3]
- 12.Solve x² + 4x − 12 = 0.[3]
Show answers and working
1. (x + 9)(x − 5)
Find two numbers that multiply to -45 and add to 4: 9 and -5. So x² + 4x − 45 = (x + 9)(x − 5).
2. (x − 6)(x + 3)
Find two numbers that multiply to -18 and add to -3: -6 and 3. So x² − 3x − 18 = (x − 6)(x + 3).
3. (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).
4. (x − 3)(x − 5)
Find two numbers that multiply to 15 and add to -8: -3 and -5. So x² − 8x + 15 = (x − 3)(x − 5).
5. x = 5 or x = -8
Factorise: (x − 5)(x + 8) = 0. One bracket must be zero: x = 5 or x = -8.
6. x = 3 or x = -1
Factorise: (x − 3)(x + 1) = 0. One bracket must be zero: x = 3 or x = -1.
7. x = -4 or x = 5
Factorise: (x + 4)(x − 5) = 0. One bracket must be zero: x = -4 or x = 5.
8. x = 2 or x = 9
Factorise: (x − 2)(x − 9) = 0. One bracket must be zero: x = 2 or x = 9.
9. x = 2 or x = 7
Factorise: (x − 2)(x − 7) = 0. One bracket must be zero: x = 2 or x = 7.
10. x = 9 or x = -3
Factorise: (x − 9)(x + 3) = 0. One bracket must be zero: x = 9 or x = -3.
11. x = -9 or x = -8
Factorise: (x + 9)(x + 8) = 0. One bracket must be zero: x = -9 or x = -8.
12. x = -6 or x = 2
Factorise: (x + 6)(x − 2) = 0. One bracket must be zero: x = -6 or x = 2.
Worked examples
Factorise x² + 1x − 12.
- Find two numbers that multiply to -12 and add to 1: 4 and -3.
- So x² + 1x − 12 = (x + 4)(x − 3).
- Answer: (x + 4)(x − 3)
Solve x² − 1x − 2 = 0.
- Factorise: (x + 1)(x − 2) = 0.
- One bracket must be zero: x = -1 or x = 2.
- Answer: x = -1 or x = 2
Solve x² − 17x + 72 = 0.
- Factorise: (x − 8)(x − 9) = 0.
- One bracket must be zero: x = 8 or x = 9.
- Answer: x = 8 or x = 9
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 Working with Factorising Quadratics lesson plan really free?
- Yes. Every lesson plans 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 Factorising Quadratics, Expanding Double Brackets. 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 Working with Factorising Quadratics?
- Move on to Factorising Quadratics in Context, Expanding Double Brackets, Completing the Square, The Quadratic Formula, which build directly on this idea.
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