Free Grade 3 Introducing Factorising Quadratics Lesson Plans
Free Grade 3 lesson plans for Introducing 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
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20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing factorising quadratics
Explain introducing factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing factorising quadratics
Calculate introducing factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing factorising quadratics
Compare introducing factorising quadratics accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing factorising quadratics
Justify introducing 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 Introducing 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 − 10x + 16.[1]
- 2.Factorise x² − 6x − 27.[1]
- 3.Factorise x² − 2x − 35.[1]
- 4.Factorise x² + 5x + 4.[1]
- 5.Solve x² − 4x + 4 = 0.[2]
- 6.Solve x² + 14x + 45 = 0.[2]
- 7.Solve x² − 10x + 25 = 0.[2]
- 8.Solve x² − 5x − 36 = 0.[2]
- 9.Solve x² − 5x + 4 = 0.[3]
- 10.Solve x² + 3x + 2 = 0.[3]
- 11.Solve x² − 3x − 4 = 0.[3]
- 12.Solve x² − 2x − 35 = 0.[3]
Show answers and working
1. (x − 2)(x − 8)
Find two numbers that multiply to 16 and add to -10: -2 and -8. So x² − 10x + 16 = (x − 2)(x − 8).
2. (x + 3)(x − 9)
Find two numbers that multiply to -27 and add to -6: 3 and -9. So x² − 6x − 27 = (x + 3)(x − 9).
3. (x + 5)(x − 7)
Find two numbers that multiply to -35 and add to -2: 5 and -7. So x² − 2x − 35 = (x + 5)(x − 7).
4. (x + 1)(x + 4)
Find two numbers that multiply to 4 and add to 5: 1 and 4. So x² + 5x + 4 = (x + 1)(x + 4).
5. x = 2 or x = 2
Factorise: (x − 2)(x − 2) = 0. One bracket must be zero: x = 2 or x = 2.
6. x = -9 or x = -5
Factorise: (x + 9)(x + 5) = 0. One bracket must be zero: x = -9 or x = -5.
7. x = 5 or x = 5
Factorise: (x − 5)(x − 5) = 0. One bracket must be zero: x = 5 or x = 5.
8. x = 9 or x = -4
Factorise: (x − 9)(x + 4) = 0. One bracket must be zero: x = 9 or x = -4.
9. x = 4 or x = 1
Factorise: (x − 4)(x − 1) = 0. One bracket must be zero: x = 4 or x = 1.
10. x = -2 or x = -1
Factorise: (x + 2)(x + 1) = 0. One bracket must be zero: x = -2 or x = -1.
11. x = 4 or x = -1
Factorise: (x − 4)(x + 1) = 0. One bracket must be zero: x = 4 or x = -1.
12. x = -5 or x = 7
Factorise: (x + 5)(x − 7) = 0. One bracket must be zero: x = -5 or x = 7.
Worked examples
Factorise x² + 12x + 27.
- Find two numbers that multiply to 27 and add to 12: 9 and 3.
- So x² + 12x + 27 = (x + 9)(x + 3).
- Answer: (x + 9)(x + 3)
Solve x² − 3x + 2 = 0.
- Factorise: (x − 2)(x − 1) = 0.
- One bracket must be zero: x = 2 or x = 1.
- Answer: x = 2 or x = 1
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
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 Introducing 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 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 Introducing Factorising Quadratics?
- Move on to Working with Factorising Quadratics, Factorising Quadratics in Context, Expanding Double Brackets, Completing the Square, which build directly on this idea.
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