Solving Quadratic Equations by Factorising
A comprehensive lesson on solving quadratic equations by factorising. Students will progress from solving equations already in factored form to factorising trinomials and solving equations that require rearrangement. The lesson culminates in applying these skills to area-based problems.
Learning objectives
- Factorise quadratic expressions of the form x² + bx + c.
- Apply the Zero Product Property to solve quadratic equations.
- Solve quadratic equations by factorising where the equation must first be rearranged to equal zero.
- Set up and solve quadratic equations from geometric contexts.
Lesson plan (60 minutes)
Introduction · 10 min
Starter: Factorising linear expressions and identifying factor pairs of numbers.
Development · 15 min
Direct Instruction: Explaining the Zero Product Property and demonstrating the step-by-step method for solving by factorising.
Guided Practice · 10 min
Guided Practice: Solving three examples on mini-whiteboards with increasing difficulty.
Independent Practice · 15 min
Independent Practice: Differentiated worksheets (Support, Core, Stretch) based on prior attainment and starter performance.
Consolidation · 10 min
Plenary: Multiple-choice quiz to check for understanding and address misconceptions.
Key vocabulary
- Quadratic Equation
- An equation where the highest power of the variable is 2 (e.g., x²).
- Factorising
- Writing an expression as a product of its factors (usually involving brackets).
- Solutions
- The values of the variable that make the equation true. Also called 'roots'.
- Trinomial
- An expression with three terms, such as x² + 5x + 6.
- Zero Product Property
- If A × B = 0, then either A = 0, B = 0, or both.
Core worksheet (first questions)
- Solve x² + 7x + 10 = 0
- Solve x² - 5x - 14 = 0
- Solve x² - 2x - 15 = 0
- Solve x² + 8x - 20 = 0
Quiz (sample)
1. Solve (x + 3)(x - 5) = 0
- A. x = 3 or x = -5
- B. x = -3 or x = 5
- C. x = 3 or x = 5
- D. x = -3 or x = -5
2. Solve x(x + 7) = 0
- A. x = 7
- B. x = -7
- C. x = 0 or x = 7
- D. x = 0 or x = -7
3. What is the first step to solve x² + 6x + 8 = 0?
- A. (x - 2)(x - 4) = 0
- B. (x + 8)(x + 1) = 0
- C. (x + 2)(x + 4) = 0
- D. (x + 6)(x + 2) = 0
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