Factorising Quadratics

Overview

This 15-minute session introduces Year 9 students to factorising quadratic expressions where (a=1) using the grid method. The lesson aligns with the National Curriculum for England focusing on algebraic manipulation and understanding of quadratic expressions.

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National Curriculum Links

• Mathematics Programme of Study (Years 7-9)
  • Algebra
  • Use algebraic methods to solve linear and quadratic equations, factorising expressions including quadratics where (a=1).
• Key Stage 3 - Number and Algebra – Solving Equations
  • Construct and solve quadratic equations using various methods (including factorising).

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Learning Objectives

By the end of this lesson, students will be able to:

• Understand and apply the grid method to factorise quadratic expressions with leading coefficient (a=1).
• Identify pairs of numbers that multiply to the constant term and add to the middle coefficient.
• Begin to develop algebraic fluency necessary for solving quadratic equations.

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Resources Needed

• Whiteboard and markers
• Mini whiteboards or scrap paper for each student
• Pre-prepared grid templates printed on handouts or projected
• Example quadratic expressions for guided practice
• Stopwatch or timer to keep to 15 minutes
• Manipulatives or colour-coded cards (optional for kinaesthetic engagement)

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Lesson Structure

1. Starter (2 minutes)

• Begin with a quick recap question on multiplying two binomials (e.g., ((x+2)(x+3) = ?)) to activate prior knowledge.
• Ask: "What is the product and how does the middle term appear?"
• Make the connection to quadratic expressions of the form (x^2 + bx + c).

2. Introduction to Grid Method (5 minutes)

• Display the quadratic expression (x^2 + 5x + 6) on the board.
• Draw a 2x2 grid on the board: label cells for (x^2), the middle term split into two, and the constant.
• Explain each quadrant: place (x^2) in the top-left, (6) in the bottom-right.
• Demonstrate identifying two numbers that multiply to 6 and add to 5 (2 and 3).
• Fill these into the other two cells (2x) and (3x).
• Show how to find the factors ((x + 2)(x + 3)) by reading across rows and columns.

3. Guided Practice (5 minutes)

• Present 2 more quadratics of the form (x^2 + bx + c) to the class: e.g.,
  1. (x^2 + 7x + 12)
  2. (x^2 + 4x + 3)
• Students use mini whiteboards/grid handouts to apply the grid method.
• Teacher circulates, checks understanding, prompts if stuck, focusing on finding the pair of numbers.

4. Quick Assessment and Reflection (3 minutes)

• Pose a short challenge: Factorise (x^2 + 6x + 8) using the grid method.
• Students write down answers quickly.
• Review answers as a class; praise correct use of method and gently correct mistakes.
• Recap key points: "Find two numbers multiplying to c, adding to b. Fill in grid and read factors."

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Differentiation & Inclusion

• Support: Provide number factor cards for students struggling to identify pairs. Use colour coding to highlight addition/multiplication connections.
• Challenge: Ask higher attaining students to explain why the method works algebraically or to extend to (a \neq 1) cases for future lessons.

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Assessment

• Informal formative assessment through observation during guided practice and the quick challenge.
• Use student mini-whiteboard responses to gauge understanding.
• Address misunderstandings immediately to ensure progress.

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Extension Ideas

• Use digital tools or apps with interactive quadratic factorising grids.
• Set a ‘factorising relay’ activity for a following lesson to enhance fluency and speed.
• Begin linking to solving quadratic equations by factorising expressions set equal to zero.

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Reflection for Teacher

• Was the grid method introduced clearly within the time?
• Did students engage with the activity confidently?
• How effective were the resources (grids, factor cards)?
• What adjustments can be made for the next lesson to deepen understanding or pace?

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This lesson plan maximises a short 15-minute window by combining visual, auditory, and kinaesthetic learning strategies in line with KS3 algebra objectives, ensuring focused, active engagement with factorising quadratics where (a=1).