aidemia--modules-lessonplan_request	Titles of parts of the lesson must be formatted as headings
What to create	Lesson plan
Which subject	Mathematics
What topic	Factorisation of quadratic expressions
What length (min)	30
What age group	Year or Grade 10
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Lesson Plan: Factorisation of Quadratic Expressions

Duration: 30 minutes
Subject: Mathematics
Year Group: 10

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Lesson Objectives

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

1. Understand the concept of quadratic expressions.
2. Identify and use the methods of factorisation specific to quadratic expressions.
3. Apply these methods to factorise quadratic expressions effectively.

Required Materials

• Whiteboard and markers
• Worksheets with quadratic expressions for practice
• Graphing calculators (optional)
• Projector (for visual aids)

Lesson Outline

Introduction (5 minutes)

• Begin with a brief recap of what a quadratic expression is, highlighting the standard form ( ax^2 + bx + c ).
• Explain that the focus of today's lesson is factorisation—transforming the quadratic expression into the product of two binomials.

Direct Instruction (10 minutes)

1. Identify Coefficients:

   • Define ( a ), ( b ), and ( c ) in the context of a quadratic expression.
   • Example: For ( 2x^2 + 7x + 3 ), identify ( a = 2 ), ( b = 7 ), ( c = 3 ).

2. Methods of Factorisation:

   • Method 1: Factor by Inspection: When the quadratic can be easily split into two factors by examining the product and sum of coefficients.
   • Method 2: Using the Quadratic Formula: State that though primarily used for finding roots, it can assist in factorisation.

3. Step-by-Step Factorisation:

   • Show how to factorise ( x^2 + 5x + 6 ) by finding two numbers that multiply to ( 6 ) (the constant term) and add up to ( 5 ) (the coefficient of ( x )).
   • Result: ( (x + 2)(x + 3) ).

Guided Practice (10 minutes)

• Distribute worksheets containing a variety of quadratic expressions for students to practise factorisation.
• Work through the first example together, then allow students to work in pairs on the next few problems, providing support as needed.

Independent Practice (5 minutes)

• Students complete the remaining questions on their own, aiming to solve at least three expressions by factorisation.

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Homework Assignment

Tasks:

1. Factorise the following quadratic expressions:

   • a) ( x^2 + 8x + 15 )
   • b) ( 3x^2 - 9x )
   • c) ( x^2 - 4x - 12 )

2. Create your own quadratic expression and factorise it.

Correct Answers:

1. a) ( (x + 3)(x + 5) )
   b) ( 3x(x - 3) )
   c) ( (x - 6)(x + 2) )

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Conclusion (2 minutes)

• Review key concepts covered in the lesson.
• Encourage students to reflect on how factorisation simplifies quadratic expressions and helps in solving equations.

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By adhering to this lesson plan, students will build a solid understanding of factorising quadratic expressions, leading to improved confidence in their mathematical abilities.