Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: Second Term
Week: 1
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Construction.
Topic: FACTORIZATION OF QUADRATIC EXPRESSION OF THE FORM ax²+bx+c where a, b, c are constants
Subject Matter: Factorizing quadratic expression of the form ax²+bx+c, Factorizing quadratic expression of the form ax²-bx+c, Factorizing quadratic expressions of the form ax²+bx-c, Factorizing quadratic expressions of the form ax²-bx-c, Solving quadratic equation of the form ax²+bx+c = 0.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

Define a quadratic expression.
State the general form of a quadratic expression.
Explain the steps involved in factorizing quadratic expressions.
Factorize quadratic expressions of the forms ax²+bx+c, ax²-bx+c, ax²+bx-c, and ax²-bx-c.
Solve quadratic equations of the form ax²+bx+c = 0 by factorization.

Affective Domain:

Appreciate the importance of factorization in solving mathematical problems.
Show confidence in applying different factorization methods.

Psychomotor Domain:

Accurately factorize given quadratic expressions.
Write down the steps for solving quadratic equations by factorization.

Collaborate with peers to solve factorization problems.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Senior Secondary Schools.
State Unified Scheme of Work for General Mathematics SSS 1.
New General Mathematics for Senior Secondary Schools 1.

Instructional Materials

The teacher will teach this lesson with the aid of:

Quadratic expressions and factors chart.
Flex banners showing expressions of the form ax²+bx+c, ax²-bx+c, ax²+bx-c and ax²-bx-c.
Whiteboard and markers.

Rationale for the Lesson

This lesson helps pupils understand how to simplify and solve quadratic expressions and equations. This skill is important for further studies in mathematics and sciences, and it enables pupils to tackle real-world problems involving quadratic relationships.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of factorization of simple algebraic expressions, expansion of algebraic expressions, and basic operations with integers.

Lesson Content/Board Summary

FACTORIZATION OF QUADRATIC EXPRESSIONS

Definition of a Quadratic Expression

A quadratic expression is an algebraic expression of degree two. This means the highest power of the variable in the expression is two.

General Form of a Quadratic Expression

The general form of a quadratic expression is ax² + bx + c, where ‘a’, ‘b’, and ‘c’ are constants, and ‘a’ is not equal to zero.

Steps to Factorize Quadratic Expressions of the form ax²+bx+c

To factorize a quadratic expression of the form ax²+bx+c:

Find two numbers whose product is (a × c) and whose sum is ‘b’.
Replace the middle term ‘bx’ with the sum of two terms formed by these two numbers.
Group the terms into pairs.
Factor out the common factor from each pair.
Factor out the common binomial factor.

Example: Factorize 2x² + 7x + 3.

Factorization of Quadratic Expressions with Different Signs

Quadratic expressions can appear with different combinations of signs for the ‘b’ and ‘c’ terms.

Form ax²+bx+c: Both numbers found will be positive. (e.g., 2x²+7x+3)
Form ax²-bx+c: Both numbers found will be negative. (e.g., 3x²-10x+8)
Form ax²+bx-c: The larger number will be positive, and the smaller number will be negative. (e.g., 2x²+5x-3)
Form ax²-bx-c: The larger number will be negative, and the smaller number will be positive. (e.g., 3x²-x-2)

Solving Quadratic Equations by Factorization

A quadratic equation is an equation of the form ax² + bx + c = 0. To solve by factorization:

Factorize the quadratic expression on one side of the equation.
Set each factor equal to zero.
Solve for the variable in each resulting linear equation. These solutions are the roots of the quadratic equation.

Example: Solve 2x² + 7x + 3 = 0.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews their previous knowledge of expanding algebraic expressions like (x+2)(x+3). The teacher then introduces the topic by explaining that factorization is the reverse process of expansion.
Pupils’ Activity: Pupils respond to greetings, recall and answer questions on expansion of algebraic expressions.
Learning Point: Pupils connect factorization to their previous knowledge of expansion.

Step 2: Definition and General Form of a Quadratic Expression

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines a quadratic expression and states its general form (ax²+bx+c), explaining the meaning of ‘a’, ‘b’, and ‘c’. The teacher gives examples of quadratic expressions.
Pupils’ Activity: Pupils listen, take notes, and identify quadratic expressions from given examples.
Learning Point: Pupils understand what a quadratic expression is and its standard form.

Step 3: Factorization of Quadratic Expressions (ax²+bx+c)

Time: 10 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher explains the steps for factorizing quadratic expressions of the form ax²+bx+c, using a clear example like 2x²+7x+3. The teacher demonstrates finding two numbers whose product is (a × c) and sum is ‘b’, then grouping and factoring.
Pupils’ Activity: Pupils observe the demonstration, follow the steps, and ask questions for clarification.
Learning Point: Pupils learn the method for factorizing quadratic expressions with positive ‘b’ and ‘c’ terms.

Step 4: Factorization of Quadratic Expressions (ax²-bx+c and ax²+bx-c)

Time: 8 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher guides pupils through examples of factorizing expressions like 3x²-10x+8 (where ‘b’ is negative, ‘c’ is positive) and 2x²+5x-3 (where ‘b’ is positive, ‘c’ is negative). The teacher emphasizes how the signs of the two numbers change based on the signs in the expression.
Pupils’ Activity: Pupils participate in solving the examples, applying the learned steps, and discussing the sign changes.
Learning Point: Pupils understand how to handle different sign combinations in quadratic expressions during factorization.

Step 5: Factorization of Quadratic Expressions (ax²-bx-c)

Time: 7 minutes
Teaching Skill: Problem Solving
Teacher’s Activity: The teacher presents an example of the form ax²-bx-c, such as 3x²-x-2. The teacher allows pupils to attempt the factorization, providing assistance and corrections as needed. The teacher ensures pupils correctly identify the product (a × c) and sum (‘b’) and apply the correct signs.
Pupils’ Activity: Pupils work individually or in pairs to factorize the given expression, applying the knowledge of signs.
Learning Point: Pupils gain confidence in factorizing all forms of quadratic expressions.

Step 6: Solving Quadratic Equations by Factorization

Time: 5 minutes
Teaching Skill: Application
Teacher’s Activity: The teacher explains that once a quadratic expression is factorized, it can be used to solve a quadratic equation (when the expression is set to zero). The teacher demonstrates how to set each factor to zero to find the roots (solutions) of the equation, using an example like 2x²+7x+3 = 0.
Pupils’ Activity: Pupils follow the steps to solve the quadratic equation and understand how factorization leads to the roots.
Learning Point: Pupils learn to apply factorization to solve quadratic equations.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define a quadratic expression.
State the general form of a quadratic expression.
Factorize the expression: x² + 5x + 6.
Factorize the expression: 3x² – 5x + 2.
Solve the equation: 2x² – x – 1 = 0.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of identifying the correct product and sum for factorization. The teacher assigns homework: Factorize 4x² – 9x + 2 and solve x² – 7x + 12 = 0.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their understanding and prepare for independent practice.

Lesson Keywords

Quadratic expression – An algebraic expression of degree two.
Factorization – The process of breaking down an expression into simpler expressions (factors) whose product is the original expression.
Constant – A fixed value in an algebraic expression.
Coefficient – A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Roots – The solutions to a quadratic equation.

Differentiation

For struggling learners, the teacher will provide additional guided practice with simpler coefficients and use a step-by-step checklist. Advanced learners will be given more complex quadratic expressions to factorize and solve, possibly including those requiring prior simplification.

Note for teachers using this lesson plan

Teachers should ensure pupils have a strong grasp of integer multiplication and addition, especially with negative numbers, as this is fundamental to successful factorization. Visual aids like charts demonstrating the product-sum method are highly beneficial.