Class: Junior Secondary School 3 (JSS3, JSS 3)
Term: 1st Term
Week: 6
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Plane Figures and Mensuration Problems
Topic: Factorization of Algebraic Expressions
Subject Matter: Factorization of expressions of the form: ax + ay, 3m + pq + 3p + mq, a² – b², a² – 2ab + b², Word problems involving factorization.

Specific Objectives

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

Cognitive Domain:
(a) Identify and apply the different methods of factorization in algebraic expressions.
(b) Solve word problems involving factorization correctly.
Affective Domain:
(a) Develop interest and confidence in solving algebraic expressions through factorization.
Psychomotor Domain:
(a) Demonstrate the steps involved in factoring given expressions correctly on the board.
Social Domain:
(a) Work collaboratively in groups to solve factorization problems and explain their methods to others.

Reference Materials

The following resources was used in planning this lesson:

9 Years Basic Education Curriculum
Lagos State Unified Scheme of work for Junior Secondary Schools
Math is Fun – “Factoring Algebraic Expressions” (https://www.mathsisfun.com/algebra/factoring.html)
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Algebra charts showing examples of factorized expressions
Flash cards of expressions for practice
Marker and whiteboard
Projector or chart showing steps of factorization
Worksheets for group exercises

Rationale for the Lesson

This lesson enables students to simplify complex algebraic expressions and solve related problems efficiently by applying the principles of factorization.

Prerequisite/Previous Knowledge

Students have been introduced to basic algebraic terms, expressions, and operations, and can expand and simplify simple expressions involving brackets.

Lesson Content/Board Summary

Factorization of Algebraic Expressions

Factorization means expressing an algebraic expression as a product of its factors. It is the reverse of expansion in algebra.

Factorization by Common Factors

This method involves taking out the highest common factor (HCF) from each term of the expression.

Examples include:

( ax + ay = a(x + y) )
Here, a is the common factor.
( 3m + pq + 3p + mq )
Rearranging: ( (3m + mq) + (3p + pq) )
Taking common factors: ( m(3 + q) + p(3 + q) )
Therefore, ( (m + p)(3 + q) ).

Factorization of Difference of Two Squares

This involves expressions of the form ( a^2 – b^2 ).
It can be factorized as ( (a + b)(a – b) ).

Examples include:

( a^2 – b^2 = (a + b)(a – b) )
( 9x^2 – 16y^2 = (3x + 4y)(3x – 4y) ).

Factorization of Perfect Squares

A perfect square trinomial is obtained when a binomial is squared.
The general forms are:

( a^2 + 2ab + b^2 = (a + b)^2 )
( a^2 – 2ab + b^2 = (a – b)^2 )

Examples include:

( a^2 – 2ab + b^2 = (a – b)^2 )
( x^2 + 6x + 9 = (x + 3)^2 ).

Word Problems Involving Factorization

Word problems often involve simplifying expressions or finding unknown quantities using factorization.

Examples include:

Factorize and simplify: ( 4x^2 – 9 ).
Solution: ( 4x^2 – 9 = (2x + 3)(2x – 3) ).
Simplify ( 5x^2y – 10xy^2 ).
Solution: Take out the common factor ( 5xy ), we have ( 5xy(x – 2y) ).

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, Guided Discovery, Group Work, Question and Answer

Instructional Procedures

To deliver this lesson, the teacher will adopt the following steps:

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher begins by asking pupils to expand simple expressions and then reverses the process to show factorization.
Pupils’ Activity: Pupils respond by expanding and simplifying examples.
Learning Point: Pupils recall previous knowledge and are introduced to the concept of factorization.

Step 2: Factorization by Common Factors

Time: 10 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher explains the method of taking out common factors and shows worked examples on the board.
Pupils’ Activity: Pupils observe and take notes, then solve similar problems.
Learning Point: Pupils understand how to factorize expressions by taking out common terms.

Step 3: Difference of Two Squares

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher presents examples of the difference of two squares and demonstrates how to factorize them.
Pupils’ Activity: Pupils identify perfect squares and factorize similar examples.
Learning Point: Pupils learn to recognize and factorize expressions of the form ( a^2 – b^2 ).

Step 4: Perfect Squares and Word Problems

Time: 10 minutes
Teaching Skill: Guided Discovery
Teacher’s Activity: The teacher introduces perfect square trinomials and gives examples of factorization in real-life word problems.
Pupils’ Activity: Pupils work in pairs to solve given word problems.
Learning Point: Pupils can apply factorization techniques to real-life mathematical problems.

Step 5: Note-Taking

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher dictates or writes the board summary for pupils to copy.
Pupils’ Activity: Pupils write the notes neatly into their exercise books.
Learning Point: Pupils keep accurate notes of the lesson content.

Step 6: Evaluation/Review

Time: 3 minutes
Teaching Skill: Questioning
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Factorize ( 2x + 2y ).
Factorize ( a^2 – 16 ).
Factorize ( x^2 – 2xy + y^2 ).
Solve: ( 3m + pq + 3p + mq ).
Pupils’ Activity: Pupils answer the questions orally and on the board.
Learning Point: Pupils demonstrate mastery of factorization techniques.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: The teacher summarizes the lesson and emphasizes the importance of factorization in solving algebraic expressions.
Pupils’ Activity: Pupils listen attentively and ask questions.
Learning Point: Pupils consolidate their understanding of factorization.

Lesson Keywords

Factorization – breaking down an expression into its simplest factors.
Common Factor – the term that divides all parts of an expression.
Difference of Two Squares – expression in the form ( a^2 – b^2 ).
Perfect Square – a number or expression obtained by squaring another.
Trinomial – an algebraic expression with three terms.

Differentiation

Provide simpler examples and step-by-step explanations for slower learners, while advanced learners solve more complex expressions and assist peers in group activities.

Note for teachers using this lesson plan

Ensure pupils understand that factorization is the reverse of expansion. Encourage neat working steps and continuous practice to build speed and accuracy.