Factorization

Grade 9 · Mathematics

Semester 1 | Period 2 | Week 10

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Subject: Mathematics

Semester: 1

Period: 2

Week: 10

WEEK 10

Class: Grade 9
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Factorization
Focus: Factorization of Expressions & Word Problems Involving Factorization

SPECIFIC OBJECTIVES:

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

  1. Factorize simple algebraic expressions of the form ax + ay.
  2. Factorize more complex expressions such as 3m + pq + 3p + mp.
  3. Apply special identities in factorization: a2−b2 , a2−2ab−b2
  4. Solve word problems involving factorization.
  5. Apply factorization techniques in real-life problem solving.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Group exercises and drills
  • Real-life application

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and marker
  • Flashcards with algebraic expressions
  • Worksheets with practice problems
  • Chart showing special products (e.g., difference of squares)

PERIOD 1 & 2: Factorization of Simple Expressions

PRESENTATION

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains that factorization means writing an expression as a product of two or more factors.

Pupils listen and ask questions.

Step 2 – Explanation

Demonstrates factorization of ax + ay by taking out the common factor. E.g., ax + ay = a(x + y).

Pupils observe and participate.

Step 3 – Demonstration

Solves 3m + 3p = 3(m + p). Explains common factors.

Pupils practice with guidance.

Step 4 – Note Taking

Writes rules and examples of factorization on the board.

Pupils copy notes.

 

NOTE ON BOARD:

  • Factorization means writing an expression as a product of factors.
  • Examples:
    • ax+ay=a(x+y)
    • 3m+3p=3(m+p)

 

EVALUATION (5 exercises):

  1. Factorize: 7x+14y
  2. Factorize: 6m+9n
  3. Factorize: 10a+5b.
  4. Factorize: 12x+18.
  5. Factorize: x2y+xy2.

CLASSWORK (5 questions):

  1. Factorize: 8p+12q.
  2. Factorize: 15m+25n.
  3. Factorize: 6ab+9ac.
  4. Factorize: x3+x2
  5. Factorize: pq+pr.

ASSIGNMENT (5 tasks):

  1. Factorize: 18x+24.
  2. Factorize: x2+xy .
  3. Factorize: 20a+25b.
  4. Factorize: 4m2+8mn.
  5. Factorize: ax+bx.

 

PERIOD 3 & 4: Special Products in Factorization

PRESENTATION

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains special cases: difference of two squares, quadratic identities.

Pupils listen.

Step 2 – Explanation

Demonstrates a2−b2=(a+b)(a−b).

Pupils observe.

Step 3 – Demonstration

Works out a2−2ab−b2.

Pupils practice with teacher guidance.

Step 4 – Note Taking

Writes examples on the board.

Pupils copy notes.

 

NOTE ON BOARD:

  • a2−b2=(a+b)(a−b)
  • a2−2ab−b2=(a−b)2−2b2 (work through simplification)

 

EVALUATION (5 exercises):

  1. Factorize: x2−9.
  2. Factorize: y2−16.
  3. Factorize: a2−25.
  4. Factorize: p2−q2.
  5. Factorize: m2−2mn−n2.

CLASSWORK (5 questions):

  1. Factorize: b2−49.
  2. Factorize: x2−y2.
  3. Factorize: c2−36.
  4. Factorize: a2−4ab−b2.
  5. Factorize: d2−2de−e2.

ASSIGNMENT (5 tasks):

  1. Factorize: k2−64.
  2. Factorize: r2−s2.
  3. Factorize: t2−81.
  4. Factorize: a2−2ab−b2.
  5. Factorize: m2−4mn−n2.

 

PERIOD 5: Word Problems Involving Factorization

PRESENTATION

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains how real-life problems can be solved using factorization.

Pupils listen.

Step 2 – Explanation

Gives example: The area of a rectangle is ax+ay. Factorize to find dimensions.

Pupils observe.

Step 3 – Demonstration

Solves more examples of factorization in word problems.

Pupils solve guided problems.

Step 4 – Note Taking

Writes solved examples on the board.

Pupils copy notes.

 

NOTE ON BOARD:

  • Word problems can be simplified using factorization.
  • Example: ax+ay=a(x+y).

EVALUATION (5 exercises):

  1. Factorize the area of a rectangle given as 10x+20y
  2. Factorize: 12m+18n to find rectangle dimensions.
  3. A farmer has x cows and y goats, factorize 5x+5y.
  4. Factorize: 8a+12b.
  5. Factorize: 15p+25q.

CLASSWORK (5 questions):

  1. Factorize: 14x+21y.
  2. A garden’s perimeter is given by 6a+9b. Factorize.
  3. Factorize the cost of buying x pens and y pencils if each costs 2 dollars: 2x+2y.
  4. Factorize: 9m+12n.
  5. Factorize: 18p+24q.

ASSIGNMENT (5 tasks):

  1. A floor area is given as 20a+25b. Factorize.
  2. Factorize the expression for the perimeter of a rectangle: 2l+2w.
  3. Factorize: 30m+45n.
  4. Factorize: 50x+60y.
  5. Form a real-life word problem that requires factorization to solve.