Comprehensive Lesson Plan for JSS 2 Mathematics – Second Term, Week 1

Subject: Mathematics

Class: JSS 2

Term: Second Term

Week: Week 1

Age: 11 – 13 years

Topic: Review of First Term Work, Expanding and Factorizing Algebraic Expressions, Solving Quadratic Equations

Sub-topic: Expansion, Factorization, and Solution of Quadratic Equations

Duration: 40 minutes

Behavioural Objectives

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

1. Recall topics taught in the previous term.
2. Expand and factorize algebraic expressions.
3. Solve quadratic equations using different methods.

Keywords

• Expansion
• Factorization
• Quadratic Equations
• Distributive Property
• Common Factors
• Difference of Squares

Set Induction

The teacher writes a simple algebraic expression on the board and asks students to expand or factorize it. The teacher connects the activity to real-life applications, such as calculating areas of rectangles with algebraic side lengths.

Entry Behaviour

Students have been introduced to basic algebraic expressions and simple equations in previous classes.

Learning Resources and Materials

• Whiteboard or blackboard
• Markers or chalk
• Handouts with practice problems
• Calculators (optional)

Building Background / Connection to Prior Knowledge

• Students previously learned about algebraic expressions.
• They were introduced to simple factorization and expansion.
• They have solved basic equations.

Embedded Core Skills

• Critical thinking
• Problem-solving
• Analytical skills

Reference Books

• Lagos State Scheme of Work
• New General Mathematics for JSS 2
• Essential Mathematics for JSS 2

Instructional Materials

• Algebra charts
• Quadratic equation formula sheet

Content Development

1. Expanding Algebraic Expressions

Expanding algebraic expressions means multiplying out brackets and simplifying by combining like terms. The distributive property is used in this process.

Examples

1. (2x + 3)(x – 4) = 2x * x + 2x * (-4) + 3 * x + 3 * (-4) = 2x² – 5x – 12
2. 4(3y – 2) – 6y = 12y – 8 – 6y = 6y – 8
3. (x + 2)(x + 5) = x² + 7x + 10
4. 3a(2a – 4) = 6a² – 12a
5. (y – 6)(y + 3) = y² – 3y – 18

2. Factorizing Algebraic Expressions

Factorization is the process of expressing an algebraic expression as a product of its factors.

Examples

1. 6x² + 15x = 3x(2x + 5)
2. x² – 9 = (x + 3)(x – 3) [difference of squares]
3. x² + 5x + 6 = (x + 2)(x + 3) [trinomial factorization]
4. 2y² – 8y = 2y(y – 4)
5. a² – 16 = (a – 4)(a + 4)

3. Solving Quadratic Equations

A quadratic equation is an equation of the form ax² + bx + c = 0.

Methods of Solving Quadratic Equations

A. Factoring Method
Example: Solve x² – 5x + 6 = 0

• Factorize: (x – 2)(x – 3) = 0
• Solve: x – 2 = 0 or x – 3 = 0
• x = 2 or x = 3

B. Completing the Square Method
Example: Solve x² – 4x + 3 = 0

• Rewrite: (x² – 4x + 4) – 1 = 0
• (x – 2)² = 1
• x – 2 = ±1
• x = 1 or x = 3

C. Quadratic Formula Method
The quadratic formula: x = (-b ± √(b² – 4ac)) / 2a
Example: Solve x² – 4x + 3 = 0

• a = 1, b = -4, c = 3
• x = (4 ± √(16 – 12)) / 2
• x = (4 ± 2) / 2
• x = 3 or x = 1

Evaluation Questions

1. Expand (2x + 5)(x – 3).
2. Expand (x – 4)(x + 6).
3. Expand (3x + 2)(2x – 1).
4. Expand and simplify (x + 5)(x – 2).
5. Expand (y – 3)(y + 7).
6. Factorize x² – 6x + 9.
7. Factorize x² + 7x + 12.
8. Factorize 4x² – 9.
9. Solve x² – 8x + 15 = 0 using factorization.
10. Solve 2x² – 3x – 2 = 0 using the quadratic formula.

Class Activity Discussion – FAQs

1. What is expansion in algebra?
2. What does factorizing an expression mean?
3. What is a quadratic equation?
4. How do you solve quadratic equations using the factorization method?
5. How do you use the quadratic formula to solve equations?
6. What is the importance of factorization?
7. What is the difference between an expression and an equation?
8. How can algebra be applied in real life?
9. What happens if an equation cannot be factorized?
10. Why is the quadratic formula useful?

Assessment – Short Answer Questions

1. Expand (x + 3)(x – 2).
2. Expand and simplify (2x + 5)(x – 4).
3. Factorize x² – 10x + 25.
4. Factorize x² – 3x – 18.
5. Solve x² – 7x + 10 = 0 using the factorization method.
6. Solve 3x² – 5x – 2 = 0 using the quadratic formula.
7. What is the quadratic formula?

Conclusion

• Summarize key points.
• Encourage further practice.
• Mark students’ work and provide feedback.