HomeJSS 2MathematicsIntroduction to Algebraic Fractions and Expansion – Complete Guide

Introduction to Algebraic Fractions and Expansion – Complete Guide

Lesson Plan: Algebraic Fractions – Introduction and Expansion of Algebraic Expressions

Subject: Mathematics

Class: JSS 2

Term: Second Term

Week: 6

Topic: Algebraic Fractions – Introduction and Expansion of Algebraic Expressions

Sub-topic: Understanding and Expanding Algebraic Fractions

Behavioral Objectives

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

  1. Define algebraic fractions.
  2. Identify examples of algebraic fractions.
  3. Expand algebraic expressions using distributive properties.
  4. Solve problems involving algebraic fractions.

Keywords

  • Algebraic Expression
  • Fraction
  • Variable
  • Numerator
  • Denominator
  • Expansion
  • Distributive Property

Set Induction (Lesson Introduction)

The teacher writes two fractions on the board: 1/2 and x/3, then asks:
“What is the difference between these two fractions?”
After the responses, the teacher explains that the second fraction is an algebraic fraction because it contains a variable.

Entry Behavior

Students have prior knowledge of basic fractions and algebraic expressions.

Learning Resources and Materials

  • Whiteboard and markers
  • Fraction charts
  • Algebraic expansion worksheets
  • Mathematics textbooks

Building Background/Connection to Prior Knowledge

  • Students have previously learned about fractions and algebraic expressions.
  • The teacher connects algebraic fractions to ordinary fractions by showing how they share similar rules.

Embedded Core Skills

  • Critical Thinking – Understanding and manipulating algebraic expressions.
  • Numeracy Skills – Simplifying algebraic fractions.
  • Problem-Solving – Expanding and simplifying algebraic expressions.

Learning Materials

Instructional Materials

  • Algebraic fraction charts
  • Practice worksheets
  • Graphing paper (optional)

Lesson Presentation

Step 1: Introduction to Algebraic Fractions

Teacher’s Activity:

  • Defines algebraic fractions as fractions where the numerator or denominator (or both) contain algebraic expressions.
  • Provides examples:
    • x2\frac{x}{2}, 3y5\frac{3y}{5}, a+b4\frac{a + b}{4}

Learner’s Activity:

  • Students give examples of algebraic fractions based on the definition.

Step 2: Expansion of Algebraic Expressions

Teacher’s Activity:

  • Introduces the distributive property to expand algebraic expressions.
  • Example: Expand 3(x + 2)
    • Solution: 3x + 6
  • Example: Expand 2(y – 4)
    • Solution: 2y – 8

Learner’s Activity:

  • Students practice expanding expressions like:
    • 4(a + 5)
    • 5(x – 3)
    • 2(3m + 7)

Step 3: Simplifying Algebraic Fractions

Teacher’s Activity:

  • Shows how to simplify algebraic fractions by dividing common terms.
  • Example: Simplify (4x² / 2x)
    • Solution: 2x
  • Example: Simplify (6a / 3a)
    • Solution: 2

Learner’s Activity:

  • Students simplify:
    • (8y² / 4y)
    • (10m / 5m)
    • (15x / 3x)

Step 4: Applying Algebraic Fractions in Problem-Solving

Teacher’s Activity:

  • Gives real-life examples where algebraic fractions are used, such as speed calculations and ratios.
  • Solves a problem:
    • “A car travels at a speed of x/4 km per hour. If it moves for 8 hours, find the total distance covered.”
    • Solution: 8 × (x/4) = 2x km

Learner’s Activity:

  • Students solve word problems involving algebraic fractions.

Evaluation Questions

  1. What is an algebraic fraction?
    a) A fraction with whole numbers only
    b) A fraction with algebraic terms in the numerator or denominator
    c) A fraction with decimal numbers
    d) A fraction with only one term

  2. Which of the following is an algebraic fraction?
    a) 3/4
    b) x/5
    c) 7
    d) 9.5

  3. Expand 4(x + 3).
    a) 4x + 12
    b) x + 12
    c) 4x + 3
    d) 4x + 6

  4. Expand 5(y – 2).
    a) 5y + 2
    b) 5y – 10
    c) y – 10
    d) 5y – 2

  5. Simplify (6x / 3).
    a) 2x
    b) x/2
    c) 6
    d) 3x

  6. Which of these is the correct expansion of 2(3a + 4)?
    a) 6a + 4
    b) 3a + 8
    c) 6a + 8
    d) 2a + 8

  7. What is the solution for 10m/5m?
    a) 5m
    b) 2
    c) 10
    d) m/2

  8. What is the expansion of 7(x – 5)?
    a) 7x – 35
    b) 7x + 5
    c) x – 35
    d) 7x + 35

  9. Expand 3(a + b).
    a) 3a + b
    b) a + 3b
    c) 3a + 3b
    d) 3(a + b)

  10. Which property is used to expand algebraic expressions?
    a) Commutative Property
    b) Associative Property
    c) Distributive Property
    d) Identity Property

Class Activity Discussion – FAQs

  1. What is an algebraic fraction?
    An algebraic fraction is a fraction where at least one part (numerator or denominator) contains a variable.

  2. How do you expand algebraic expressions?
    Use the distributive property to multiply each term inside the bracket by the outside term.

  3. Why do we simplify algebraic fractions?
    To make calculations easier and more understandable.

  4. What is the difference between an algebraic fraction and a normal fraction?
    A normal fraction has only numbers, while an algebraic fraction contains variables.

  5. How do you simplify (4x² / 2x)?
    Divide both terms by 2x to get 2x.

Assessment – Short Answer Questions

  1. Define an algebraic fraction.
  2. Expand 6(x + 2).
  3. Simplify (9a / 3a).
  4. What is the expansion of 2(4b + 5)?
  5. Solve: If a bus moves at a speed of x/5 km per hour for 10 hours, find the total distance.
  6. Expand 3(y – 7).
  7. Simplify (12x² / 4x).

Conclusion

The teacher summarizes key points on algebraic fractions and their expansion. Students complete additional practice problems as homework.

Tags: