HomeJSS 2MathematicsWord Problems on Algebraic Fractions – JSS 2 Mathematics Lesson Plan

Word Problems on Algebraic Fractions – JSS 2 Mathematics Lesson Plan

MATHEMATICS LESSON PLAN FOR JSS 2 – WEEK 2

Topic: Word Problems on Algebraic Fractions

Lesson Plan Structure

1. General Information

  • Subject: Mathematics
  • Class: JSS 2
  • Term: Second Term
  • Week: 2
  • Age: 11 – 13 years
  • Topic: Word Problems on Algebraic Fractions
  • Sub-topic: Solving real-life problems involving algebraic fractions
  • Duration: 40 minutes

2. Behavioural Objectives

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

  1. Define and explain algebraic fractions.
  2. Solve word problems involving algebraic fractions.
  3. Apply the concepts of addition, subtraction, multiplication, and division in algebraic fractions to solve real-life problems.
  4. Interpret algebraic fraction problems and represent them mathematically.

3. Keywords

  • Algebraic fraction
  • Numerator
  • Denominator
  • Simplification
  • Lowest common denominator (LCD)

4. Set Induction (5 minutes)

  • The teacher asks students to recall what they learned about algebraic fractions in the previous term.
  • The teacher presents a simple real-life problem: “If John eats 1/3 of a cake and Peter eats 1/4 of the same cake, how much of the cake is left?”
  • The teacher leads students to discuss how fractions are used in daily activities.

5. Entry Behaviour

Students should have prior knowledge of:

  • Basic fractions (addition, subtraction, multiplication, and division).
  • Algebraic expressions.
  • Finding the least common denominator (LCD).

6. Learning Resources and Materials

  • Whiteboard and markers
  • Chart showing examples of algebraic fractions
  • Flashcards with word problems
  • Handouts with practice exercises

7. Building Background/Connection to Prior Knowledge

  • The teacher reminds students about basic fractions.
  • The teacher explains how fractions appear in everyday activities, such as sharing food, measuring distances, and dividing money.
  • The teacher connects fractions to algebraic fractions by replacing numbers with variables.

8. Embedded Core Skills

  • Critical thinking
  • Problem-solving
  • Analytical skills
  • Communication skills

9. Learning Materials

  • Lagos State Scheme of Work
  • Mathematics textbook for JSS 2

10. Instructional Materials

  • Worked examples on flashcards
  • Charts with step-by-step solutions

11. Lesson Content

Definition of Algebraic Fractions

An algebraic fraction is a fraction in which the numerator, denominator, or both contain algebraic expressions (letters and numbers).

Examples of Algebraic Fractions

  1. x/3
  2. (2y + 1)/(y – 4)
  3. (3x – 2)/(x² + x – 6)

Solving Word Problems on Algebraic Fractions

When solving word problems, follow these steps:

  1. Identify the key information in the question.
  2. Write an algebraic fraction equation.
  3. Simplify the fractions if necessary.
  4. Solve for the unknown variable.
  5. Interpret the solution in relation to the problem.

Examples of Word Problems on Algebraic Fractions

Example 1:
Ade spent 1/5 of his salary on transport, 1/4 on feeding, and 1/10 on savings. What fraction of his salary is left?

Solution:
Total spent = 1/5 + 1/4 + 1/10
Find the LCD of 5, 4, and 10, which is 20.
Convert each fraction:

  • 1/5 = 4/20
  • 1/4 = 5/20
  • 1/10 = 2/20

Total spent = (4/20) + (5/20) + (2/20) = 11/20
Remaining fraction = 1 – 11/20 = 9/20

Answer: Ade has 9/20 of his salary left.

12. Evaluation Questions (15 Questions, Multiple Choice)

  1. An algebraic fraction is a fraction that contains ______.
    a) Only numbers
    b) Only letters
    c) Letters and numbers
    d) Only symbols

  2. What is the sum of 1/x + 2/x?
    a) 1/x
    b) 2/x
    c) 3/x
    d) 4/x

  3. If 2/x + 3/y = 5, what is the LCD of the fractions?
    a) xy
    b) x + y
    c) x – y
    d) x/y

  4. What is the LCD of 1/2, 1/3, and 1/4?
    a) 6
    b) 8
    c) 12
    d) 24

  5. Solve: (3/x) – (2/x) = ?
    a) 1/x
    b) 5/x
    c) (3 – 2)/x
    d) 3x – 2x

  6. Which of the following is an algebraic fraction?
    a) x + 3
    b) 3/x
    c) 5
    d) x² + 2x + 3

  7. What is the value of x in (x/3) + (x/4) = 7?
    a) 12
    b) 21
    c) 36
    d) 42

  8. Express 5/(x + 3) – 2/(x + 3) as a single fraction.
    a) 3/(x + 3)
    b) (5 – 2)/(x + 3)
    c) (2 – 5)/(x + 3)
    d) 7/(x + 3)

  9. Find the sum of (2x/3) + (4x/5).
    a) 10x/15
    b) 22x/15
    c) 6x/8
    d) 10x/8

  10. Simplify: (x² – 9)/(x + 3).
    a) x – 3
    b) x + 3
    c) (x – 3)(x + 3)/(x + 3)
    d) x – 3 (incorrect cancellation)

  11. If 3/(x + 1) = 5/(x – 2), find x.
    a) x = 3
    b) x = 5
    c) x = -1
    d) x = 2

  12. Solve (x + 2)/4 = 3/8.
    a) x = 2
    b) x = 4
    c) x = 6
    d) x = 8

  13. Find the value of y in (y/3) – (y/6) = 2.
    a) y = 6
    b) y = 12
    c) y = 18
    d) y = 24

  14. Solve: (3x + 1)/(x – 2) = 2.
    a) x = 1
    b) x = 2
    c) x = 3
    d) x = 5

  15. If (x + 5)/4 = (x – 2)/3, find x.
    a) x = 7
    b) x = 8
    c) x = 9
    d) x = 10

13. Class Activity Discussion – FAQs (15 Questions with Answers)

  1. What is an algebraic fraction?

    • An algebraic fraction is a fraction where the numerator or denominator (or both) contains algebraic expressions.

  2. How do you simplify algebraic fractions?

    • Factorize if possible, cancel out common factors, and simplify the expression.

  3. Why do we find the least common denominator (LCD) when solving algebraic fraction equations?

    • We find the LCD to make the denominators the same, which allows us to add or subtract the fractions easily.

  4. How do we solve word problems involving algebraic fractions?

    • Identify the variables, write the equation, simplify the fractions, solve for the unknown, and interpret the answer.

  5. Can algebraic fractions have negative exponents?

    • Yes, but negative exponents should be rewritten as positive by taking the reciprocal of the term.

  6. What is the difference between an algebraic fraction and a numerical fraction?

    • A numerical fraction has only numbers, while an algebraic fraction contains variables (letters).

  7. How do we multiply algebraic fractions?

    • Multiply the numerators together and the denominators together, then simplify if possible.

  8. How do we divide algebraic fractions?

    • Multiply by the reciprocal of the divisor (flip the second fraction and multiply).

  9. Why do we factor algebraic fractions before simplifying?

    • Factoring helps us identify common terms that can be canceled out to simplify the fraction.

  10. What should we do when the denominator contains a binomial?

    • If possible, factor the denominator and check if common terms can be canceled.

  11. How do we check if our answer is correct in algebraic fractions?

    • Substitute the value of the variable into the original equation to verify the result.

  12. Can an algebraic fraction be equal to zero?

    • Yes, if the numerator is zero and the denominator is nonzero.

  13. What happens if the denominator of an algebraic fraction is zero?

    • The fraction is undefined because division by zero is not possible.

  14. How do we solve complex algebraic fraction equations?

    • Use the LCD to clear the fractions, then solve the resulting algebraic equation.

  15. Why is algebraic fraction important in real life?

    • Algebraic fractions are used in calculations involving ratios, proportions, and problem-solving in science and finance.

14. Presentation Structure

Teacher’s Activities

  1. Revises previous topics on fractions.
  2. Introduces algebraic fractions with real-life examples.
  3. Demonstrates how to solve word problems step by step.
  4. Guides students in solving practice problems.
  5. Provides corrections and feedback.

Learners’ Activities

  1. Answer oral questions on basic fractions.
  2. Follow step-by-step examples on the board.
  3. Solve given problems individually or in groups.
  4. Participate in class discussions.

15. Assessment – Short Answer Questions (10 Questions)

  1. Define an algebraic fraction.
  2. Solve (3/x) + (2/y) = ?
  3. If 1/3 of a cake is eaten and 1/4 is given away, how much is left?
  4. Solve (x + 3)/4 = 5/8.
  5. Simplify (2x – 4)/(x – 2).
  6. What is the LCD of 1/x and 1/y?
  7. Express 5/(x – 3) + 2/(x – 3) as a single fraction.
  8. A man gave away 1/2 of his land and sold 1/4. How much land remains?
  9. Find the value of x in (x/3) + (x/5) = 8.
  10. A student spends 1/6 of his allowance on books and 1/3 on food. What fraction is left?

  11. If (3/x) + (5/x) = 4, find x.

  12. Solve: (x + 1)/2 = (x – 3)/3.

  13. Find the missing fraction: (2/x) + (4/x) = ?

  14. A trader spends 1/5 of his profit on rent and 1/10 on transport. What fraction of his profit is left?

  15. Simplify: (x² – 16)/(x – 4).

  16. Express (3/x) – (1/x) as a single fraction.

  17. If (x/2) + (x/3) = 5, find x.

16. Conclusion

  • The teacher summarizes key points on algebraic fractions.
  • The teacher encourages students to practice similar word problems at home.
  • The teacher gives a short homework assignment on algebraic fractions.
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