Understanding Multiplication and Division of Fractions, Prime Numbers, and Factors Mathematics JSS 1 First Term Lesson Notes Week 9

Subject: Mathematics
Class: JSS 1
Term: First Term
Week: 9
Age: 12 years
Topic: Fractions Continued
Sub-topic: i. Multiplication and Division of Fractions ii. Prime Numbers and Factors
Duration: 40 minutes

Behavioural Objectives

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

1. Multiply and divide fractions.
2. Identify prime numbers and factors of given numbers.

Keywords

Multiplication, Division, Fractions, Prime Numbers, Factors

Set Induction

Start with a discussion on how fractions can be multiplied and divided, using visual aids such as fraction bars or pizzas. Introduce prime numbers and factors with examples like finding common factors of simple numbers.

Entry Behaviour

Students should be familiar with basic operations on fractions and understand the concept of factors and prime numbers.

Learning Resources and Materials

1. Fraction strips or visual aids
2. Whiteboard and markers
3. Worksheets with fraction problems
4. Prime number charts
5. Calculators

Building Background/Connection to Prior Knowledge

Students should recall previous lessons on fraction addition and subtraction and basic multiplication and division.

Embedded Core Skills

1. Numerical operations
2. Problem-solving
3. Critical thinking

Content

1. Multiplication of Fractions:
   • Multiply the numerators together and the denominators together.
   • Example: 2/5 × 3/4 = (2 × 3)/(5 × 4) = 6/20 = 3/10 (simplified).
2. Division of Fractions:
   • Multiply by the reciprocal of the second fraction.
   • Example: 3/4 ÷ 2/3 = 3/4 × 3/2 = (3 × 3)/(4 × 2) = 9/8 (or 1 1/8 as a mixed number).
3. Prime Numbers:
   • Numbers greater than 1 with exactly two factors: 1 and itself.
   • Examples: 2, 3, 5, 7, 11.
4. Factors:
   • Numbers that divide exactly into another number.
   • Example: Factors of 12 are 1, 2, 3, 4, 6, 12.

Evaluation

1. Multiply: 1/2 × 2/3.
2. Divide: 5/6 ÷ 1/3.
3. What is the result of 3/4 × 4/5?
4. Divide: 7/8 ÷ 2/3.
5. List the prime numbers between 1 and 15.

Class Activity Discussion

1. How do you multiply fractions?
   • Multiply the numerators and denominators.
2. What is the process for dividing fractions?
   • Multiply by the reciprocal of the divisor.
3. What is a prime number?
   • A number with exactly two factors: 1 and itself.
4. How do you find factors of a number?
   • List all numbers that divide evenly into the given number.
5. What is the reciprocal of a fraction?
   • Flip the numerator and denominator.
6. How do you simplify the product of fractions?
   • Multiply and then simplify the resulting fraction.
7. Why is division of fractions done using the reciprocal?
   • To convert division into multiplication, making it easier.
8. Can a number be both prime and a factor of another number?
   • Yes, if it divides evenly into another number.
9. What are the prime factors of 30?
   • 2, 3, and 5.
10. How do you handle improper fractions in multiplication or division?
    • Convert to mixed numbers or simplify after operations.
11. What is an example of multiplying fractions in real life?
    • Adjusting recipe quantities.
12. How do you divide fractions in a recipe problem?
    • Convert to multiplication by the reciprocal.
13. What are factors of 24?
    • 1, 2, 3, 4, 6, 8, 12, 24.
14. Find the prime numbers less than 20.
    • 2, 3, 5, 7, 11, 13, 17, 19.
15. How do you simplify 8/12 after division?
    • Divide numerator and denominator by their greatest common divisor.

Presentation

1. Step 1: Review multiplication and division of fractions with examples.
2. Step 2: Introduce prime numbers and factors with clear definitions and examples.
3. Step 3: Solve problems together, ensuring understanding of each concept.

Teacher’s Activities

1. Explain multiplication and division of fractions.
2. Teach about prime numbers and factors.
3. Provide examples and practice problems.

Learners’ Activities

1. Solve multiplication and division problems involving fractions.
2. Identify prime numbers and factors in given sets of numbers.
3. Discuss their answers and methods with the class.

Assessment

1. Review students’ answers for accuracy in fraction operations.
2. Check understanding of prime numbers and factors.

Evaluation Questions

1. Multiply: 4/7 × 2/5.
2. Divide: 9/10 ÷ 3/4.
3. What is 5/8 × 2/3?
4. Divide: 8/9 ÷ 4/5.
5. List the factors of 15.
6. Identify the prime numbers between 1 and 20.
7. What is the reciprocal of 3/4?
8. Simplify the fraction 12/15 after multiplication.
9. How do you find the prime factors of 18?
10. What is the product of 7/8 and 1/2?

Conclusion

The teacher will review student work, clarify any misunderstandings, and provide additional practice as needed.