Highest Common Factor HCF Mathematics Primary 5

Lesson Plan Presentation

Subject: Mathematics
Class: Primary 5
Term: Second Term
Week: 2
Topic: HCF – The Use of Prime Factors
Duration: 45 minutes

Entry Behaviour:
Recall previous knowledge of factors and prime numbers.

Key Words:
HCF, Prime factors, Factors, Numbers.

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

Define HCF and understand its importance.
Use prime factors to find the HCF of given numbers.

Embedded Core Skills:
Critical thinking, problem-solving, and number sense.

Learning Materials:
Chalkboard, chalk, worksheets, prime factor charts.

Content:

Factors and Prime Numbers:

Factors: Factors are numbers that divide another number without leaving a remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12.
Prime Numbers: Prime numbers have only two factors: 1 and the number itself. For example, 2, 3, 5, and 7 are prime numbers.

Introduction to HCF:

HCF (Highest Common Factor): HCF is the largest number that divides two or more numbers without leaving a remainder.
Significance: HCF is crucial in simplifying fractions and solving various mathematical problems efficiently.

Defining HCF:

HCF as Highest Common Factor: HCF is an acronym for the Highest Common Factor. It represents the largest number that is a factor of two or more given numbers.

Relevance in Simplifying Fractions:

Simplifying Fractions: HCF helps simplify fractions by dividing both the numerator and denominator by their common factor, making the fraction smaller without changing its value.

Illustrating the Concept with Examples:

Example 1: Find the HCF of 12 and 18.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6
- HCF = 6
Example 2: Simplify the fraction 24/36 using HCF.
- Prime factors of 24: 2^3 * 3
- Prime factors of 36: 2^2 * 3^2
- Common factors: 2^2 * 3 = 12
- Simplified fraction: 24/36 = (24 ÷ 12) / (36 ÷ 12) = 2/3

Through these examples, students can grasp the concept of HCF and its practical application in simplifying fractions.

Factors are numbers that ______ another number without leaving a remainder.
- a. Add
- b. Multiply
- c. Divide
- d. Subtract
Prime numbers have ______ factors.
- a. One
- b. Two
- c. Three
- d. Four
HCF stands for ______.
- a. Highly Common Fraction
- b. Highest Common Factor
- c. High Calculated Figure
- d. Hyper Complex Formula
HCF is crucial in ______ fractions.
- a. Adding
- b. Simplifying
- c. Multiplying
- d. Dividing
The Largest number that divides two or more given numbers without leaving a remainder is called ______.
- a. Lowest Common Multiple
- b. Highest Common Factor
- c. Greatest Common Denominator
- d. Basic Common Divisor
Simplifying fractions using HCF involves dividing both ______ by their common factor.
- a. Numerator and denominator
- b. Denominator and numerator
- c. Only numerator
- d. Only denominator
Example 1: Find the HCF of 15 and 20. Common factors: 1, 5. HCF = ______.
- a. 1
- b. 5
- c. 10
- d. 15
Example 2: Simplify the fraction 48/72 using HCF. Common factors: 2^3 * 3 = ______.
- a. 6
- b. 12
- c. 24
- d. 48
The relevance of HCF in solving problems efficiently is because it finds the ______ common to given numbers.
- a. Smallest factor
- b. Largest factor
- c. Least common multiple
- d. Greatest common multiple
In finding the HCF of 30 and 45, if the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30, and the factors of 45 are 1, 3, 5, 9, 15, 45, the common factors are ______.
- a. 1, 2, 3, 5
- b. 1, 3, 5, 15
- c. 1, 3, 5
- d. 1, 3, 5, 9
In simplifying the fraction 36/54 using HCF, the simplified fraction is ______.
- a. 2/3
- b. 3/2
- c. 4/5
- d. 5/4
The concept of HCF is particularly useful in ______ fractions into their simplest form.
- a. Complicating
- b. Simplifying
- c. Expanding
- d. Multiplying
Example 3: Find the HCF of 24 and 32. Common factors: 1, 2, 4, 8. HCF = ______.
- a. 2
- b. 4
- c. 8
- d. 16
The primary importance of HCF lies in its ability to simplify fractions and make them ______.
- a. Larger
- b. Smaller
- c. More complicated
- d. Stay the same
Example 4: Simplify the fraction 60/90 using HCF. Common factors: 2 * 3^2. Simplified fraction: ______.
- a. 2/3
- b. 3/2
- c. 4/5
- d. 5/4

Presentation

Step 1: Introduction (5 min)

Briefly discuss factors and prime numbers.
Introduce the concept of HCF and its significance in mathematics.
Example 1:
Find the HCF of 28, 42, and 90.
1. Prime factors:
  - 28: 2*2 * 7
  - 42: 2 * 3 * 7
  - 90: 2 * 3*3 * 5
  - HCF = 2
2. Common prime factors:
  - Identify the common prime factors: 2
3. Multiply the common prime factors:
  - HCF = 2
Example 2:
Find the HCF of 14, 56, and 70.
1. Prime factors:
  - 14: 2 * 7
  - 56: 2*2*2 * 7
  - 70: 2 * 5 * 7
2. Common prime factors:
  - Identify the common prime factors: 2 and 7.
3. Multiply the common prime factors:
  - HCF = 2 * 7 = 14
Example 3:
Find the HCF of 32, 60, and 76.
1. Prime factors:
  - 32: 2^5 (Two raised to power 5 times five)
  - 60: 2^2 * 3 * 5 (2 raised to power 2 times 3 times 4)
  - 76: 2^2 * 19 (Two raised to power 2 times 19)
2. Common prime factors:
  - Identify the common prime factors: 2^2.
3. Multiply the common prime factors:
  - HCF = 2^2 = 4
Encourage pupils to follow these steps for other examples, emphasizing the importance of identifying and multiplying the common prime factors to find the HCF.

Step 2: Understanding HCF (10 min)

Define HCF as the Highest Common Factor.
Explain its relevance in simplifying fractions and solving problems.
Use simple examples to illustrate the concept.

Step 3: Prime Factorization (15 min)

Teacher’s Activities:

Teach the prime factorization method.
Demonstrate finding prime factors for a few numbers.
Show how to use prime factors to identify the HCF.

Learners Activities:

Engage students in finding prime factors of given numbers.
1. Find the HCF of 18, 24, and 36.
  - a. 4
  - b. 6
  - c. 8
  - d. 12
2. Calculate the HCF of 15, 25, and 35.
  - a. 3
  - b. 5
  - c. 7
  - d. 15
3. Determine the HCF of 48, 72, and 96.
  - a. 8
  - b. 12
  - c. 16
  - d. 24
4. What is the HCF of 27, 45, and 63?
  - a. 3
  - b. 9
  - c. 15
  - d. 27
5. Find the HCF of 60, 90, and 120.
  - a. 15
  - b. 20
  - c. 30
  - d. 40
6. Calculate the HCF of 16, 24, and 32.
  - a. 4
  - b. 6
  - c. 8
  - d. 16
7. Determine the HCF of 36, 54, and 72.
  - a. 6
  - b. 9
  - c. 18
  - d. 27
8. What is the HCF of 20, 30, and 40?
  - a. 5
  - b. 10
  - c. 20
  - d. 40
9. Find the HCF of 80, 120, and 160.
  - a. 20
  - b. 40
  - c. 80
  - d. 120
10. Calculate the HCF of 22, 33, and 44.
- a. 2
- b. 4
- c. 11
- d. 22
1. Determine the HCF of 28, 35, and 42.
- a. 7
- b. 14
- c. 21
- d. 28
1. What is the HCF of 54, 81, and 108?
- a. 9
- b. 18
- c. 27
- d. 54
1. Find the HCF of 63, 105, and 126.
- a. 7
- b. 9
- c. 21
- d. 63
1. Calculate the HCF of 30, 50, and 70.
- a. 5
- b. 10
- c. 20
- d. 30
1. Determine the HCF of 45, 75, and 90.
- a. 15
- b. 30
- c. 45
- d. 75
Practice identifying the HCF using prime factors.
Work on exercises individually and in groups.

Assessment:

Observe students’ participation in prime factorization activities.
Check accuracy in identifying the HCF using prime factors.

Evaluation:

What does HCF stand for?
Why is finding the HCF important in mathematics?
Explain the concept of prime factors.
How do you find the prime factors of a number?
Define a prime number.
If the prime factors of 24 are 2, 2, 2, and 3, what is the HCF of 24?
Find the prime factors of 36.
What is the HCF of 45 and 60 using prime factors?
How does HCF help in simplifying fractions?
Apply prime factorization to find the HCF of 28 and 42.

Conclusion:

Summarize the key points covered in the lesson.
Assign practice exercises for homework.
Address any questions or concerns from the students.

Tags:FIRST TERM LESSON NOTE, MATHEMATICS, Primary 6

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