HomePrimary 4MathematicsHighest Common Factor (H.C.F.) Mathematics Primary 4 First Term Lesson Notes Week 11

Highest Common Factor (H.C.F.) Mathematics Primary 4 First Term Lesson Notes Week 11

Mathematics Primary 4 First Term Lesson Notes Week 11 Lesson Plan:

Understanding Highest Common Factor (H.C.F.)

Subject: Mathematics
Class: Primary 4
Term: First Term
Week: 11
Age: 9 years
Topic: Highest Common Factor (H.C.F.)
Sub-topic: H.C.F. of Numbers
Duration: 1 hour

Behavioural Objectives:

  • Pupils will be able to identify factors of numbers from 1 to 99.
  • Pupils will find the H.C.F. of two or more numbers.
  • Pupils will apply H.C.F. to solve real-life problems and quantitative reasoning.

Keywords: Highest Common Factor, Common Factors, H.C.F., Quantitative Reasoning

Set Induction:

  • Start by asking pupils if they have ever shared objects evenly, such as candies or toys, and discuss how H.C.F. helps find the largest number of items each person can receive.

Entry Behaviour:

  • Review the concept of factors and how they divide a number evenly.

Learning Resources and Materials:

  • Number charts
  • Whiteboard and markers
  • Worksheets with H.C.F. problems
  • Counters or manipulatives for hands-on practice

Building Background/Connection to Prior Knowledge:

  • Connect to prior knowledge of multiplication and division, emphasizing how factors are numbers that divide another number exactly.

Embedded Core Skills:

  • Problem-solving
  • Critical thinking
  • Mathematical reasoning

Learning Materials:

  • Number charts
  • Worksheets
  • Counters

Reference Books:

  • Lagos State Scheme of Work
  • Primary Mathematics Textbook

Instructional Materials:

  • Whiteboard and markers
  • Flashcards with numbers

Content:

  1. Introduction to H.C.F.:
    • Define H.C.F. as the largest number that divides two or more numbers exactly.
  2. Finding H.C.F.:
    • Listing Factors Method: List all factors of each number and find the greatest common one.
    • Prime Factorization Method: Break each number into its prime factors, then identify the common factors and multiply them.
    • Common Divisor Method: Identify and divide by the highest common number that divides all given numbers.
  3. Real-Life Applications:
    • Track races: Determine the maximum number of laps each runner can complete together.
    • Traffic lights: Find the greatest interval at which different lights will synchronize.

Evaluation:

  1. The H.C.F. of 12 and 18 is _____. (a) 6 (b) 9 (c) 12 (d) 3
  2. Find the H.C.F. of 8 and 14. (a) 2 (b) 4 (c) 7 (d) 1
  3. What is the H.C.F. of 15 and 25? (a) 5 (b) 10 (c) 15 (d) 25
  4. The H.C.F. of 20 and 30 is _____. (a) 10 (b) 5 (c) 15 (d) 20
  5. Find the H.C.F. of 24 and 36. (a) 12 (b) 18 (c) 6 (d) 24
  6. The H.C.F. of 45 and 60 is _____. (a) 15 (b) 30 (c) 20 (d) 10
  7. What is the H.C.F. of 50 and 75? (a) 25 (b) 15 (c) 10 (d) 5
  8. The H.C.F. of 9 and 27 is _____. (a) 9 (b) 3 (c) 18 (d) 27
  9. Find the H.C.F. of 14 and 21. (a) 7 (b) 14 (c) 21 (d) 1
  10. The H.C.F. of 22 and 44 is _____. (a) 22 (b) 11 (c) 44 (d) 2
  11. What is the H.C.F. of 30 and 45? (a) 15 (b) 30 (c) 45 (d) 5
  12. Find the H.C.F. of 12 and 28. (a) 4 (b) 2 (c) 12 (d) 6
  13. The H.C.F. of 50 and 100 is _____. (a) 50 (b) 25 (c) 10 (d) 5
  14. What is the H.C.F. of 16 and 24? (a) 8 (b) 16 (c) 24 (d) 4
  15. The H.C.F. of 18 and 27 is _____. (a) 9 (b) 6 (c) 18 (d) 27

Class Activity Discussion:

  1. How do you find the H.C.F. of 20 and 30? (Answer: List factors or use prime factorization.)
  2. Why is it important to know the H.C.F. in daily life? (Answer: Helps with evenly dividing items or schedules.)
  3. How can you use H.C.F. to solve problems with track races? (Answer: Determine the largest number of laps or sections that fit evenly.)
  4. Explain how H.C.F. helps in synchronizing traffic lights. (Answer: Find the largest common interval for the lights to change together.)
  5. How would you find the H.C.F. of 28 and 42? (Answer: List factors or use prime factorization.)

Presentation:

  1. Step 1: Review the concept of factors and how to list them.
  2. Step 2: Introduce H.C.F. and demonstrate methods to find it.
  3. Step 3: Facilitate hands-on practice and real-life problem-solving using H.C.F.

Teacher’s Activities:

  • Explain H.C.F.: Use visual aids and examples to show how to find the H.C.F.
  • Facilitate Practice: Guide pupils through exercises and real-life problems involving H.C.F.
  • Monitor Progress: Check pupils’ understanding and provide feedback.

Highest Common Factor (H.C.F.)

Grade 4

Topic: Highest Common Factor (H.C.F.)

1. What is the Highest Common Factor (H.C.F.)?

Definition:

  • The Highest Common Factor (H.C.F.), also known as the Greatest Common Divisor (G.C.D.), is the largest number that can exactly divide two or more numbers without leaving a remainder.

Example:

  • For 12 and 15, the factors are:
    • 12: 1, 2, 3, 4, 6, 12
    • 15: 1, 3, 5, 15
    • The common factors are 1 and 3. The largest common factor is 3. So, the H.C.F. of 12 and 15 is 3.

2. Writing Factors of Numbers from 1 to 99

Steps:

  1. Identify Factors:
    • Factors of 18: 1, 2, 3, 6, 9, 18
    • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Practice Problems:

  • List the factors of 20.
  • List the factors of 30.

3. Identifying Common Factors of Two Numbers

Steps:

  1. Find Factors:
    • For 24: 1, 2, 3, 4, 6, 8, 12, 24
    • For 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  2. Identify Common Factors:
    • Common factors of 24 and 36 are 1, 2, 3, 4, 6, 12
    • H.C.F.: 12

Practice Problems:

  • Find the H.C.F. of 30 and 45.
  • Find the H.C.F. of 56 and 72.

4. Solving Quantitative Problems Related to H.C.F.

Example 1:

  • Problem: Two ropes are 36 meters and 60 meters long. What is the longest length of rope that can be used to cut both ropes into equal pieces?
    • Solution: Find the H.C.F. of 36 and 60.
      • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
      • Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
      • Common Factors: 1, 2, 3, 4, 6, 12
      • H.C.F.: 12

Example 2:

  • Problem: Two numbers have an H.C.F. of 8 and their least common multiple (L.C.M.) is 72. If one number is 24, find the other number.
    • Solution: Use the formula: H.C.F. × L.C.M. = Product of the Numbers
      • 8 × 72 = 24 × Other Number
      • 576 = 24 × Other Number
      • Other Number = 576 ÷ 24
      • Other Number = 24

Practice Problems:

  • The H.C.F. of 18 and 27 is:
    • a) 3
    • b) 6
    • c) 9
  • Find the H.C.F. of 48 and 60.
    • a) 12
    • b) 15
    • c) 18

5. Importance of H.C.F.

  • Track Races: Helps in finding the longest lap length that can evenly fit into different track lengths.
  • Traffic Lights: Helps in determining the longest interval when traffic lights will change together.

Summary:

  • H.C.F. is useful for finding the largest number that divides two or more numbers.
  • Practice: Helps in solving real-life problems related to equal distribution and dividing items fairly.

Practice Questions:

  1. Find the H.C.F. of 20 and 30.
    • a) 5
    • b) 10
    • c) 15
  2. The H.C.F. of 36 and 48 is:
    • a) 6
    • b) 12
    • c) 18
  3. If two numbers are 45 and 75, what is their H.C.F.?
    • a) 5
    • b) 15
    • c) 25

Learners’ Activities:

  • Practice Exercises: Solve problems involving H.C.F. individually and in groups.
  • Real-Life Application: Discuss and solve practical problems using H.C.F.

Assessment:

  • Evaluate Work: Review pupils’ answers and understanding of H.C.F. through exercises and discussions.
  • Apply Knowledge: Assess ability to solve real-life problems using H.C.F.

Conclusion:

  • Review Concepts: Summarize key points about H.C.F. and its applications.
  • Provide Feedback: Mark pupils’ work, offer guidance, and ensure understanding of the lesson.

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