H.C.F, Factor Method and Prime Factors for Primary 4

Class: Primary 4
Term: 1st Term
Week: 4
Age: 9 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: L.C.M, Finding LCM of Numbers Up to 60.
Topic: H. C. F
Subject Matter: HCF of 2-digit numbers, identifying HCF using multiplication table, finding HCF using prime factor method, finding HCF using long division method, practice questions on HCF.

Specific Objectives

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

Cognitive Domain:

• Define Highest Common Factor (HCF).
• Identify the HCF of two-digit numbers using a multiplication table.
• Find the HCF of given numbers using the prime factor method.
• Find the HCF of given numbers using the long division method.
• Solve practice questions on HCF.

Affective Domain:

• Show interest in finding the HCF of numbers.
• Appreciate the importance of HCF in solving mathematical problems.
• Collaborate with peers to solve HCF problems.

Psychomotor Domain:

• Accurately apply the steps for finding HCF using different methods.
• Present clear and correct solutions to HCF problems.

Social Domain:

• Work cooperatively with classmates during group activities.
• Ask questions to clarify any difficulties encountered.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary 4)
• State Unified Scheme of Work (Primary 4)
• New General Mathematics for Primary Schools 4
• https://www.education.gov.ng/curriculum
• https://www.oer.ng/maths-primary

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbooks
• Multiplication charts
• Whiteboard or chalkboard
• Markers or chalk
• Flashcards with numbers

Rationale for the Lesson

Understanding HCF is important because it helps pupils simplify fractions and solve problems involving sharing items into equal groups. This knowledge lays a foundation for more advanced mathematical concepts and real-life applications.

Prerequisite/Previous Knowledge

Pupils are assumed to have prior knowledge of factors, multiples, prime numbers, and basic multiplication and division.

Lesson Content/Board Summary

Highest Common Factor (HCF)

Definition of HCF

The Highest Common Factor (HCF) of two or more numbers is the largest number that divides exactly into all of them without leaving a remainder. It is also known as the Greatest Common Divisor (GCD).

Finding HCF using Multiplication Table (for 2-digit numbers)

This method involves listing all the factors of each number and then identifying the largest factor common to both. This is suitable for smaller numbers.

The steps are:

• List all the factors of the first number.
• List all the factors of the second number.
• Identify the common factors from both lists.
• The largest of these common factors is the HCF.

Example: 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
• The HCF of 12 and 18 is 6.

Finding HCF using Prime Factor Method

This method involves expressing each number as a product of its prime factors.

The steps are:

• Find the prime factors of each number.
• Write each number as a product of its prime factors.
• Identify the common prime factors.
• Multiply the common prime factors together to get the HCF.

Example: Find the HCF of 24 and 36.

• Prime factors of 24: 2 x 2 x 2 x 3
• Prime factors of 36: 2 x 2 x 3 x 3
• Common prime factors: 2, 2, 3
• HCF = 2 x 2 x 3 = 12

Finding HCF using Long Division Method

This method is particularly useful for larger numbers.

The steps are:

• Divide the larger number by the smaller number.
• Take the remainder and divide the previous divisor by it.
• Repeat the process until the remainder is zero.
• The last non-zero divisor is the HCF.

Example: Find the HCF of 30 and 42.

• 42 ÷ 30 = 1 remainder 12
• 30 ÷ 12 = 2 remainder 6
• 12 ÷ 6 = 2 remainder 0
• The last non-zero divisor is 6.
• Therefore, the HCF of 30 and 42 is 6.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews the previous lesson on factors and multiples. The teacher then introduces the topic HCF by asking pupils what they understand by “common factors” and “highest”.
Pupils’ Activity: Pupils respond to the teacher’s questions and listen attentively.
Learning Point: Pupils recall previous knowledge and are introduced to the new topic.

Step 2: Explanation of HCF and identification using multiplication table

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines HCF and demonstrates how to find the HCF of 2-digit numbers using a multiplication chart by listing factors and identifying the highest common factor (e.g., HCF of 12 and 18).
Pupils’ Activity: Pupils listen, observe the examples, and ask questions for clarity.
Learning Point: Pupils understand the definition of HCF and can identify it using the multiplication table for smaller numbers.

Step 3: Finding HCF using Prime Factor Method

Time: 10 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher explains the prime factor method for finding HCF. The teacher works through an example on the board (e.g., HCF of 24 and 36), guiding pupils through each step of finding prime factors and multiplying common ones.
Pupils’ Activity: Pupils pay attention, copy the example, and participate in identifying prime factors.
Learning Point: Pupils learn how to find HCF using the prime factor method.

Step 4: Finding HCF using Long Division Method

Time: 10 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher introduces the long division method for HCF, explaining its steps. The teacher demonstrates with an example (e.g., HCF of 30 and 42) on the board, showing how to divide and use remainders.
Pupils’ Activity: Pupils watch the demonstration, take notes, and ask questions.
Learning Point: Pupils learn how to find HCF using the long division method.

Step 5: Practice Questions

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher provides a few practice questions for pupils to attempt using the different methods learned. The teacher moves around the classroom to offer support and check pupils’ work.
Pupils’ Activity: Pupils solve the given questions individually or in pairs.
Learning Point: Pupils apply the learned methods to solve HCF problems.

Step 6: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is the Highest Common Factor (HCF) of two numbers?
2. Mention two methods for finding the HCF of numbers.
3. Find the HCF of 15 and 20 using the multiplication table.
4. Find the HCF of 18 and 24 using the prime factor method.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 7: Conclusion

Time: 0 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the different methods for finding HCF. The teacher assigns homework: Find the HCF of 45 and 60 using any two methods.
Pupils’ Activity: Pupils listen to the summary and copy the homework.
Learning Point: Pupils consolidate their understanding and apply it independently.

Home Task: Solve three new exercises on H. C. F. Show each step and check each answer.

Lesson Keywords

• HCF – Highest Common Factor, the largest number that divides exactly into two or more numbers.
• Factor – A number that divides another number exactly without leaving a remainder.
• Prime Factor – A factor that is also a prime number.
• Long Division Method – A systematic way to find HCF, especially for larger numbers, by repeatedly dividing remainders.
• Common Factor – A factor that two or more numbers share.

Differentiation

For pupils who grasp the concept quickly, the teacher can provide more challenging HCF problems involving three numbers. For pupils needing more support, the teacher will provide additional guided practice with simpler numbers and visual aids like factor trees or multiplication grids, and encourage peer tutoring.

Note for teachers using this lesson plan

Ensure pupils have a solid understanding of prime numbers and basic division before introducing the HCF methods. Encourage pupils to try different methods to deepen their understanding. Emphasize the real-life applications of HCF to make the lesson more relatable.