Lesson Notes By Weeks and Term v3 - Primary 4
HCF
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HCF
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Subject: General Mathematics
Class: Primary 4
Term: 1st Term
Week: 3
Theme: Numbers And Numeration
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Watch on YouTubeSee Facebook postThis topic introduces the concept of the Highest Common Factor (HCF) of numbers, building upon students' prior knowledge of factors and multiplication. Understanding HCF is fundamental for developing number sense and is a prerequisite for more advanced mathematical concepts such as fractions (simplification). In the Nigerian context, HCF has practical applications in daily life, such as fair distribution of resources, planning group activities, or arranging items efficiently.
Specific Performance Objectives:
This section provides the foundational knowledge and step-by-step methodology for teaching HCF of 2-digit numbers. 2.
1. Factors Definition: A factor of a number is a number that divides it exactly, leaving no remainder. In other words, when you multiply two whole numbers to get a product, both numbers are factors of that product.
Example: To find the factors of 12: 1 x 12 = 12 (1 and 12 are factors) 2 x 6 = 12 (2 and 6 are factors) 3 x 4 = 12 (3 and 4 are factors) The factors of 12 are 1, 2, 3, 4, 6, and
1
2. Key points for teachers: Every number has 1 and itself as factors. Factors are always less than or equal to the number itself. Students should be encouraged to list factors systematically (e.g., starting from 1 and pairing them up). 2.
2. Common Factors Definition: Common factors are the factors that two or more numbers share. They are the numbers that appear in the list of factors for each of the given numbers.
Example: Find the common factors of 12 and
1
8. Factors of 12: {1, 2, 3, 4, 6, 12} Factors of 18: {1, 2, 3, 6, 9, 18} Comparing the lists, the numbers that appear in both are 1, 2, 3, and
6. Therefore, the common factors of 12 and 18 are 1, 2, 3, and 6. 2.
3. Highest Common Factor (HCF)
Definition: The Highest Common Factor (HCF) is the largest number among the common factors of two or more numbers. It is sometimes referred to as the Greatest Common Divisor (GCD). Methodology for Finding HCF of 2-digit Numbers: Step 1: List all factors for each of the given numbers.
Step 2: Identify the common factors by comparing the lists of factors.
Step 3: Select the highest (largest) number from the common factors.
Worked Example 1: Find the HCF of 24 and
3
6. Step 1: List the factors of each number.
Factors of 24: 1 x 24 = 24 2 x 12 = 24 3 x 8 = 24 4 x 6 = 24 Factors of 24: {1, 2, 3, 4, 6, 8, 12, 24} Factors of 36: 1 x 36 = 36 2 x 18 = 36 3 x 12 = 36 4 x 9 = 36 6 x 6 = 36 Factors of 36: {1, 2, 3, 4, 6, 9, 12, 18, 36} Step 2: Identify the common factors. Common factors of 24 and 36 are the numbers present in both lists: {1, 2, 3, 4, 6, 12} Step 3: Select the highest common factor. From the common factors {1, 2, 3, 4, 6, 12}, the highest number is
1
2. Therefore, the HCF of 24 and 36 is
1
2. Worked Example 2: Find the HCF of 30 and
4
5. Step 1: List the factors of each number.
Factors of 30: {1, 2, 3, 5, 6, 10, 15, 30} Factors of 45: {1, 3, 5, 9, 15, 45} Step 2: Identify the common factors.
Common factors of 30 and 45 are: {1, 3, 5, 15} Step 3: Select the highest common factor. The highest number from the common factors is
1
5. Therefore, the HCF of 30 and 45 is
1
5. This section outlines practical activities for lesson delivery in a Nigerian classroom. 3.
1. Introduction (5 minutes)
Teacher Activity: Begin by reviewing multiplication facts and the concept of 'factors'. Ask students to recall what factors are. Pose simple questions like, "What numbers can divide 10 exactly?" or "List the factors of 8." Student Activity: Students respond to questions, listing factors of small numbers (e.g., 6, 10, 15). 3.
2. Presentation of New Concept (15 minutes)
Teacher Activity: Introduce the term "Common Factors." Write two 2-digit numbers on the board (e.g., 12 and 18). Guide students to list factors for each number. (e.g., "Let's find the factors of 12 together: 1, 2, 3, 4, 6,
1
2. Now, factors of 18: 1, 2, 3, 6, 9, 18."). Using visual aids (e.g., drawing circles or highlighting), identify factors common to both lists. (e.g., 1, 2, 3, 6). Introduce the term "Highest Common Factor (HCF)" and explain that it is the largest number among the common factors. Point to '6' as the HCF in the example of 12 and
1
8. Demonstrate another example (e.g., HCF of 20 and 30) step-by-step on the board, verbalizing each stage: listing factors, identifying common factors, selecting the highest.
Student Activity: Students actively participate in listing factors for the numbers given by the teacher. They observe and identify common factors as guided by the teacher. Students listen attentively to the explanation of HCF and follow the step-by-step demonstration. 3.
3. Activity 1: Group Factor Listing (10 minutes)
Teacher Activity: Divide the class into small groups (e.g., 4-5 students per group). Assign each group two different 2-digit numbers (e.g., Group A: 16 and 24; Group B: 28 and 42; Group C: 15 and 25).
Instruct each group to: List all the factors for their first number. List all the factors for their second number. Identify the common factors. Monitor group work, provide guidance, and correct misconceptions.
Student Activity: In their groups, students collaboratively list factors for their assigned numbers. They discuss and agree on the common factors. A group representative records their findings. 3.
4. Activity 2: Determining HCF (10 minutes)
Teacher Activity: Call on each group to present their findings from Activity
1. After they present their common factors, ask them to identify the HCF. Guide the class to confirm if their answers are correct. Emphasize the importance of finding all factors first.
Student Activity: Group representatives present their factors and common factors. Students collectively identify the HCF from their common factors. The class participates in peer-checking and discussion of the results. 3.
5. Consolidation and Wrap-up (5 minutes)
Teacher Activity: Recap the steps to find the HCF: (1) Find all factors of each number, (2) List the common factors, (3) Pick the highest common factor. Ask quick questions to check understanding (e.g., "What is the biggest common factor of 10 and 15?").
Student Activity: Students answer questions and participate in a brief review of the day's lesson. The teacher should work through these examples with the students, providing scaffolding and allowing students to contribute to each step.
Question 1: Find the HCF of 18 and
2
7. Solution: Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 27: 1, 3, 9, 27 Common Factors: 1, 3, 9 Highest Common Factor (HCF): 9
Commentary: Emphasize the systematic listing of factors to avoid missing any. Check for understanding of "common" and "highest." Question 2: Two traders, Amina and Chike, have kola nuts. Amina has 24 kola nuts, and Chike has 32 kola nuts. They want to share their kola nuts equally into the largest possible number of small bags, with each bag containing the same number of kola nuts. How many kola nuts will be in each bag?
Solution: (This is a word problem, so the HCF will be the answer to "how many kola nuts will be in each bag" i.e. the largest equal number they can divide by).
Factors of 24 (Amina's kola nuts): 1, 2, 3, 4, 6, 8, 12, 24 Factors of 32 (Chike's kola nuts): 1, 2, 4, 8, 16, 32 Common Factors: 1, 2, 4, 8 Highest Common Factor (HCF): 8 Therefore, there will be 8 kola nuts in each bag.
Commentary: Discuss how "largest possible number" implies finding the HC
F. Relate it to real-life sharing scenarios in a Nigerian market or family setting.
Question 3: Determine the HCF of 40 and
6
0. Solution: Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Common Factors: 1, 2, 4, 5, 10, 20 Highest Common Factor (HCF): 20
Commentary: For larger numbers, remind students to be extra careful in listing all factors. Encourage them to use multiplication facts to help find factors quickly. 8.
1. Remediation (for struggling learners): Review Basic Multiplication: Students struggling with factors often have weak multiplication table knowledge. Provide flashcards or quick drills for multiplication facts (especially for numbers up to 12).
Use Manipulatives: Provide physical objects like bottle caps, counting sticks, or pebbles. For example, to find factors of 12, have them arrange 12 items into equal rows (e.g., 1 row of 12, 2 rows of 6, 3 rows of 4). This concrete representation helps visualize factors.
Focus on Smaller Numbers: Start with very small 2-digit numbers (e.g., HCF of 6 and 9) before moving to larger ones.
Pair Work/Peer Tutoring: Pair struggling learners with more capable peers for guided practice.
Step-by-Step Template: Provide a template with blank spaces for "Factors of X:", "Factors of Y:", "Common Factors:", "HCF:" to guide their writing process. 8.
2. Extension (for high-achieving learners): HCF of Three Numbers: Challenge them to find the HCF of three 2-digit numbers (e.g., HCF of 12, 18, and 24). This requires them to extend the concept of commonality to an additional list of factors. Introduction to Prime Factorization Method (Conceptual): Briefly introduce that there's another method using prime factors, without going into deep detail. Show them how to break numbers into prime factors and pick common ones. This can spark interest for future learning. For instance, for 12 = 2x2x3 and 18 = 2x3x3, the common prime factors are one 2 and one 3, so HCF = 2x3 =
6. Complex Word Problems: Provide more challenging word problems that require students to first identify that HCF is the appropriate operation to solve the problem (e.g., problems involving measurements, sharing across multiple groups).
Market Trading and Packaging: A market woman in Onitsha market wants to package small sachets of water into larger packs for sale. If she has 48 sachets of one brand and 60 sachets of another, she can use HCF to find the largest number of sachets she can put into identical packs without mixing brands, ensuring no sachets are left over. This helps in efficient packaging and pricing.
Community Projects and Grouping: In a community development project in a rural Nigerian village, 36 volunteers are to be divided into working groups, and 48 new trees are to be planted. If each group needs to have the same number of volunteers, and each group needs to plant the same number of trees, HCF can help determine the largest possible size of each group of volunteers or the number of trees each group will handle, ensuring fairness and efficiency.
Farming and Land Division: A farmer in Benue State wants to divide a rectangular piece of land into the largest possible identical square plots. If the land is 30 metres long and 42 metres wide, finding the HCF of 30 and 42 (which is 6) tells him that the side length of the largest square plots he can create is 6 metres. This helps in efficient land use and planning for different crops.