### Lesson Plan: HCF (Highest Common Factor) and LCM (Least Common Multiple)
#### Grade Level: Primary 6
#### Duration: 60 minutes
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### Learning Objectives:
- Understand the concepts of Highest Common Factor (HCF) and Least Common Multiple (LCM).
- Learn methods to find the HCF and LCM.
- Apply these concepts to solve real-world problems.
### Materials Needed:
- Whiteboard and markers
- Math notebooks and pencils
- Worksheets on HCF and LCM
- Projector (optional for visual aids)
- Calculators (if needed)
### Key Vocabulary:
- Factors
- Multiples
- Prime Factorization
- Common Factors
- Common Multiples
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### Lesson Outline:
#### Introduction (10 minutes)
1. **Greeting and Motivation**:
- Start the lesson with a fun riddle or math-related joke to engage students.
- Introduce the topic by exploring its real-world applications (e.g., sharing equal parts, scheduling recurring events).
2. **Review of Prior Knowledge**:
- Briefly review what factors and multiples are.
- Ask simple questions like: "What are the factors of 12?" or "What are the first five multiples of 3?"
#### Direct Instruction (20 minutes)
1. **Explanation of HCF**:
- Define HCF as the greatest number that can divide two or more numbers without leaving a remainder.
- Demonstrate finding the HCF using the list method and the prime factorization method.
- Example: Find the HCF of 12 and 18.
- List Method: Factors of 12 (1, 2, 3, 4, 6, 12) and Factors of 18 (1, 2, 3, 6, 9, 18). The common factors are 1, 2, 3, 6. The HCF is 6.
- Prime Factorization Method: 12 = 2^2 * 3, 18 = 2 * 3^2. Common prime factors are 2 and 3. Multiply them to get the HCF: 2 * 3 = 6.
2. **Explanation of LCM**:
- Define LCM as the smallest number that is a multiple of two or more numbers.
- Demonstrate finding the LCM using the list method and prime factorization.
- Example: Find the LCM of 4 and 5.
- List Method: Multiples of 4 (4, 8, 12, 16, 20 ...) and Multiples of 5 (5, 10, 15, 20, 25 ...). The first common multiple is 20. Therefore, the LCM is 20.
- Prime Factorization Method: 4 = 2^2, 5 = 5. The LCM is found by taking the highest powers of all primes: 2^2 and 5, thus LCM = 4 * 5 = 20.
#### Guided Practice (15 minutes)
1. **Class Activity**:
- Provide a few problems on the board and solve them together as a class.
- Example Problems: Find the HCF and LCM of (15 and 25), (6 and 8).
- Encourage students to work in pairs to foster collaborative learning.
#### Independent Practice (10 minutes)
1. **Worksheet Activity**:
- Distribute worksheets with a mix of problems on HCF and LCM.
- Circulate the room to provide assistance and give feedback as needed.
#### Closure (5 minutes)
1. **Review and Summarize**:
- Summarize key points about HCF and LCM.
- Ask a few students to share what they learned or found interesting about the lesson.
2. **Assignment**:
- Provide a homework assignment that includes real-life application problems involving HCF and LCM.
- Example: "A school wants to give pencils and notebooks such that each student gets the same number of each item. If the school has 24 pencils and 36 notebooks, what is the maximum number of students that can receive the items?"
#### Assessment:
- Formative: Observe student participation and responses during class discussion and activities.
- Summative: Evaluate the worksheet and homework assignment to determine understanding.
#### Differentiation:
- **For advanced students**: Offer challenging problems that involve more than two numbers.
- **For struggling students**: Provide additional step-by-step examples and one-on-one support during practice.
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This lesson plan aims to provide a comprehensive understanding of HCF and LCM while ensuring students engage with and apply the concepts in a meaningful way.