Prime Factors

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Subject: Mathematics

Semester: 1

Period: 2

Week: 9

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School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 9
Lesson Duration: 45 minutes
Week & Period: Week 9, Period 2
Topic: Prime Factors
Sub-topic: Factor Trees and Prime Factorization

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

1. Define prime factors.
2. Perform prime factorization of two-digit numbers.
3. Use factor trees to find prime factors.

Previous Knowledge
Students already know prime numbers and factors.

Instructional Materials
Charts, number cards, factor tree diagrams

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: What are the factors of 24?

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

✅ Definitions and Explanations:

• Factor: A number that divides another number exactly, with no remainder.
  🔹 Example: 3 is a factor of 12 because 3 × 4 = 12.
• Prime Number: A number with exactly two factors — 1 and itself.
  🔹 Examples: 2, 3, 5, 7, 11, 13, 17, 19...
• Prime Factor: A factor of a number that is also a prime number.
  🔹 Example: The prime factors of 18 are 2 and 3.
• Prime Factorization: Writing a composite number as a product of its prime factors (only prime numbers multiplied together).
  🔹 Example:

24=2×2×2×3=2³×3

 

🔢 Expanded Examples (Step-by-step):

Example 1: Prime Factorization of 24

• Start with: 24
• Divide by 2:

24÷2=12

12÷2=6

6÷2=3

3÷3=1

• Prime factors: 2 × 2 × 2 × 3
• Final Answer:

24=2³×3

Example 2: Prime Factorization of 36

• Start with: 36
• Divide by 2:

36÷2=18

18÷2=9

9÷3=3

3÷3=1

• Prime factors: 2 × 2 × 3 × 3
• Final Answer:

36=2²×3²

Example 3: Prime Factorization of 45

• Start with: 45
• Divide by 3:

45÷3=15

15÷3=5

5÷5=1

• Prime factors: 3 × 3 × 5
• Final Answer:

45=3²×5

🧠 Learners’ Activities (Expanded):

1. Factor Tree Construction:
   • Each student picks a number (between 20–100).
   • They build a factor tree by breaking the number down until only prime numbers remain.
   • Example: Start with 60 → 2 × 30 → 2 × 2 × 15 → 2 × 2 × 3 × 5.
2. Division Ladder Method:
   • In pairs, students use short division to repeatedly divide by prime numbers.
   • Example:

2 ∣ 60

2 ∣ 30

3 ∣ 15

5 ∣ 5

→ Prime Factors: 2 × 2 × 3 × 5

3. Matching Game:
   • Prepare cards with numbers and cards with prime factorizations.
   • Learners match them (e.g., “48” matches “2⁴ × 3”).
4. GCF/LCM Connection Activity:
   • Use prime factors to find the Greatest Common Factor and Least Common Multiple of two numbers (e.g., 12 and 18).

 

✅ Assessment Checks:

Oral Questions:

• “What are the prime factors of 60?”
• “Is 5 a prime factor of 30?”
• “Can 4 be a prime factor? Why or why not?”

Quick Check Worksheet (Sample Questions):

1. Find the prime factors of 56.
2. Write the prime factorization of 81.
3. What is the product of the prime factors of 90?
4. True or False: All factors of a number are prime.
5. Use a factor tree to break down 72.

Challenge Question:

• Use prime factorization to find the GCF of 36 and 60.

📝 Notes (Expanded & Detailed):

• Prime factorization is essential in simplifying fractions, finding GCF/LCM, and solving algebra problems later.
• Emphasize that all composite numbers can be written as products of prime numbers (Fundamental Theorem of Arithmetic).
• Visual aids like factor trees and division ladders make abstract concepts more concrete.
• Use real-world context where possible (e.g., finding the largest number of equal-sized teams or equal-length cuts of rope).

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reviews factor trees and prime factorization.

Evaluation Method (Expanded):
Exit slip/quiz: Find the prime factors of 60.

Assignment (Expanded):
Complete textbook questions on prime factorization.

Follow-up Activity:
Students use prime factorization to find LCM and GCF in homework.

Differentiation / Inclusive Strategies
Weaker learners use guided factor tree examples.

Teacher’s Reflection (After Class)
• What worked well? ___________________________________________
• What needs improvement? ____________________________________
• Students’ engagement level: ☑ High ☑ Medium ☑ Low