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Subject: Mathematics
Semester: 1
Period: 3
Week: 14
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 4
Date: Week 14
Lesson Duration: 45 minutes
Week & Period: Week 14, Period 3
Topic: Factors and Multiples
Sub-topic: Finding Factors and Multiples
Learning Objectives
By the end of the lesson, students should be able to:
- Define and identify factors and multiples of numbers.
- Find prime factors of a number.
- Use factor trees to determine prime factors.
Previous Knowledge
Students already know basic multiplication tables.
Instructional Materials
Mathematics textbook for Grade 4, multiplication charts, factor tree diagrams.
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher writes 12 on the board and asks: “Which numbers can divide 12 exactly without a remainder?” Students list them aloud.
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definition: A factor of a number is any whole number that divides that number exactly without leaving a remainder. For example, factors of 12 are numbers that can be multiplied together to give 12, such as 1, 2, 3, 4, 6, and 12. Each of these divides 12 perfectly:
- 12 ÷ 1 = 12
- 12 ÷ 2 = 6
- 12 ÷ 3 = 4
- 12 ÷ 4 = 3
- 12 ÷ 6 = 2
- 12 ÷ 12 = 1
Definition: A multiple of a number is the product of that number and any whole number. Multiples represent repeated addition of the number. For example, multiples of 4 are:
4 (4×1), 8 (4×2), 12 (4×3), 16 (4×4), 20 (4×5), and so on.
Detailed Explanation:
- Factors are like the “building blocks” of numbers, helping us understand how a number can be divided or broken down.
- Multiples are the results of repeated addition or multiplication of the original number by whole numbers. They form sequences that grow indefinitely.
- Understanding factors and multiples is essential for topics such as simplifying fractions, finding common denominators, and solving problems involving divisibility.
Prime Factorization:
Prime factorization means expressing a number as a product of prime numbers only. Prime numbers are numbers greater than 1 that have no other factors besides 1 and themselves (e.g., 2, 3, 5, 7, 11, 13…).
Example:
24 = 2 × 2 × 2 × 3 or 24 = 2³ × 3¹
This means 24 can be broken down into three 2’s and one 3 multiplied together.
Factor Tree:
A factor tree is a visual method to break down a number into its prime factors step by step.
Example: Factor tree for 24
- Start with 24
- Split into two factors: 12 × 2
- Break 12 into 6 × 2
- Break 6 into 3 × 2
Now, list all prime factors from the ends of the tree: 2, 2, 2, 3.
So, 24 = 2 × 2 × 2 × 3
More Examples:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
- Prime factorization of 36:
36 → 6 × 6 → 2 × 3 × 2 × 3 = 2² × 3² - Prime factorization of 48:
48 → 8 × 6 → 2 × 4 × 2 × 3 → 2 × 2 × 2 × 2 × 3 = 2⁴ × 3¹
Learners’ Activities (Expanded):
- Factor Tree Construction: Students create factor trees for 36, 48, 60, and 72. This hands-on activity helps them visualize breaking numbers down into prime factors.
- Multiples Listing: In groups, learners list multiples of 7 up to 70, then identify common multiples between 7 and 5, or 7 and 10, practicing recognition of common multiples.
- Factor Identification: Give learners numbers such as 24, 30, 42 and ask them to list all factors, then check answers with a partner.
- Matching Game: Match factors and multiples flashcards. For example, flashcard "Factors of 18" matched with "1, 2, 3, 6, 9, 18."
Assessment Checks:
- What are the first five multiples of 9? (Answer: 9, 18, 27, 36, 45)
- List all factors of 18. (Answer: 1, 2, 3, 6, 9, 18)
- Prime factorize 30 using a factor tree. (Answer: 2 × 3 × 5)
- Is 25 a factor of 100? Explain. (Answer: Yes, because 100 ÷ 25 = 4 with no remainder)
- Which of these numbers are multiples of 4: 12, 15, 20, 33? (Answer: 12 and 20)
Notes (Expanded & Detailed):
Factors and multiples are foundational concepts that link closely to many areas of mathematics. Understanding factors helps in division, finding greatest common factors (GCF), and simplifying fractions. Recognizing multiples is important for least common multiples (LCM), which is vital in adding and subtracting fractions with different denominators. Prime factorization is a powerful tool for breaking down numbers to their simplest components and is essential in advanced topics such as LCM, GCF, and algebraic factorization.
Extended Practice Assignments:
- Find all factors of 24, 36, 40, and 54.
- List the first 10 multiples of 8 and 12, then identify the common multiples.
- Create factor trees for 45, 60, and 90.
- Explain in writing why every number has 1 and itself as factors.
- Find the prime factorization of 84 and 100.
These exercises, examples, and assessments ensure students not only memorize definitions but understand and apply the concepts in problem-solving and real-life contexts.
C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Factors divide numbers; multiples are repeated products. Prime factors are expressed through factor trees.
Evaluation Method (Expanded):
Exit slip/quiz: Write the factors of 20 and the first five multiples of 6.
Teacher will collect slips and provide oral feedback.
Assignment (Expanded):
Draw factor trees for 60 and 72.
Follow-up Activity:
Students find factors and multiples of their age number.
Differentiation / Inclusive Strategies
Teacher provides multiplication charts for slower learners and encourages peer collaboration.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low