Divisibility Rules & Prime/Composite Numbers

Grade 5 · Mathematics

Semester 1 | Period 1 | Week 3

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Subject: Mathematics

Semester: 1

Period: 1

Week: 3

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 3
Lesson Duration: 45 minutes
Week & Period: Week 3, Period 1
Topic: Divisibility Rules & Prime/Composite Numbers
Sub-topic: Rules for 1–10; Prime and Composite Numbers

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

  1. State divisibility rules for numbers 1–10.
  2. Identify prime numbers up to 50.
  3. Distinguish between prime and composite numbers.

Previous Knowledge
Students already know multiplication tables up to 12.

Instructional Materials
Charts of numbers, sieve of Eratosthenes chart, markers

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Quick mental math: 24 ÷ 2, 45 ÷ 5, 27 ÷ 3.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

🔍 Full Definitions

Divisibility Rule
A shortcut to check if one number can be divided exactly by another (no remainder), without doing full division.

✏️ Divisibility Rules (1–10):

Divisor

Rule

Example

Not Divisible Example

2

Number is even (ends in 0, 2, 4, 6, 8)

24 (✓)

27 (✗)

3

Sum of digits is divisible by 3

123 → 1+2+3 = 6 → ✓

124 → 1+2+4 = 7 → ✗

4

Last two digits form a number divisible by 4

316 → "16" ÷ 4 = 4 (✓)

318 → "18" ÷ 4 = 4.5 (✗)

5

Ends in 0 or 5

75 (✓)

74 (✗)

6

Number is divisible by both 2 and 3

54 (✓) → even, and 5+4=9 (✓)

50 (✗)

8

Last 3 digits divisible by 8

1,120 → 120 ÷ 8 = 15 (✓)

1,122 → 122 ÷ 8 = 15.25 (✗)

9

Sum of digits divisible by 9

153 → 1+5+3=9 (✓)

152 → 1+5+2=8 (✗)

10

Ends in 0

340 (✓)

345 (✗)

 

🔢 Prime & Composite Numbers

  • Prime Numbers are numbers with exactly two distinct factors: 1 and itself.
    • Smallest prime number: 2 (also only even prime)
    • Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
  • Composite Numbers have more than two factors.
    • Examples: 4 (1, 2, 4), 6 (1, 2, 3, 6), 8, 9, 10, 12...
  • 1 is neither prime nor composite.

 

🧠 Conceptual Notes

  • Every number greater than 1 is either prime or composite.
  • Divisibility rules help us test quickly without doing full division.
  • Prime numbers are the building blocks of all numbers—used in factorization, coding, and more.

 

🧪 Learners’ Activities (Expanded)

  1. Divisibility Chart Game
    • Learners are given numbers (e.g., 12, 15, 18, 21, 25, 30).
    • In groups, they test each number against the rules for 2, 3, 4, 5, 6, and 10.
    • Fill in a table showing which rules apply to each number.
  2. Sieve of Eratosthenes Activity
    • Learners are given a chart of numbers 1–50.
    • As a class:
      • Cross out multiples of 2 (after 2),
      • Then multiples of 3 (after 3),
      • Then 5, then 7...
      • Remaining uncrossed numbers are prime.
    • Color-code the chart: primes in blue, composites in red.
  3. Sorting Game
    • Teacher reads numbers out loud (between 1–50).
    • Learners raise green cards for prime, red cards for composite.
  4. Peer Quiz
    • In pairs, students quiz each other:
      • "Is 33 divisible by 3?"
      • "Is 45 a composite number?"

 

📝 More Examples

  • Divisibility Examples:
    • Is 136 divisible by 4? Look at last 2 digits: 36 → 36 ÷ 4 = 9 → ✓
    • Is 128 divisible by 6? Even: ✓, 1+2+8=11 (not divisible by 3) → ✗
  • Prime/Composite Classification:
    • 17 → only 1 and 17 → Prime
    • 27 → 1, 3, 9, 27 → Composite

 

✅ Assessment Checks (Formative)

  1. Oral Q&A:
    • “Is 29 a prime or composite number?”
    • “What are the divisibility rules for 3 and 5?”
    • “Why is 1 not a prime number?”
  2. Quick Quiz:
  3. a) Circle all numbers divisible by 2:
    13, 24, 35, 18, 11, 66
  4. b) Which of the following are prime numbers?
    2, 6, 9, 11, 17
  5. c) Is 84 divisible by 4?
  6. Exit Ticket:
    On a small card, each learner writes:
    • A number divisible by 3 but not by 2
    • A prime number between 10 and 30
    • A composite number under 20

 

📌 Notes (Expanded & Detailed)

  • Why we learn this:
    Divisibility rules help save time and reduce mistakes. They’re useful when simplifying fractions, factoring, or solving word problems.
  • Cross-topic connection:
    Prime numbers are needed in GCF (Greatest Common Factor) and LCM (Least Common Multiple).
    Divisibility also comes into play in fractions, algebra, and coding.
  • Misconceptions to Address:
    • Some students think all odd numbers are prime—this is false.
    • 1 is not a prime number.
    • Even numbers (except 2) are never prime.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reinforces key rules and definitions.

Evaluation Method (Expanded):
Exit slip/quiz: Write whether 18 is divisible by 3, 27 divisible by 5, and if 31 is prime or composite.

Assignment (Expanded):
Textbook questions on divisibility rules and primes up to 100.

Follow-up Activity:
Learners make posters showing prime numbers under 50.

Differentiation / Inclusive Strategies
Pair struggling learners with stronger ones.

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