Mathematics · Class 5

Active learning ideas

Prime and Composite Numbers

Active learning helps students grasp prime and composite numbers by letting them touch, move, and test numbers themselves. When students sieve numbers or build factor trees, they see patterns that dry worksheets cannot show. These hands-on experiences build lasting understanding of number structure.

• CBSE Learning Outcomes
• NCERT: N-2.3

• 15–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Jigsaw
• 35 min · Small Groups

Small Groups: Sieve of Eratosthenes Chart

Prepare a 1-100 number grid on chart paper for each group. Instruct students to circle 2 and cross out its multiples starting from 4, then repeat with 3, 5, and so on up to 10. Groups discuss and list primes found, then share with the class.

Differentiate between prime and composite numbers based on their factor count.

Facilitation Tip

During the Sieve of Eratosthenes Chart, remind students to circle 2 first and then cross off every second number in one colour, then move to the next uncrossed number and repeat.

What to look for

Present students with a list of numbers (e.g., 15, 19, 21, 23, 27). Ask them to circle the prime numbers and put a square around the composite numbers. Then, ask them to provide the factors for two of the composite numbers listed.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 02

• Jigsaw
• 25 min · Pairs

Pairs: Prime Factor Tree Race

Provide numbers like 24, 36, 48 on cards. Pairs draw factor trees, dividing by smallest primes until reaching primes only. First accurate pair wins a point; rotate roles and check classmates' trees for verification.

Analyze the significance of prime numbers as the 'building blocks' of all other numbers.

Facilitation Tip

For the Prime Factor Tree Race, set a visible timer and encourage pairs to call out their findings so others can check and learn from mistakes.

What to look for

Give each student a card with a composite number (e.g., 36). Ask them to perform prime factorization for this number and write the result as a product of primes. Also, ask them to list two factors of the number that are not prime.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 03

• Jigsaw
• 20 min · Whole Class

Whole Class: Number Hunt Relay

Divide class into teams. Call a number; first student from each team runs to board, states if prime or composite with one factor pair example. Correct answer scores; incorrect passes to next teammate.

Construct a method to find all prime numbers up to a certain limit.

Facilitation Tip

In the Number Hunt Relay, assign each team a range of numbers so no two teams overlap, which keeps the room orderly and focused.

What to look for

Pose the question: 'Why is the number 1 neither prime nor composite?' Guide students to explain that prime numbers must have exactly two factors (1 and themselves), and composite numbers must have more than two factors. Discuss how 1 only has one factor.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 04

• Jigsaw
• 15 min · Individual

Individual: Prime Factorisation Puzzle

Give worksheets with composites to factorise using division ladders. Students colour primes in one colour, composites in another. Collect and display correct ones for class review.

Differentiate between prime and composite numbers based on their factor count.

Facilitation Tip

With the Prime Factorisation Puzzle, ask students to colour-code prime factors so peers can quickly verify their work.

What to look for

Present students with a list of numbers (e.g., 15, 19, 21, 23, 27). Ask them to circle the prime numbers and put a square around the composite numbers. Then, ask them to provide the factors for two of the composite numbers listed.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teachers should avoid simply listing primes and composites. Instead, let students discover patterns through guided activities. Research shows that when students actively mark, erase, and debate, their retention of number theory concepts improves significantly. Always connect prime factorization back to multiplication facts students already know, making new learning feel like a natural extension.

Students will confidently separate primes from composites up to 100, explain why 1 is neither, and break composites into prime factors without hesitation. They will use the Sieve of Eratosthenes correctly and justify their steps in small-group and whole-class discussions.

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Watch Out for These Misconceptions

• During the Sieve of Eratosthenes Chart, watch for students marking 1 as prime.

  Ask them to count the factors of 1 aloud and compare it to the definition on the board. Remind them to skip 1 entirely as it does not fit either category.

• During the Prime Factor Tree Race, watch for students labeling odd composites like 9 or 15 as prime.

  Have peers quickly check the factors by building a mini factor tree. Discuss why these numbers have more than two factors during the race debrief.

• During the Prime Factor Tree Race, watch for students repeatedly dividing only by 2, even when the number is odd.

  Use a whiteboard ladder diagram to show the correct sequence of smallest prime factors. Ask teams to explain their steps to the class to reinforce the method.

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Methods used in this brief

• Jigsaw