Grade 4: Prime & Composite

Warm up with a quick recall on the board. Test whether a number has exactly two factors (prime) or more (composite) using arrays. Learn that 1 is neither.

A prime number has exactly two factors, 1 and itself, so it cannot be split into smaller equal groups larger than one. A composite number has more than two factors. The number 1 is neither, because it has only one factor. Primes are the building blocks of every other number, which is why factors need to be secure first. Model the method clearly, thinking aloud:

• Build on factors: a number is prime if the only rectangle you can make from its counters is a single row (7 counters only make 1 x 7).
• List the factors of a number in pairs and count them: exactly two means prime, more than two means composite.
• Learn the primes to 20 by heart (2, 3, 5, 7, 11, 13, 17, 19) and use the Sieve of Eratosthenes on a hundred square to find the rest.
• Stress the two special cases: 2 is the only even prime, and 1 is neither prime nor composite.
• Practise sorting numbers into prime and composite, explaining the factor count each time.

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

Circulate and look for these, they are the usual sticking points:

• Calling 1 a prime number (it has only one factor, so it is neither).
• Assuming every odd number is prime (9, 15 and 21 are composite).
• Forgetting that 2 is prime because it is even.
• Deciding a number is prime without actually checking all its factors.
• Calling 1 prime, and assuming all odd numbers are prime (9, 15).

Pull the class back together. Ask one child to explain prime & composite in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.