Question 1: Identify whether the following numbers are prime or composite: 17, 21, 13, 50.

Answer: ["prime","composite","prime","composite"]

Question 2: Calculate the number of prime numbers between 1 and 30.

Answer: 11

Question 3: Construct a triangle on the grid with sides of prime length and explain why the sides are prime.

Answer: Students draw sides of lengths, e.g., 3 and 5, and explain these are prime because they have no divisors other than 1 and themselves.

Question 4: List all prime factors of 84.

Answer: ["2","3","7"]

Question 5: Determine whether 49 is prime or composite and justify your answer.

Answer: composite, because 49=7×7

Question 6: Identify all prime numbers less than 20.

Answer: ["2","3","5","7","11","13","17","19"]

Question 7: Find the smallest composite number greater than 30.

Answer: 32

Question 8: Explain why 2 is the only even prime number.

Answer: Because all other even numbers are divisible by 2 and at least one other number, so only 2 has exactly two distinct positive divisors.

Question 9: What are the prime factors of 150?

Answer: ["2","3","5"]

Question 10: Identify any mistakes in the following statement: 'All prime numbers are odd.'

Answer: The statement is false because 2 is a prime number that is even.

Question 11: List all prime numbers between 50 and 60.

Answer: ["53","59"]

Question 12: Challenge: Prove that any prime number greater than 3 can be expressed in the form 6k ± 1 for some integer k.

Answer: Students write a proof demonstrating that all primes > 3 are of the form 6k ± 1 by analyzing divisibility and modular arithmetic.