Question 1: List all the factor pairs of 36.

Answer: [1,36], [2,18], [3,12], [4,9], [6,6]

Question 2: Find the factor pairs of 48.

Answer: [1,48], [2,24], [3,16], [4,12], [6,8]

Question 3: Explain why the pairs (1, n) and (n, 1) are always factor pairs of a number n.

Answer: Because multiplication is commutative, multiplying 1 by n or n by 1 results in n, so both pairs are factors.

Question 4: Calculate the number of factor pairs for 60.

Answer: 8

Question 5: Plot the points representing the factor pairs of 24 on the grid below. (Students will draw on the grid.)

Answer: Points at (1,24), (2,12), (3,8), (4,6), and their reverses

Question 6: Construct a rectangle on the grid with side lengths corresponding to a factor pair of 20.

Answer: Construct sides of length 4 and 5 on the grid.

Question 7: Identify a mistake in the following list of factor pairs for 36: (1,36), (2,18), (3,12), (4,9), (6,6), (9,4).

Answer: The pair (9,4) is a reverse of (4,9) and not a new pair; it’s redundant, so the list should not include duplicates.

Question 8: Find all factor pairs of 100 and explain any patterns observed.

Answer: Factor pairs: (1,100), (2,50), (4,25), (5,20), (10,10). Pattern: pairs mirror around the square root, and the number of pairs is related to the number of divisors.

Question 9: Given a number n = 81, list all its factor pairs and determine if it has a perfect square as a factor pair.

Answer: Factor pairs: (1,81), (3,27), (9,9). Yes, (9,9) is a perfect square pair.

Question 10: Compare the factor pairs of 16 and 20. Which number has more factor pairs and why?

Answer: 16 has 3 pairs; 20 has 4 pairs. 20 has more because it has more divisors.

Question 11: Find the factor pairs of 64. Then, identify which pair involves the smallest and largest factors.

Answer: Pairs: (1,64), (2,32), (4,16), (8,8). Smallest: 1, Largest: 64.