Question 1: List all the factor pairs of 36.

Answer: 1×36, 2×18, 3×12, 4×9, 6×6

Question 2: Calculate the number of factor pairs for 48.

Answer: 10

Question 3: A rectangular garden has a length that is 3 times its width. The total area is 192 m². Find the possible pairs of length and width.

Answer: Width = 4m, Length=12m; Width=6m, Length=18m

Question 4: Plot the graph of y = 2x for x from 1 to 10 on the grid.

Answer: Students draw a line passing through points (1,2), (2,4), ..., (10,20).

Question 5: Construct a triangle on the grid with side lengths that form a factor pair of 56.

Answer: Any triangle with sides 7 and 8, for example, forming a factor pair (7,8).

Question 6: Identify the common mistake when students list factor pairs of 24 and correct it.

Answer: Missing pairs or repeating pairs; correct listing is 1×24, 2×12, 3×8, 4×6.

Question 7: How many factor pairs does 100 have? Show your working.

Answer: 9

Question 8: A factory produces boxes with a base area of 120 cm². If the length and width are integers and are factor pairs of 120, what are the possible dimensions?

Answer: Possible pairs: (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12).

Question 9: Find all factor pairs of 81 and identify which are also perfect squares.

Answer: 1×81, 3×27, 9×9; perfect square pair: 9×9

Question 10: Explain why the number 45 has fewer factor pairs than 60.

Answer: Because 45 has fewer divisors, specifically fewer factor pairs, than 60 due to its prime factorization.

Question 11: Identify the error in this list of factor pairs for 50: (1,50), (2,25), (5,10), (10,5).

Answer: Repeating pairs in reverse order; only unique pairs are needed.