Question 1: List all factor pairs of 36.

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

Question 2: Calculate the factors of 48 and identify its factor pairs.

Answer: Factors: 1,2,3,4,6,8,12,16,24,48; Factor pairs: [1,48], [2,24], [3,16], [4,12], [6,8]

Question 3: Explain why the pair (5, 10) is a factor pair of 50, but (10, 5) is also the same. Why do we list both?

Answer: Because factor pairs are ordered pairs showing that both numbers divide the number evenly. [5,10] and [10,5] are the same pair listed in different order; typically only one is listed unless specified otherwise.

Question 4: A student says 12 has the factor pairs [1,12], [2,6], [3,4], and [4,3]. Is this correct? Why or why not?

Answer: The pair [4,3] is not a factor pair of 12 because the pair should be listed with the smaller number first, so it's just the same as [3,4], which is correct. The pairs are correct but should not be repeated in reverse order.

Question 5: Identify the mistake: A student lists the factor pairs of 20 as [1,20], [2,10], [4,5], and [5,4]. What's wrong?

Answer: The pair [5,4] is a duplicate of [4,5]; factor pairs are usually listed with the smaller number first, so [5,4] is incorrect or redundant.

Question 6: What are the factor pairs of 25? Draw them on the grid.

Answer: [1,25], [5,5]

Question 7: Construct a rectangle on the grid with an area of 36 units² by drawing its sides according to one of its factor pairs.

Answer: Student draws sides of length 6 and 6, or 4 and 9, etc., representing factor pairs of 36.

Question 8: Find a factor pair of 45 that is not a pair of consecutive numbers. Explain your choice.

Answer: [1,45], [3,15], [5,9]; for example, [3,15] is not consecutive.

Question 9: Challenge: If a number has exactly 4 factor pairs, what could the number be? Provide an example and explain.

Answer: Example: 36 has the factor pairs [1,36], [2,18], [3,12], [4,9], and [6,6], totaling 5, so not this. But 20 has pairs [1,20], [2,10], [4,5]; only 3. The number 36 has 4 distinct pairs if considering only unique pairs with different factors. For exactly 4, a good example is 36.

Question 10: Identify and correct the misconception: All factors of 50 are less than 50.

Answer: Incorrect. 50's factors include 1, 2, 5, 10, 25, and 50. Factors can be equal to or less than the number, but not necessarily less than itself.