Question 1: List the first five common multiples of 4 and 6.

Answer: 12, 24, 36, 48, 60

Question 2: Calculate the least common multiple (LCM) of 8 and 12.

Answer: 24

Question 3: Find the next three common multiples of 3 and 5 beyond 15.

Answer: 30, 45, 60

Question 4: Plot the graph of y=2x for x values from 1 to 5.

Answer: Points: (1,2), (2,4), (3,6), (4,8), (5,10)

Question 5: Construct a triangle on the grid with sides of lengths 3, 4, and 5 units (show possible positions).

Answer: Student's drawing should reflect a 3-4-5 right triangle.

Question 6: A bus arrives every 15 minutes, and a train arrives every 20 minutes. At what time(s) do both arrive simultaneously after 8:00 AM?

Answer: At 8:00 AM, 8:15 AM, 8:30 AM, 8:45 AM, 9:00 AM, etc.

Question 7: Find the least common multiple of 9 and 12 and explain the steps.

Answer: LCM is 36; prime factors 9=3^2, 12=2^2*3, LCM=2^2*3^2=36

Question 8: Identify a common multiple of 7 and 9 that is less than 63 and explain why.

Answer: 63; because 7*9=63 and it's the first common multiple.

Question 9: A factory produces items in batches of 12 and 15. After how many items will both batches align to produce items simultaneously?

Answer: 180 items (LCM of 12 and 15 is 60; 60*3=180)

Question 10: A student notices that the multiples of 4 and 9 appear on a number line. Which is the first common multiple greater than 36?

Answer: 36 or 72, but first greater than 36 is 72

Question 11: Identify and correct the mistake: 'The common multiples of 5 and 8 are 20, 30, 40, 50. So, 30 is a common multiple.'

Answer: Mistake: 30 is not a multiple of 8; common multiples of 5 and 8 are 40, 80, etc.