Question 1: If y is inversely proportional to x, and when x = 4, y = 6, find the value of y when x = 3.

Answer: 8

Question 2: Given y = k / x, and y = 12 when x = 3, find the constant k.

Answer: 36

Question 3: Use the value of k from the previous question. What is y when x = 6?

Answer: 6

Question 4: Plot the graph of y = 24 / x for x values from 1 to 6.

Answer: Students will plot points such as (1,24), (2,12), (3,8), (4,6), (5,4.8), (6,4)

Question 5: Construct a triangle with sides proportional to 3, 4, and 5, reflecting inverse proportion concepts.

Answer: Students draw a triangle on the grid with sides proportional to these lengths

Question 6: If y = 10 / x, find the value of y when x = 2. Then, find y when x = 5.

Answer: 5 and 2

Question 7: A machine takes 4 hours to complete a task when working at a certain speed. If the speed is doubled, how long will the task take? Explain your reasoning.

Answer: 2 hours (since time inversely proportional to speed)

Question 8: An inverse proportion problem: When x = 5, y = 8. Find y when x = 20.

Answer: 2

Question 9: Identify the error in this statement: 'Since y is inversely proportional to x, if x doubles, y also doubles.'

Answer: The error is that y should be halved when x doubles, not doubled.

Question 10: Given y = 15 / x, what is the value of y when x = 3? Now, if y is known to be 5, what is the value of x?

Answer: 5 and 3

Question 11: Challenge: The constant of inverse proportionality is 20. Write the equation for y in terms of x, and determine y when x = 10.

Answer: y=20/x, so y=2