Question 1: Calculate the cube of 3.

Answer: 27

Question 2: Identify whether 64 is a cube number. If yes, specify its cube root.

Answer: Yes, cube root is 4

Question 3: A student states that 125 is not a cube number. Is this correct? Explain your reasoning.

Answer: No, 125 is a cube number because 5^3=125.

Question 4: Plot the graph of y=x^3 for x values from -3 to 3. (Draw on grid.)

Answer: See full answer key

Question 5: Construct a cube with side length 4 units on the grid. How many unit cubes does this larger cube contain?

Answer: 64

Question 6: Identify the common misconception: A student calculates 5^3 as 15. Describe the mistake and correct it.

Answer: Mistake: confusing cube with multiplication. Correct: 5^3=125

Question 7: A number is mistakenly identified as a cube because its square root is a whole number. Give an example of such a number and explain why this is incorrect.

Answer: Example: 16, because √16=4, but 16 is not a cube. Cubes are perfect cubes like 8 or 27.

Question 8: A student claims 216 is NOT a cube number because 6^3=216. Is this correct? Justify your answer.

Answer: Incorrect. 216 is a cube because 6^3=216.

Question 9: Identify and correct the mistake: 'Since 81 is a perfect square, it must be a perfect cube too.'

Answer: Mistake: Not all perfect squares are perfect cubes. 81 is not a cube.

Question 10: Challenge: Find a two-digit number that is both a perfect square and a perfect cube. Explain your reasoning.

Answer: Number: 64, since 8^2=64 and 4^3=64, it's both a perfect square and cube.

Question 11: Error Analysis: A student writes that 125 is not a cube because it is not a perfect square. Identify and correct the misconception.

Answer: Misconception: Cubes are not required to be perfect squares. 125=5^3, so it is a cube.