Question 1: Calculate the cube of 4. Write your answer clearly.

Answer: 64

Question 2: What is 7³? Show your working.

Answer: 343

Question 3: Identify the common mistake in calculating 5³ and explain how to correct it.

Answer: Incorrect answer: 15; Correct answer: 125; Mistake: Confusing cube with square, or multiplying 5×5×5 instead of cubing 5.

Question 4: Construct a cube with side length 3 units on the grid. Measure and verify its volume.

Answer: 27

Question 5: A student claims 6³ = 216. Is this correct? Justify your answer.

Answer: Yes, 6³ = 6×6×6 = 216. The student is correct.

Question 6: Plot the graph of y = x³ for x = 1, 2, 3, 4 on the grid.

Answer: Points: (1,1), (2,8), (3,27), (4,64)

Question 7: Explain the misconception: A student says 9³ = 81 because 9×9 = 81.

Answer: Incorrect. 9³ means 9×9×9, which equals 729. The mistake is confusing square and cube.

Question 8: Calculate 10³. Show your working.

Answer: 1000

Question 9: Identify which of the following is NOT a perfect cube: 1, 8, 27, 50, 125. Explain why.

Answer: 50 is not a perfect cube because there is no integer n such that n³ = 50.

Question 10: A cube has a side length of 2 units. What is its volume? If a student calculates 2×2×2, what common mistake might they make?

Answer: Volume is 8. Mistake: Student might forget to cube and multiply incorrectly, e.g., 2+2+2 instead of 2×2×2.

Question 11: Challenge: Find an example of a number between 10 and 20 that is a perfect cube. Justify your answer.

Answer: No number between 10 and 20 is a perfect cube, as 2³ = 8 and 3³ = 27. Therefore, none exist.