Question 1: Write the first five square numbers.

Answer: 1, 4, 9, 16, 25

Question 2: Identify which of the following numbers are perfect squares: 36, 50, 81, ninety-six, 100.

Answer: ["36","81","100"]

Question 3: Construct a square with side length 4 units on the grid. How many squares are contained within the larger square?

Answer: 16

Question 4: What pattern do you notice in the sequence of square numbers 1, 4, 9, 16, 25, 36?

Answer: Each number is the square of its position in the sequence (n^2).

Question 5: A square number is multiplied by 2. If the original square number is 25, what is the result?

Answer: 50

Question 6: A box contains numbers: 1, 4, 9, 16, 25, 36, 49, 64. Which numbers are perfect squares? Explain your reasoning.

Answer: 1, 4, 9, 16, 25, 36, 49, 64; all are perfect squares because they are the squares of numbers 1 through 8.

Question 7: If a number is a perfect square, what can you say about its prime factors? Give an example.

Answer: All prime factors appear in pairs (even exponents). For example, 36 = 2^2 * 3^2.

Question 8: Identify the error: 'The number 50 is a perfect square because 7^2 = 49 and 8^2=64, so 50 is between these squares.' Is this correct? Why or why not?

Answer: No, 50 is not a perfect square because it is not the square of an integer; it's between 7^2=49 and 8^2=64.

Question 9: Plot the graph of y = x^2 for x from 1 to 5 on the grid.

Answer:

Question 10: A tile pattern shows the number of tiles as 1, 4, 9, 16, 25, 36, 49, 64. How many tiles are needed for the 10th pattern? Show your reasoning.

Answer: 100, because the pattern is the square of the position (10^2).

Question 11: Challenge: Find a perfect square that is also a multiple of 18. Explain your reasoning.

Answer: 36, because 36 = 6^2 and 36/18=2, so 36 is both a perfect square and divisible by 18.