Question 1: Estimate the upper bound of 456 using the nearest hundred. Show your working.

Answer: 500

Question 2: Determine the lower bound of 3.78 when rounded to two decimal places.

Answer: 3.78

Question 3: Calculate the upper bound of the number 0.0063 when rounded to four decimal places.

Answer: 0.0064

Question 4: Plot the graph of y = 2x for x values between 0 and 5 on the grid.

Answer:

Question 5: Construct a triangle with sides of 5, 7, and 9 units. Use the grid to draw accurately.

Answer:

Question 6: A box contains 1234 apples. The store manager estimates this as approximately 1200 apples. Identify if this is an upper or lower bound and explain why.

Answer: Lower bound because 1200 is less than 1234, serving as a conservative estimate.

Question 7: A number rounded to the nearest hundred is 700. What is the range of possible original numbers?

Answer: 650 to 749

Question 8: Explain why 499 is the lower bound when rounding 499 to the nearest hundred, and give the corresponding upper bound.

Answer: 499 is the lower bound because any number from 450 to 499 rounds to 500; the upper bound is 549.

Question 9: Solve: If the actual number is 876, what is its upper bound when rounded to the nearest hundred?

Answer: 900

Question 10: Identify and correct the mistake: A student states that 999 rounds to 1000, but the lower bound for rounding to the nearest thousand is 500. Explain the mistake.

Answer: The mistake is in the lower bound; for rounding to the nearest thousand, the lower bound is 500, but 999 rounds to 1000, which is correct. The mistake is assuming 999 is outside the bounds.