Section C Practice Problems

Problem 1

There are 418 students at a school. Han estimates that each student drinks about 5 glasses of water in one day.

  1. About how many glasses of water do all of the students drink in one day?
  2. About how many glasses of water do all of the students drink in one week?
  3. About how many glasses of water do all of the students drink in one month?
  4. About how long does it take all of the students to drink 1,000,000 glasses of water?
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Solution

Sample responses:

  1. 2,000. I multiplied 400 by 5.
  2. 14,000. I multiplied 2,000 by 7.
  3. 56,000. I multiplied 14,000 by 4.
  4. Around 18 months. I multiplied 56,000 by 10 and that is 560,000, which is a little more than half of one million. 

Problem 2

Colorado is 610 kilometers long and 450 kilometers wide.

  1. New Mexico is about 596 kilometers long and 552 kilometers wide. Is the area of Colorado greater than or less than the area of New Mexico? Explain your reasoning.
  2. What is the area of Colorado?
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Solution
  1. Less. Sample response: The length is about the same, but the width is less. I also can see on the map that it is smaller.
  2. 274,500 square km. Sample response: I found 61×4561 \times 45, and then multiplied that by 100. 

Problem 3

A large cargo ship carries between 10,000 and 15,000 shipping containers. About how many cargo ships are needed to carry the 210,000 containers of plastic the U.S. ships for recycling each year? Explain or show your reasoning.

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Solution
15 to 20 cargo ships. Sample response: I know ten 10,000s is 100,000, so twenty-one 10,000s is 210,000. I also know that 14×15=21014 \times 15 = 210, so 14×15,000=210,00014 \times 15,000 = 210,000.

Problem 4

Han reads that the length of Florida is 721 kilometers and its width is 582 kilometers. Han says, "Florida is larger than New Mexico!" Do you agree? Explain or show your reasoning.

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Solution

Sample responses:

  • Yes, it's longer than New Mexico and wider than New Mexico so Florida is bigger.
  • No, I don't know how to find the area of Florida because it is a funny shape but I can see on the map that it is not nearly as big as New Mexico. The width measurement of Florida is misleading because it includes that long skinny part that does not add much area. 

Problem 5

The Pentagon has 5 floors. The Empire State Building has 102 floors. Noah says that the Empire State Building is larger. Do you agree? Explain how you know.

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Solution

Sample response: No, the Empire State Building is a lot taller than, a little more than 20 times as tall as, the Pentagon. But the Pentagon has more floor space, more than twice as much floor space as the Empire State Building. That means that the volume of the Pentagon is probably bigger than the volume of the Empire State Building since I can estimate the volume by multiplying the floor area by the height of the floors.