Section C Practice Problems

Problem 1

  1. Jada’s class drinks 2 gallons of milk at lunch. What is the amount of milk in cups?

  2. The third graders at Jada’s school drink 3 times as much milk as Jada’s class. What is the amount in quarts?
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Solution

Sample response:

  1. 32 cups. There are 16 cups in a gallon and 2×16=322 \times 16 = 32.
  2. 24 quarts. There are 4 quarts in a gallon so Jada's class drank 8 quarts, and then 3 times as much is 3×83 \times 8 or 24 quarts.

Problem 2

Diego sees a snake that is 9 inches long at the pet store. The world's longest snake, a python, is 10 yards long. How many times longer is the python than the snake Diego sees at the pet store? Explain or show your reasoning.

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Solution

Sample response: There are 3 feet in a yard, so 10 yards is 30 feet. There are 12 inches in a foot, so that’s 30×1230 \times 12 or 360 inches. 4×9=364 \times 9 = 36, so  40×9=36040 \times 9 = 360. The python is 40 times as long as the snake Diego saw.

Problem 3

  1. Andre draws a rectangle that is 6 centimeters long and 5 centimeters wide. What is the perimeter of Andre’s rectangle?
  2. Jada draws a rectangle with side lengths that are 4 times as long as Andre’s rectangle. What is the perimeter of Jada's rectangle?
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Solution

Sample responses:

  1. 22 centimeters, since 5+6+5+6=225 + 6 + 5 + 6 = 22.
  2. 88 centimeters, since Jada’s rectangle is 24 centimeters long and 20 centimeters wide and 20+24+20+24=8820 + 24 + 20 + 24 = 88.

Problem 4

  1. A rectangle has a perimeter of 19 centimeters. One side is 4 centimeters. How long is the other side of the rectangle?

  2. A square has a perimeter of 19 centimeters. How long is each side of the square? Explain or show your reasoning.

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Solution
  1. 5125\frac{1}{2} cm. Sample response: Two sides are 4 cm and that leaves 19−819 - 8 or 11 cm for the other two sides. Since those sides are the same length, they are 5125\frac{1}{2} cm each, since 512+512=115\frac{1}{2} + 5\frac{1}{2} = 11.
  2. 4344\frac{3}{4} cm. Sample response: If the sides were 4 cm, that would make the perimeter 4×4=164 \times 4 = 16. I need another 3 cm. If I make each side 14\frac{1}{4} cm longer that gives me 44\frac{4}{4} or 1 more cm, 17 cm for the perimeter. Then another 14\frac{1}{4} cm makes the perimeter 18 cm and one more 14\frac{1}{4} gives me a square with a perimeter of 19 cm. That's 4+14+14+144 + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} or 4344\frac{3}{4} cm total. 

Problem 5

A furlong is 220 yards. It is a unit usually used to measure the distance of horse races. A mile is 5,280 feet. Mai reads that a furlong is 18\frac{1}{8} mile. Is this true? Explain or show your reasoning.

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Solution

It's true. Sample response: 220 yards is 660 feet, and I need to see if 8 groups of 660 feet make 5,280 feet. 8×6608 \times 660 is (8×600)+(8×60)(8 \times 600) + (8 \times 60), which is 4,800+4804,800+480 or 5,​280 feet. 

Problem 6

Many of the length measurements we use today have interesting histories. Choose one of them, such as a foot, a yard, or a marathon, and investigate its origin.

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Solution

Sample response: A marathon is a long-distance run named after an Ancient Greek named Pheidippides, who ran from Marathon to Athens to tell people of a victory in an important battle.