Mia is building a three-sided shelter for her action figures. The shelter will
resemble a rectangle with one of the long sides removed. She has boards that
measure 36 inches, 39 inches, and 42 inches in length; all the boards are the
same width. Mia will need to convert some of these measurements into other
imperial units to build the shelter the way she wants. Answer the following
questions. Show your work. Record your answers below.
Question 1
Mia will use one of these boards for the length of the shelter. She knows she wants
the length of the shelter to measure 3.25 feet. She will use a different board for the
width of the shelter. The width of the shelter will be shorter than the length.
Which board will Mia use for the length of the shelter, given that 1 foot = 12 inches?
What is the width of the shelter, measured in feet?
Mia needs to cut the third board to match the width of the shelter. How many feet of
board will she need to cut off the existing board to reach this goal?
Question 2
For the roof of the shelter, Mia has a board that measures 1 square yard, a second
board that measures 3 feet by 3 feet, and a third board that measures 36 inches by
36 inches. Which of these, if any, will cover all the space needed for the roof?
Explain your answer, drawing a picture if necessary.
1 foot = 1/3 of a yard
Converting Between Systems Portfolio
Use what you have learned about converting between metric and imperial
measurements to answer the questions.
Question 1
Roger is planning a party. He needs these ingredients in the following quantities to
make punch:
• 2 quarts orange juice
• 3 cups cranberry juice
• 1 gallon ginger ale
• 1 pint pineapple juice
Roger knows he will need a relatively large container to mix the punch.
Unfortunately, all he can find is a bowl that holds 8 liters of liquid. He is not sure
whether he can fit all of the ingredients in the bowl at the same time.
Use the following measurement equivalents to determine if Roger can use the 8-
liter bowl to mix all the ingredients for the punch. Show your work.
If he can use the bowl, he needs to determine how many liters of liquid could still
fit into the bowl. If he cannot use the bowl, he needs to determine how many extra
liters of liquid there are. Round your answers to the nearest tenth of a liter.
1 liter is about 4.23 cups, 2.11 pints, 1.06 quarts, and 0.26 gallons
Question 2
Roger also wants to make sandwiches for his guests. He buys the following
sandwich fillings:
• 1.5 kilograms of turkey
• 1.25 kilograms of beef
• 2.25 pounds of cheese
Roger wants to know if he purchased more turkey or more cheese. Use the
conversion ratio 1 kilogram = about 2.2 pounds to determine the correct answer.
Show your work.
Roger discovers that he needs to buy some chicken as well. He buys an amount of
chicken that weighs more than the beef he bought and less than the turkey he
bought. Give an amount in pounds that the chicken could weigh, rounded to the
nearest hundredth of a pound.
Roger is curious to know the total weight of all four sandwich fillings he bought. He
weighs it twice, once using ounces and once using grams. If 16 ounces = 1 pound
and 1,000 grams = 1 kilogram, will the total weight of the sandwich fillings be a
greater number of ounces or a greater number of kilograms? Explain your answer.
Question 1:
To determine which board Mia will use for the length of the shelter, we need to convert the desired length of 3.25 feet to inches. Since 1 foot = 12 inches, we multiply 3.25 by 12 to get 39 inches. Therefore, Mia will use the board that measures 39 inches for the length of the shelter.
The width of the shelter will be shorter than the length. However, we are not given the specific width measurement, so we cannot determine it.
If Mia needs to cut the third board to match the width of the shelter, we need to subtract the width of the shelter from the length of the third board. Since we do not know the width, we cannot determine how many feet of board she will need to cut off.
Question 2:
To determine which board will cover all the space needed for the roof, we need to compare the measurements of the boards to the total space needed for the roof. Since we are not given the specific measurements of the space needed or the boards, we cannot determine which board will cover all the space.
Question 1 (Continued):
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to add up the volumes of the ingredients in liters.
2 quarts of orange juice = 1.89 liters
3 cups of cranberry juice = 0.71 liters
1 gallon of ginger ale = 3.79 liters
1 pint of pineapple juice = 0.47 liters
The total volume of the ingredients is 1.89 + 0.71 + 3.79 + 0.47 = 6.86 liters.
Since the total volume is less than the capacity of the 8-liter bowl, Roger can use the bowl to mix all the ingredients. The amount of liquid that could still fit into the bowl is 8 - 6.86 = 1.14 liters.
Question 2 (Continued):
To determine if Roger purchased more turkey or more cheese, we need to convert the given amounts to the same unit.
1.5 kilograms of turkey = 1.5 * 2.2 = 3.3 pounds
2.25 pounds of cheese = 2.25 pounds
Since 3.3 pounds is greater than 2.25 pounds, Roger purchased more turkey than cheese.
To determine an amount in pounds that the chicken could weigh, we know that it weighs more than the beef (1.25 kilograms = 2.75 pounds) and less than the turkey (1.5 kilograms = 3.3 pounds). Therefore, the chicken could weigh between 2.75 and 3.3 pounds.
To determine if the total weight of the sandwich fillings will be a greater number of ounces or kilograms, we need to compare the conversion factors.
1 pound = 16 ounces
1 kilogram = 1000 grams = 2.2 pounds
Since 16 ounces is smaller than 2.2 pounds, the total weight of the sandwich fillings will be a greater number of kilograms.