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 oun
Question 1:
To find which board Mia will use for the length of the shelter, we need to convert the desired length of 3.25 feet into inches. Since 1 foot is equal to 12 inches, we can multiply 3.25 by 12 to get:
3.25 feet * 12 inches/foot = 39 inches
So, 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. Since the width is not given, we can use the remaining two boards to determine the width. Looking at the options, the board that is shorter than 39 inches is the one that measures 36 inches.
To convert the width of the shelter from inches to feet, we divide the measurement by 12.
36 inches / 12 inches/foot = 3 feet
So, the width of the shelter will be 3 feet.
To determine the amount of the third board that Mia needs to cut off to match the width of the shelter, we subtract the width of the shelter (3 feet) from the original width of the board (42 inches).
42 inches - 3 feet * 12 inches/foot = 42 inches - 36 inches = 6 inches
So, Mia needs to cut off 6 inches of board to match the width of the shelter.
Question 2:
To determine which board will cover all the space needed for the roof, we need to compare the measurements of the boards given.
1 square yard = (3 feet * 3 feet) = 9 square feet
36 inches = 36 inches * 1 foot/12 inches = 3 feet
So, the second board that measures 3 feet by 3 feet will cover all the space needed for the roof.
Question 1:
To determine which board Mia will use for the length of the shelter and the width of the shelter, we need to convert the measurements to the same unit.
Given:
1 foot = 12 inches
We want the length of the shelter to measure 3.25 feet.
To convert inches to feet, we divide the number of inches by 12.
3.25 feet = 3.25 * 12 inches = 39 inches
So, Mia will use the board that measures 39 inches for the length of the shelter.
For the width of the shelter, we need to choose a board that is shorter than the length.
To determine the width of the shelter in feet, we divide the width in inches by 12.
Since we don't have the exact measurements for the width, we cannot determine which board Mia will use for the width.
To find out how many feet of board Mia will need to cut off the third board to match the width of the shelter, we need the exact measurements of the width.
Question 2:
To determine which board will cover all the space needed for the roof, we need to convert the measurements to the same unit.
Given:
1 foot = 1/3 yard
We have:
1 square yard
3 feet by 3 feet
36 inches by 36 inches
To convert square yards to square feet, we multiply by 9 (since 1 yard = 3 feet).
1 square yard = 1 * 9 square feet = 9 square feet
We see that the second board, measuring 3 feet by 3 feet, covers exactly 9 square feet, which matches the size of the first board.
Therefore, the second board will cover all the space needed for the roof.
As for drawing a picture, since we can understand the dimensions and calculations without one, it's not necessary.
Now, moving on to the questions about Roger and the punch:
Question 1:
To determine if Roger can use the 8-liter bowl to mix all the punch ingredients, we need to convert the quantities of each ingredient to liters.
Given:
1 liter is about 4.23 cups, 2.11 pints, 1.06 quarts, and 0.26 gallons
Converting the quantities:
2 quarts = 2 * 1.06 liters ≈ 2.12 liters
3 cups = 3 * 0.24 liters ≈ 0.72 liters
1 gallon = 1 * 3.79 liters ≈ 3.79 liters
1 pint = 1 * 0.47 liters ≈ 0.47 liters
Total volume of punch ingredients = 2.12 + 0.72 + 3.79 + 0.47 liters ≈ 7.1 liters
Since the total volume of punch ingredients is less than the capacity of the bowl (8 liters), Roger can use the 8-liter bowl to mix all the ingredients.
To determine how many liters of liquid could still fit into the bowl, we subtract the total volume of punch ingredients from the capacity of the bowl:
8 liters - 7.1 liters = 0.9 liters
So, approximately 0.9 liters of liquid could still fit into the bowl.
Question 2:
To determine if Roger purchased more turkey or more cheese, we need to convert the quantities to the same unit.
Given:
1 kilogram ≈ 2.2 pounds
Converting the quantities:
1.5 kilograms ≈ 1.5 * 2.2 pounds ≈ 3.3 pounds (turkey)
2.25 pounds (cheese)
Since 3.3 pounds (turkey) is greater than 2.25 pounds (cheese), Roger purchased more turkey.
Finally, for the amount of chicken, we know that it weighs more than the beef (1.25 kilograms) and less than the turkey (1.5 kilograms).
Therefore, the amount of chicken could weigh anywhere between 1.25 kilograms and 1.5 kilograms.
As for the question about the total weight of the sandwich fillings, the provided information is not sufficient for us to perform the conversion between ounces and grams and determine if the total weight will be greater in ounces or grams.
Question 1:
To determine which board Mia will use for the length of the shelter, we need to find the board that is closest to 3.25 feet.
The measurements of the boards are:
36 inches = 3 feet
39 inches = 3.25 feet
42 inches = 3.5 feet
Therefore, Mia will use the 39-inch board for the length of the shelter.
The width of the shelter will be shorter than the length. However, the width of the shelter is not given in feet, so we cannot determine the exact measurement without additional information.
To find how many feet of the third board Mia needs to cut off to match the width of the shelter, we need to know the desired width of the shelter in feet. Since this information is missing, we cannot determine the answer.
Question 2:
To determine which board, if any, will cover all the space needed for the roof, we need to compare the areas of the boards.
The board that measures 1 square yard has an area of 1 yard × 1 yard = 1 square yard.
The second board measures 3 feet × 3 feet = 9 square feet.
The third board measures 36 inches × 36 inches = 1296 square inches ÷ 12 inches = 108 square feet.
Comparing the areas:
1 square yard = 9 square feet
1 square yard < 9 square feet
Therefore, the board that measures 1 square yard will not cover all the space needed for the roof.
Answer: None of the boards will cover all the space needed for the roof.
Question 1 (from the conversion portfolio):
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the quantities of the ingredients into liters.
2 quarts orange juice = 2 quarts × 1.06 liters per quart = 2.12 liters
3 cups cranberry juice = 3 cups × 0.24 liters per cup = 0.72 liters
1 gallon ginger ale = 1 gallon × 3.79 liters per gallon = 3.79 liters
1 pint pineapple juice = 1 pint × 0.47 liters per pint = 0.47 liters
Total volume of ingredients = 2.12 liters + 0.72 liters + 3.79 liters + 0.47 liters = 7.1 liters
Since the total volume of the ingredients is less than 8 liters, Roger can use the 8-liter bowl to mix all the ingredients for the punch.
The amount of liquid that could still fit into the bowl is 8 liters - 7.1 liters = 0.9 liters.
Question 2:
To determine whether Roger purchased more turkey or more cheese, we need to compare the weights of turkey and cheese in the same unit.
1.5 kilograms of turkey = 1.5 kilograms × 2.2 pounds per kilogram = 3.3 pounds
2.25 pounds of cheese = 2.25 pounds
Since 3.3 pounds > 2.25 pounds, Roger purchased more turkey than cheese.
To find the amount in pounds that the chicken could weigh, we know it must be more than 1.25 kilograms (weight of beef) and less than 1.5 kilograms (weight of turkey).
1.25 kilograms × 2.2 pounds per kilogram = 2.75 pounds
1.5 kilograms × 2.2 pounds per kilogram = 3.3 pounds
Therefore, the chicken could weigh between 2.75 pounds and 3.3 pounds, rounded to the nearest hundredth of a pound.
To determine the total weight of all four sandwich fillings using ounces and grams, we need to convert the weights of the fillings to the same unit.
1.5 kilograms of turkey = 1.5 kilograms × 1000 grams per kilogram × 0.035 ounces per gram ≈ 52.92 ounces
1.25 kilograms of beef = 1.25 kilograms × 1000 grams per kilogram × 0.035 ounces per gram ≈ 43.75 ounces
2.25 pounds of cheese = 2.25 pounds × 16 ounces per pound ≈ 36 ounces
Total weight in ounces = 52.92 ounces + 43.75 ounces + 36 ounces = 132.67 ounces
Total weight in grams = 1.5 kilograms × 1000 grams per kilogram + 1.25 kilograms × 1000 grams per kilogram + 2.25 pounds × 453.59 grams per pound ≈ 5025.65 grams
Since 16 ounces = 1 pound and 1,000 grams = 1 kilogram, the total weight in ounces is greater than the total weight in grams.
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