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Question 1:

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 using this information. Be sure to work out your problems on paper and use a calculator if needed.



1a. 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?

(2 points)
Responses

Board 1 that measures 36 inches
Board 1 that measures 36 inches

Board 2 that measures 39 inches
Board 2 that measures 39 inches

Board 3 that measures 42
Board 3 that measures 42
Question 2




1b. Use the information from question 1a to solve this question.

What is the width of the shelter, measured in FEET? *Remember the width will be shorter than the length.

(2 points)
Responses

3 feet
3 feet

3.25 feet
3.25 feet

3.5 feet
3.5 feet
Question 3




1c. 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?

(2 points)
Responses

6 inches or 0.5 feet
6 inches or 0.5 feet

3 inches or 0.25 feet
3 inches or 0.25 feet

12 inches or 1 foot
12 inches or 1 foot
Question 4




1d. 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?

1 foot = 1/3 of a yard

(2 points)
Responses

The board measuring 1 square yard
The board measuring 1 square yard

The board measuring 3 feet by 3 feet
The board measuring 3 feet by 3 feet

The board measuring 36 inches by 36 inches
The board measuring 36 inches by 36 inches

None of these boards will work

1 answer

To answer the questions based on the information provided regarding Mia's shelter for her action figures, let’s proceed step-by-step.

Question 1a:

Mia wants the length of the shelter to measure 3.25 feet. To convert this length into inches:

  • 3.25 feet * 12 inches/foot = 39 inches

Mia has three boards to choose from:

  • Board 1 = 36 inches
  • Board 2 = 39 inches
  • Board 3 = 42 inches

Since she needs a board that is at least 39 inches for the length, the correct board is Board 3 that measures 42 inches (even though Board 2 is exactly 39 inches, Mia will opt for Board 3 to ensure she has more than 39 inches).

Response for Question 1a:

  • Board 3 that measures 42 inches

Question 2:

Given that the width of the shelter will be shorter than the length (39 inches), we have Board 1 and Board 2 as options, with Board 1 having 36 inches in length. Converting 36 inches to feet:

  • 36 inches / 12 inches/foot = 3 feet

Since this is shorter than the length (39 inches), the width will be 3 feet.

Response for Question 1b:

  • 3 feet

Question 3:

Mia will need to cut down Board 3 (42 inches) to match the width (36 inches). To find out how much needs to be cut off:

  • Existing board length = 42 inches
  • Desired width = 36 inches
  • Amount to cut = 42 inches - 36 inches = 6 inches

In feet, to express 6 inches:

  • 6 inches / 12 inches/foot = 0.5 feet

Response for Question 1c:

  • 6 inches or 0.5 feet

Question 4:

Now we need to determine which of the available boards can cover the roof area. The roof needs to cover an area equivalent to the surface area of the shelter, which we can calculate. Length of shelter = 39 inches and width of shelter = 36 inches.

  • Area = length × width = 39 inches × 36 inches = 1404 square inches.
  • To convert this area into square feet:
    • 1404 square inches / (12 inches/foot)² = 1404 / 144 = 9.75 square feet.

Next, we check the roof boards:

  1. Board measuring 1 square yard:
    • 1 square yard = 3 feet × 3 feet = 9 square feet (this is less than 9.75 square feet).
  2. Board measuring 3 feet by 3 feet:
    • Area = 3 feet × 3 feet = 9 square feet (this is also less than 9.75 square feet).
  3. Board measuring 36 inches by 36 inches:
    • 36 inches = 3 feet (so 36 inches by 36 inches = 3 feet × 3 feet = 9 square feet), again less than 9.75 square feet.

None of the boards are able to cover the required area of 9.75 square feet.

Response for Question 1d:

  • None of these boards will work

In summary, here are the final responses to all questions:

  1. Board 3 that measures 42 inches
  2. 3 feet
  3. 6 inches or 0.5 feet
  4. None of these boards will work