Math Lesson: 5 Aviation-Based Word Problems for Teaching Area and Unit Conversions

One of the most challenging parts of being a math teacher, I've often thought, is coming up with interesting and relevant word problems for math homework and exams. I'm always on the look out for new sources for realistic math problems, particularly for the basic math to algebra levels. I recently picked up a copy of "Mathematics in Aviation" by George Osteyee published in 1943. Talk about a treasure! This book is filled with examples of math problems ranging from simple fractions and decimals to trigonometry, all based on the aviation of the day. This book was designed primarily to provide teaching materials for high school students interested in pre-flight aeronautics.

In this article I will give five word problems based on 1940s aviation that require the student to calculate area and do basic unit conversions from feet to inches, etc. I could see these problems being used in a basic math course, pre-algebra, or in the introductory weeks of an algebra class. The basic concepts the student would need to understand are:

Area of a Rectangle = Length * Width
1 foot = 12 inches
1 yard = 3 feet

Aviation Area Word Problem #1:
How many square inches of sheet metal are required for a fuselage part with these dimensions: 45 in. by 78 in.? How much material will be left over if this part is cut from a sheet 4 ft. by 7. ft?

Answer:
Sheet metal needed = 45 * 78 = 3510 sq. in.

To find the metal left over we must first convert our metal sheet's dimensions into inches. There are 12 inches in a foot.

Area of our original sheet = (4*12)*(7*12) = 4032 sq. in.
Metal left over = 4032 - 3510 = 522 sq. in.

Aviation Area Word Problem #2:
How many rolls of airplane floor covering would be required to cover 1120 sq. ft. of floor surface if the material comes in 40-yd. rolls 3 in. wide?

Answer:
To answer this we need to convert our rolls of material into square feet. There are 3 feet in a yard and 12 inches in a foot.

Area of one roll of material = (40*3)*(3/12) = 30 sq. ft.

Next we need to divide our flooring by the area of a roll = 1120 / 30 = 37.33. Since the question is "how many rolls of airplane floor cover would be required" the final answer would be 38. One would not purchase only part of a roll.

Aviation Area Word Problem #3:
The total deck space for passengers in a Pan American clipper is 748 sq. ft. If the plane is designed to accommodate 34 passengers, how many square feet are there per passenger?

Answer:
This is a simple division problem. Divide the total deck space by the number of passengers: 748/34 = 22 sq. ft.

This total deck space problem could be modified or upgraded to an algebraic problem where one or more of these constants are defined as a variable.

Aviation Area Word Problem #4:
If a sheet of duralumin for use in plane construction contains 5265 sq. in. and is 3.5 ft. wide, how long is it?

Answer:
This is also a simple division problem with unit conversion. The student needs to recognize that Area = Length * Width, and that he has been given the area and width. Because the area is given in sq. in. and the width is given in sq. ft., he needs to convert the width to inches. (Remember there are 12 inches in a foot.)

Length = 5265 / (3.5*12) = 125.36 inches or approx. 10.45 ft.

Aviation Area Word Problem #5:
If a clear dope will cover 30 sq. ft. of surface per gallon, how many gallons will be required to cover a surface of 250 sq. ft? If pigmented dope covers 90 sq. ft. per gallon, how many gallons are required for the same area?

Answer:
In the context of aviation "dope" is the name of a special kind of glue used on airplane fabrics. Both of these problems can be solved with simple division.

Number of gallons of clear dope = 250 / 30 = 8.33 gallons. As it is unlikely that you would be able to purchase only part of a gallon, you would have to purchase 9 gallons of clear dope to get the job done.

Number of gallons of pigmented dope = 250 / 90 = 2.78 gallons. You would have to purchase 3 gallons of pigmented dope to get the job done.

Blessings!

Source
George Osteyee. Mathematics in Aviation