### Ratios and Proportions

- Students

- Glenn Research Center

- Math

- Exploring Engineering and Technology

- 05-08
- 09-12

- 030 min(s)

- 060 min(s)

Event Focus

If you were given all the dimensions of the Space Shuttle, could you make a 1:25 scale model? Since the Shuttle is 122 feet tall, how tall would your model be? Would it fit in your pocket, on your desk, or would you have to build it in a parking lot?

Description

**This module is appropriate for video conference AND web conference presentation.**

The program focuses on how ratios relate two quantities, how their size has meaning, and how they are important at NASA.

Aeronautical engineers use ratios and proportions every day. The very first aeronautical engineers, Wilbur and Orville Wright, used ratios and proportions to design and test their aircraft and they are used by modern engineers in today's space program.

The Ratios and Proportions event demonstrates real world applications of math and physics principles as applied to aerodynamics. It shows participants why they "have to learn" graphing, problem-solving using fractions, decimals, and ratios and proportions.

Instructional Objectives

Engage |
The learners will discuss the definition of a ratio and examples of ratios. |

Explore |
The learners will investigate the combining of small right triangles to make larger and larger right triangles in the same ratio. |

Explain |
The learners will explain how the ratios of the sides of right triangles can be applied to everyday situations. |

Elaborate |
The learners will further discuss applications of ratios and scale models in the design and testing of aircraft. |

Evaluate |
The learners will evaluate their understanding of ratios by determining the favorable sizes of ratios like lift to drag and accidents per mile. |

## Sequence of Events

Pre-Conference Activities

What is a ratio? Go to Webmath to find out.

You can also ask "Dr. Math" about ratios Ask Dr. Math

Learn about writing ratios in different forms at Working with Ratios.

Vocabulary:

Ratio: comparing one quantity to another. An aspect ratio compares a wing's length to its cord.

Fraction: comparing one quantity to another, specifically comparing a numerator to a denominator.

Numerator: the top number in a fraction. In 3/7, the 3 is the numerator.

Denominator: the bottom number in a fraction. In 3/7, the 7 is the denominator.

Percent: a number comparison that converts a ratio to parts out of one hundred.

Cord: the length of a straight line drawn from the leading edge of a wing to the trailing edge.

Proportion: comparing of two ratios. Two is to nine as four is to eighteen. They can be used to solve problems like If a hanger can hold four aircraft, how many hangers would be needed to hold thirty-six aircraft?

Lift: an upward force generated by the wings of an aircraft.

Drag: a force generated by the air resisting a body moving through it; comparable to friction. Drag keeps as aircraft from moving forward.

Videoconference Activities

In this event the presenter will question the students as to what a ratio is and what are some of the ways that they are expressed. Decimals, fractions, percents, scale, and proportions will be discussed and examples used to show how they relate. He will discuss how a ratio is a comparison of two quantities, such as miles per gallon and cost per gallon. He will show how this is expressed mathematically by division. At this point he may have the class do an exercise such as calculate the ratio of boys to total students in the class.

The presenter will demonstrate a series of similar triangles to show how the ratio of the opposite to adjacent sides is always the same and how this allows us to carry out a number of applications using these ratios called trigonometry. Measurements and calculations will be done to demonstrate these relationships.

Models of the Space Shuttle in different scales are used to show how engineers can collect data from a small scale model and then use ratios to find out what this would be on a full scale device without having to build the full-scale device. Using ratios can save large amounts of time and money.

Finally the presenter will discuss what we can know from the size of a ratio. He will ask questions like, "What does it mean if the ratio if nearly one? What can you tell about a ratio that is much greater than one?". Some actual aeronautical engineering ratios like lift to drag are used to exemplify this concept. The engineer wants a lot of lift and little drag, so a large number for the ratio is desirable.

Some of the questions that have been asked during this module in the past are:

"How are ratios and decimals and percentages the same?"

"Why do you need to use ratios? When will you ever use them?"

"Can you give me some examples of ratios that you commonly use right now?"

"When might it be important for a ratio to have a value larger than one? smaller that one?"

Post-Conference Activities

Using what you have learned about ratios, now where do you think a 1:25 scale model of the 122 foot tall Space Shuttle would fit in your pocket, on your desk, or would you have to keep it in a parking lot?

To extend you knowledge about ratios and how to use them, try some of the following activities:

Grades 5-8

For some ratio applications to aeronautics using trigonometry take a look at Lift to Drag Ratio or try Glide angle as used by the Wright Brothers

## Standards

NCTM MATH STANDARDS

Number and Operations Standard

- Understand numbers, ways of representing numbers, relationships among numbers, and number systems

GRADES 6-8 understand and use ratios and proportions to represent quantitative relationships

Measurement Standard

- Apply appropriate techniques, tools, and formulas to determine measurements.

GRADES 6-8 solve problems involving scale factors, using ratio and proportion