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All About Ratios: Math You Use Everyday

Target Audience: Students

Hosting Center: Glenn Research Center

Subject Category: Math 

Unit Correlation: Exploring Engineering and Technology

Grade Level:

  • 5-8
  • 9-12

Minimum Delivery Time: 030 min(s)

Maximum Connection Time: 060 min(s)


Event Focus

If you were given a 1:75 scale model of the Space Shuttle, would it fit in your pocket, on your desk, or would it have to stay in your driveway?   What are ratios and how do we interpret them?

 

Description

This module is appropriate for videoconference AND web conference presentation.

This program focuses on how ratios relate two quantities, how the size of a ratio has meaning in many contexts, how we use ratios in our every day lives, and how they are important to NASA.

The Ratios program demonstrates real world applications of math to areas such as velocity of vehicles, the cost of goods, and the consideration of an hourly wage. It shows participants why they are going to need this math skill in their future lives.

 

Instructional Objectives

 

Engage

The learners will decide whether or not to take an easy, legal job for $1,000.

Explore

The learners will explore a variety of ways that we can compare quantities.

Explain

The learners will explain different ways that ratios can be expressed.

Elaborate

The learners will evaluate their understanding of ratios by discussing their application in scale models.

Evaluate

The learners will explain how the size of a ratio can be favorable or unfavorable


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.

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 can be expressed. In making the point that almost any quantity can be compared in a ratio, the presenter will show them a water bottle and a wooden dowel and ask the students to come up with a number of different ways that the two can be compared. Decimals, fractions, percents, scale, and proportions will be discussed and examples used to show how they could relate two different quantities.

The presenter will demonstrate the many ways that we use ratios in out daily lives. He will ask them is they will take a job that pays $1,000 and then draw out that they need to know the time required as well. Salaries are ratios of time and money. He will discuss how we always use ratios to compare numerous quantities, such as miles per gallon and cost per gallon. He will show how division expresses this mathematically.

Models of the Space Shuttle in wind tunnels will be used to illustrate 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, money, and lives.

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 large 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 1:75 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

The Math League

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 

 

 

Page Last Updated: August 29th, 2014
Page Editor: NASA Administrator