All About Ratios: Math You Use Everyday
Target Audience: Students
Hosting Center: Glenn Research Center
Subject Category: Math
Unit Correlation: Exploring Engineering and Technology
Minimum Delivery Time: 030 min(s)
Maximum Connection Time: 060 min(s)
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?
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.
The learners will decide whether or not to take an easy, legal job for $1,000.
The learners will explore a variety of ways that we can compare quantities.
The learners will explain different ways that ratios can be expressed.
The learners will evaluate their understanding of ratios by discussing their application in scale models.
The learners will explain how the size of a ratio can be favorable or unfavorable
Sequence of Events
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.
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.
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?"
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:
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
Apply appropriate techniques, tools, and formulas to determine measurements.
GRADES 6-8 solve problems involving scale factors, using ratio and proportion