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Proportional RelationshipsBy Janie Solinski-Ruddy for use with Chirping Crickets

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Proportions are Comparisons of Two Equal Ratios

A relationship where one number of the ratio increases by the same factor as the other number in a ratio is said to be DIRECTLY PROPORTIONAL

A relationship where one number of the ratio decreases by the same factor as the other number in a ratio increases is said to be INVERSLY PROPORTIONAL.

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Directly Proportional Relationships

• Number of calories in a candy bar as the number of sugar grams increases.

• The hours of studying and the grade on a test.

• The number of hours that the lights are on in a home and the cost of the electric bill.

• Provide Your Own Example!

Evan Amoshttp://en.wikipedia.org/wiki/Reese's_Fast_Break#mediaviewer/File:Candy-Reeses-Fast-Break-Broken.jpg

http://www.public-domain-image.com/objects-public-domain-images-pictures/electronics-devices-public-domain-images-pictures/electric-lights-pictures/light-bulb.jpg.html

+Inversely Proportional Relationships• The hours spent exercising and Body Mass

Index

• The faster you drive the fewer hours it takes to get to your destination

• The more people who help paint a fence, the number of hours needed to paint the fence by each person decreases.

• Provide an Example of your own!

Borden 31http://commons.wikimedia.org/wiki/File:Painting_a_Fence.JPG

Senior Airman Myles Stepphttp://www.altus.af.mil/shared/media/photodb/photos/111021-F-BT139-620.jpg

+Can a Directly Proportional Relationship be Represented Graphically?

Create a graph that you think will show a directly proportional relationship.

Does your graph look similar? A directly proportional relationship will form, usually, an increasing line.

Sewaquhttp://en.wikipedia.org/wiki/Least_squares#mediaviewer/File:Linear_regression.svg

+Can an Inversely Proportional Relationship be Represented Graphically?

Create a graph that you think will show an inversely proportional relationship.

Does your graph look similar?

Renze, John and Weisstein, Eric W. "Scatter Diagram." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ScatterDiagram.htmlhttp://mathworld.wolfram.com/ScatterDiagram.html