In the previous lessons, you studied different ways to represent proportional relationships. You organized information into tables and graphs. You also wrote equations modeling the proportional relationships. Proportional relationship equations are of the form y = kx, where k is the constant of proportionality. Today you will find connectionsbetween different representations of the same proportional relationship, explore each representation more deeply, and learn shorter ways to go from one representation to another. As you work today, keep these questions in mind:
How can you see growth in the rule?
How do you know your rule is correct?
What does the representation tell you?
What are the connections between the representations?
4-55. Graeme earns $4.23 for each half hour that he works. How much money does he earn during a given amount of time?
A. Represent this situation using a table
B. What is the constant of proportionality (or the unit rate)? How can you find it from a table?
C. How can you use a table to determine if a relationship is proportional?
4-56. Jamie ran 9.3 miles in 1.5 hours. How far can she run in a given amount of time, if she runs at a constant rate?
A. Represent this situation with a graph.
B. What is the constant of proportionality? How can you find it on a graph?
C. How can you use a graph to determine if a relationship is proportional?
4-57. A recipe calls for 2 cups of of flour to make two regular batches of cookies. Shiloh needs to make multiple batches of cookies.
A. Represent this situation with an equation.
B. What is the constant of proportionality? How can you identify it in an equation?
C. How can you use an equation to determine if a relationship is proportional?
4-58. CONNECTIONS WEB FOR PROPORTIONAL RELATIONSHIPS
Your teacher will assign your team a situation from the previous problems. Your team’s task is to create a poster showing every way you can represent the proportional relationship and the connections between each representation. Use the web at right to help you get started.
4-59. LEARNING LOG
In your Learning Log, create a generic connections web for proportional relationships. For each representation, explain how you know the relationship is proportional. Title this entry “Connections Web for Proportional Relationships” and label it with today’s date.
Unit Rate
A rate is a ratio that compares, by division, the amount one quantity changes as another quantity changes.
A unit rate is a rate that compares the change in one quantity to a one unit change in another quantity. For example, miles per hour is a unit rate, because it compares the change in miles to a change of one hour. If an airplane flies 3000 miles in 5 hours and uses 6000 gallons of fuel, you can compute several unit rates.
It uses or
It travels at .
1.