1 Rates are used in many situations to describe and compare information. For example, you might compare the gas mileage of different vehicles when you are buying a car. (Gas mileage refers to how many miles each car can travel per gallon of gas.) You may also want to determine the print quality of a printer by comparing different printers’ numbers of dots per square inch. In banking, the percent of interest earned per dollar (called “interest rate”) is an important rate to consider. Today you will focus on different ways to display rates in tables and graphs as a way to compare information. As you work with your team, ask each other these questions: Which quantities can we compare? Are the ratios equivalent? How else can the ratio be expressed?

2 Wendy’s Data Time (seconds) Distance (meters) The local news station is selecting this week’s student for “Athlete of the Week.” Wendy and Yoshie, sprinters on the track team, are both finalists. They are trying to decide who is fastest based on recent race data. Wendy’s times are represented in the table above. a)Copy the table and use the relationship shown in it to complete the table for Wendy. How can you use the table to find Wendy’s running rate? How can you write her rate as a ratio? Explore using the 7-14 & 15 Student eTool (Desmos).7-14 & 15 Student eTool b)Yoshie can run 70 meters in 11 seconds, which can be expressed by the ratio 70 meters:11 seconds. Do the two runners travel at the same speed? If not, who is running faster? Explain your reasoning.

3 a)Create a table of values for Yoshie’s running rate similar to the one for Wendy in problem 7 ‑ 14. Work with your team to decide how to set up the table and complete it. b)Using the coordinate grid on the Lesson 7.1.2A Resource Page or the 7-14 & 15 Student eTool (Desmos), plot pairs of values from each table and create a line for Yoshie and a line for Wendy. Use color or another means to distinguish and label the two lines. Lesson 7.1.2A Resource Page7-14 & 15 Student eTool c)Based on the graph, who is running faster? Does this match your conclusion from part (b) of problem 7-14? Justify your answer. d)The graph at right shows information for Vanessa, last week’s Athlete of the Week. What is Vanessa’s rate? If she were to race Yoshie and Wendy, who would win? Explore using the 7-14 & 15 Student eTool (Desmos)7-14 & 15 Student eTool 15. To compare the two runners, the news station wanted to make a graph of their rates.

4 16. TRAINING FOR THE TRIATHLON A triathlon is a race in which participants swim, bike, and run specific distances. Participants start by swimming. After swimming, they jump out of the water, get dressed as fast as they can, and ride a bicycle. After they complete the biking section, the participants finish the race by running several miles. Diane is preparing for her first triathlon. She used the graph to analyze one of her practice sessions. Use the graph at right to help you answer the questions below. During which segment of the race (a, b, or c) did Diane go the fastest? Explain your reasoning. Explore using the 7-16 Student eTool (Desmos) or the Lesson 7.1.2B Resource Page.7-16 Student eToolLesson 7.1.2B Resource Page a)During which segment of the race (a, b, or c) did Diane go the fastest? Explain your reasoning. b)Use the graph to determine the distance traveled during each segment of the race. c)How much time did it take Diane to complete each segment of the race? d)Write a rate (in miles per minutes) for each segment of the race.

5 17. Edgar is training to be on the cross-country team at his high school. Edgar has training runs that are two different lengths. One trail is 4 miles, and he usually completes it in 0.5 hours (30 minutes). If he runs the 10-mile trail, it usually takes him 1.25 hours (75 minutes) a).Graph points for the length and time of Edgar’s run on a graph. Does it make sense to connect the points? Where could you add a point to show how far he has traveled after 0 minutes? b)Helena is a long-distance runner. Once a week, she does a 17-mile training run that usually takes her 2 hours. Does she run slower or faster than Edgar? How do you know?

6 18. Match each situation in parts (a) through (d) with its graph below. Then state the rate in a ratio of miles to minutes a).Family A travels 30 miles in 25 minutes. b)Family B travels 60 miles in an hour. c)Family C travels 50 miles in an hour. d)Family D travels 60 miles in 1hours. e)One graph below was not matched with a situation from parts (a) through (d). If Family E is represented by the unmatched graph, describe the rate of travel for Family E as a ratio of miles to minutes.

7 Tonight’s homework is… Review & Preview, problems # Show all work and justify your answers for full credit.