MILES PER GALLON

Enduring Understanding: Develop a better understanding of how to use data from a table to create a graph and make a prediction of values not included in the data set. How to compare two sets of data.

Essential Questions:

  • What is an informative title for a graph?
  • What are appropriate intervals for the x- and y-axes?
  • How is the dependent and independent variable determined?
  • How is a fitted line determined?
  • How is a fitted line represented as an equation?
  • How is a fitted line used to make a prediction?
  • What does the slope of the graph mean within a scenario dealing with miles per gallon and speed?

Lesson Overview:

  • Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to driving habits; speed at which people drive; cost of gasoline; how much effect the cost of gasoline has on people’s driving habits and on other aspects of their lives.
  • What is meant by dependent and independent variable?
  • Discuss a “fitted line”—What is it? How would a person use a fitted line? How would you show an understanding of a fitted line? Why do you think a fitted line is used? What would happen if a person inaccurately used a fitted line? What operations are necessary to create a fitted line?
  • When reading a graph, where are the x- and y-intercepts? What is the relationship between the intercepts and the context of any problem?
  • What is meant by a meaningful title for a graph?
  • How are the intervals on a graph determined?
  • How can you support a conclusion that you make? What evidence from graphs can be used to support/justify your conclusion?
  • Use resources from your building.

EALRs/GLEs

1.2.3

1.4.4

1.5.4

3.2.2

5.1.1

Item Specifications: ME02; PS03; AS02; SR04; MC01

Assessment:

  • Use WASL format items that link to what is being covered by the classroom activity
  • Include multiple choice questions

Miles Per Gallon

An engineer collects data showing the speeds of a Passenger Car and its average

miles per gallon, M.

Engineer’s Data for a Passenger Car’s Speed and

Miles per Gallon

Speed

(s) /

Miles per Gallon

(M)
30 / 18
35 / 20
40 / 23
45 / 25
50 / 28
55 / 30

Analyze the Data:

  1. Graph the data from the table.

______

  1. Draw a line that fits the data set (fitted line).
  2. Write an equation that describes the fitted line ______
  1. What is the y-intercept? ______In real-world terms, what does the y-

intercept represent in the context of this situation? ______

______

Is that a meaningful value in the context of this situation? ______

______

  1. Is there a x-intercept? ______If so, what is it? ______

Does the x-intercept have any meaning within the context of this situation? ______

______

______

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  1. What is a realistic maximum x-value? ______
  1. Determine the slope of the graph: ______
  1. What does the slope mean within the context of this situation? ______

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  1. Using your model, predict the miles per gallon at 70 miles per hour.

The table below is the rest of the engineer’s data:

Engineer’s Data for a Passenger Car’s Speed and

Miles per Gallon

Speed

(s) /

Miles per Gallon

(M)
60 / 29
65 / 26
70 / 25
75 / 23
  1. On the same graph that you used for the first table, graph the data from this table in a different color.
  1. How does this new data compare with the prediction that you made in question #9?

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  1. Given the current situation with an apparent gasoline shortage and high prices for gasoline and as a member of the committee for saving gasoline, you are being asked to make a recommendation to others regarding what they could do to reduce the amount of gasoline used while driving. How does this second set of data have an influence on you with regards to how fast you drive? Why?

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13. Which is the slope of the line on the graph?

O A. -4

O B. -3

O C. 3

O D. 4

14. Amanda left her downtown office and rode a bus at an average speed of 20 miles per hour to a parking lot where her car was parked. She drove home at an average speed of 50 miles per hour. The entire distance she traveled was 75 miles, and the time spent riding the bus and driving home was 2 hours.

Which measure is closest to the distance from the parking lot to her house?

O A. 20 mi.

O B. 35 mi.

O C. 58 mi.

O D. 72 mi.

15.

Car Atravels for three hours.

Which is the number of kilometers that Car A is ahead of Car B?

O A. 2

O B. 10

O C. 20

O D. 25