How can I organize data? Can I use this data to make a prediction? What does a point represent? Is there a connection between the two variables?

Transcription

1 Common Core Standard: 8.SP.1 How can I organize data? Can I use this data to make a prediction? What does a point represent? Is there a connection between the two variables? CPM Materials modified by Mr. Deyo

2 Title: IM8 Ch Is There A Relationship? Date: Learning Target By the end of the period, I will create scatterplots and identify whether there is a relationship between two sets of data. I will also draw a line of best fit and use it to make predictions. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.

3 Home Work: Sec Desc. Date Due Review & Preview 3 Problems: 7 17, 7 18, 7 19

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5 Vocabulary 1) Association 2) Positive Association 3) Negative Association 4) Line Of Best Fit

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7 7.1.2 Is There A Relationship? In Lesson 7.1.1, you looked at single data sets, such as world population. Often, you need to compare two measurements to answer a question or to see a connection between two types of data. For example, comparing the odometer reading of a car to the price of a car can help determine if these factors are related. In this lesson, you will study scatterplots, a new tool for visually presenting data, as a way to relate two sets of measurements. You will be asked to analyze the data to see if you can make predictions or come to any conclusion about the relationships that you find. As you work, keep these questions in mind: How can I organize data? Can I use this data to make a prediction? What does a point represent? Is there a connection between the two variables?

8 7 13. HOW MUCH IS THAT CAR? Nate and Rick were discussing cars again. Nate claimed that cars with lower odometer readings were more expensive than cars with higher odometer readings. His evidence was that his car with 23,000 miles was worth more than Rick s car with 31,000 miles. To investigate Nate s claim, the boys collect data from several car advertisements and graph the information from the table. Price (Thousands of Dollars) Does the information in the table support Nate s claim? That is, do you believe Nate s claim that cars with a lower odometer reading cost more money? Odometer Reading (Thousands of Miles)

9 7 14. Melissa looked at the data from problem 7 13 and said, I need to be able to see the data as a picture. I cannot tell if there is a relationship from the lists of numbers. She decided to use a box plot. Her box plots for odometer reading and price are shown. Do these pictures help you decide if Nate is correct? Why or why not?

10 Price (Thousands of Dollars) a,b,c. Melissa wondered if a coordinate graph could help determine if there was a relationship in Nate s data from problem a) Follow the directions below to create a scatterplot of the data for Melissa. Set up a graph showing Odometer Reading on the x axis and Price on the y axis. Label equal intervals on each axis so that all of the data will fit on the graph. Plot the data points from problem b) Describe the scatterplot you just created. What do you notice about how the points are placed on the graph? Do you see any patterns? Odometer Reading (Thousands of Miles) c) Place an additional point on your graph for Nate s car that has an odometer reading of 23,000 miles. Explain your strategy for deciding where to put the point.

11 Price (Thousands of Dollars) d,e,f. When a relationship exists, one way to help show a trend in the data is to place a line or curve that, in general, represents where the data falls. This line, sometimes called a line of best fit, does not need to touch any of the actual data points. Instead, it shows where the data generally falls. The line is a mathematical model of the data. Models of data help you describe the data more easily and help you make predictions for other cars with different mileages. d) With your team, decide where a line of best fit could be placed that would best model the data points. Are there any limits to where your line makes sense? e) Using the line of best fit, can you predict the price of a car with an odometer reading of 80,000 miles? If so, explain how the line of best fit helps. If not, explain why it is not helpful Odometer Reading (Thousands of Miles) f) Based on the scatterplot, would you agree with Nate s claim that cars with a higher odometer reading cost less? Use the scatterplot to justify your answer.

12 7 16a. Sometimes what you know about relationships can help you predict what data will look like when it is graphed. For each situation below: Look at the scatterplots and use your experience to decide which statement fits each scatterplot. Decide if there is a relationship between the data. That is, as one quantity changes, does the other change in a predictable way? If there is a relationship, describe it in a sentence. If there is no relationship, explain why you think there is not one. a) How fast a dog can run and the length of the dog's fur. Which scatterplot matches? What's the relationship? Why / Why not?

13 7 16b. Sometimes what you know about relationships can help you predict what data will look like when it is graphed. For each situation below: Look at the scatterplots and use your experience to decide which statement fits each scatterplot. Decide if there is a relationship between the data. That is, as one quantity changes, does the other change in a predictable way? If there is a relationship, describe it in a sentence. If there is no relationship, explain why you think there is not one. b) A person's age and their body temperature. Which scatterplot matches? What's the relationship? Why / Why not?

14 7 16c. Sometimes what you know about relationships can help you predict what data will look like when it is graphed. For each situation below: Look at the scatterplots and use your experience to decide which statement fits each scatterplot. Decide if there is a relationship between the data. That is, as one quantity changes, does the other change in a predictable way? If there is a relationship, describe it in a sentence. If there is no relationship, explain why you think there is not one. c) The child's age and the size of his or her feet. Which scatterplot matches? What's the relationship? Why / Why not?

15 7 16d. Sometimes what you know about relationships can help you predict what data will look like when it is graphed. For each situation below: Look at the scatterplots and use your experience to decide which statement fits each scatterplot. Decide if there is a relationship between the data. That is, as one quantity changes, does the other change in a predictable way? If there is a relationship, describe it in a sentence. If there is no relationship, explain why you think there is not one. d) Outdoor temperature and the percentage of people wearing long sleeve shirts. Which scatterplot matches? What's the relationship? Why / Why not?

16 7 17. HOW MUCH IS THAT CAR? chapter/ch7/lesso Nate and Rick were still talking about cars. Nate claimed that cars with more horsepower were more expensive than cars with less horsepower. His reason was that his 300 horsepower sports car was worth more than Rick s 120 horsepower small economy car. To investigate Nate s claim, the boys looked up information about their friends cars. The table here shows the results. a) Does the information in the table support Nate s claim that cars with more horsepower cost more? Is there a relationship between horsepower and the price of a car? b) Set up a graph and plot the points from the table. Now do you believe Nate s claim? Explain your reasoning.

17 7 18a. Look at the scatterplots and use your experience to decide which statement fits each scatterplot. If there is a relationship, describe it in a sentence. chapter/ch7/less a) A city s average daytime temperature in January and its latitude. Recall that the equator is at 0 latitude and the poles are at 90 latitude. Which scatterplot matches? What's the relationship? Why / Why not?

18 7 18b. Look at the scatterplots and use your experience to decide which statement fits each scatterplot. If there is a relationship, describe it in a sentence. chapter/ch7/less b) Weight of a car and its speed in a traffic jam on the freeway. Which scatterplot matches? What's the relationship? Why / Why not?

19 7 18c. Look at the scatterplots and use your experience to decide which statement fits each scatterplot. If there is a relationship, describe it in a sentence. chapter/ch7/less c) Number of pets a student has at home and his or her grades. Which scatterplot matches? What's the relationship? Why / Why not?

20 7 18d. Look at the scatterplots and use your experience to decide which statement fits each scatterplot. If there is a relationship, describe it in a sentence. chapter/ch7/less d) Cost of a person s home and the value of his or her car. Which scatterplot matches? What's the relationship? Why / Why not?

21 7 19. Match the system of equations in the left column with its solution in the right column. a) 6x y = 4 3x + y = 5 1) (0, 4) chapter/ch7/le b) x = y + 4 2x + 3y = 12 2) (3, 7) c) 5x 2y = 1 y = 2x + 1 3) (1, 2)

22 7 20. Use the rectangle to answer the following questions. chapter/ch7/l a) Find the area of the entire rectangle. (Explain how you found your solution.) b) Calculate the perimeter of the figure.

23 7 21a,b. Evaluate each expression below for a when a = 2, if possible. 3 a) 24a b) 3a

24 7 21c,d. Evaluate each expression below for a when a = 2, if possible. 3 a 0 c) d) 0 a

25 7 22. The school library has 6500 titles in its collection of books, magazines, and reference materials. The librarian is presenting information about the library to the parent association, and she made the graph. a) According to the graph, what percent of the collection are nonfiction books? homework/homework/category/cc/textbook/cc3/ chapter/ch7/lesson/7.1.2/problem/7 22 b) Could the librarian have presented this information in a histogram? Why or why not? c) How many of the books in the library are fiction?