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Unit 4 Lesson 6Demonstrating Mastery

Unit 4 Lesson 6 demonstrating mastery1M.8.SP.2To demonstrate mastery of the objectives in this lesson you must be able to:Know that straight lines are widely used to model relationships between two quantitative variables.Informally fit a straight line to a scatter plot that shows linear association.Informally assess the model fit by judging the closeness of the data points to the line.

To demonstrate mastery of the objectives in this lesson you must be able to: Know that straight lines are widely used to model relationships between two quantitative variables. Informally fit a straight line to a scatter plot that shows linear association. Informally assess the model fit by judging the closeness of the data points to the line.

2Performance Task for Demonstration of MasteryTask: You are one of the managers for the Tigers basketball team. Your job is to keep track of playing time and points scored for each player during the season. The coach wants to use the data to help plan for next years season and needs your assistance. To help the coach you will:fit a straight line to data displayed in a scatter plot.make predictions based on the graph of a line that has been fit to data.

Task: You are one of the managers for the Tigers basketball team. Your job is to keep track of playing time and points scored for each player during the season. The coach wants to use the data to help plan for next years season and needs your assistance. To help the coach you will: fit a straight line to data displayed in a scatter plot.make predictions based on the graph of a line that has been fit to data.

3The average minutes played and average points scored for the players on the Tigers Basketball Team.Average minutes played124618221416516152710145Average points scored10362018141231412268124

The averages of playing time and points scored collected after 25 games are displayed in the table. 4

To construct a scatter plot of these data, you need to determine the independent and dependent variable. In this case, the number of points scored depends on the amount of playing time. Therefore, average points scored is your dependent variable and should be graphed on the y-axis. The average minutes played is your independent variable and should be graphed on the x-axis. Use ordered pairs to graph each point (12,10), (4,2), (6,6) etc.. Be sure to use appropriate scales on the axes. The scatter plot clearly indicates a positive linear association indicating that the more minutes you play the more points you score. 5Task ContinuedDraw a line in the plot that you think would fit the trend in the data.Use your line to answer the following questions for the coach.What is your prediction of the points scored for a player that plays an average of 11 minutes? What is your prediction of the points scored for a player that plays an average of 6 minutes?How many minutes would the coach need to play a player in order for him to average 14 points?Use the line to predict the average points scored when averaging 18 minutes of playing time? How far off was your prediction from the actual average points?

When informally fitting a line, you want to find a line for which the points in the scatter plot tend to be the closest. 7Task AnswersA player that plays an average of 11 minutes will average scoring approximately 9 points. A player that plays an average of 6 minutes will average scoring approximately 5 points. The coach would need to play a player an average of 17 minutes in order for him to average 14 points per game.The line indicates that a player will average 15 points when he plays an average of 18 minuets per game. The observed data was 16 points, so the line predicted an average score of 1 point less than the observed value.

When using a line to predict the outcome, you take all of the points into consideration, and your prediction is based on an overall pattern rather than just one or two points. 8