scatter plot - a graphical display of data graphed on the coordinate plane showing a relationship between two sets of data

positive correlation - a trend in the data of a scatterplot in which the two sets of data are either both increasing or both decreasing

negative correlation - a trend in the data of a scatterplot in which as one set of data increases the other set of data decreases

no correlation - when there is no relationship in the two sets of data 

trend line - the line on the scatterplot that shows the trend in the data

line of best fit - the line on the scatterplot that best shows the trend in the data

bivariate - data that shows the relationship between two variables or two sets of data

univariate - data that involves a single relationship of one variable

outlier - a value that is much greater or much less than the rest of the data

linear regression - the process of finding a linear equation that best describes a set of points

quadratic regression - the process of finding a quadratic equation that best describes the relationship between two sets of data

cubic regression - the process of finding a cubic equation that best describes the relationship between two sets of data

Students will create a scatter plot for this bivariate data and find the trend line to describe the correlation of the data with 98% accuracy.

Students will write a summary report for the collection of data to compare the two types of graphical representations and the differences and similarities between the data with 95% comprehension.

60 - 80 minutes

• NCAA Sports Statistics:  http://www.ncaa.com/statistics/index.html
• Scatter Plots: http://illuminations.nctm.org/ActivityDetail.aspx?ID=146
• graph paper
• Laptop computer
• Paper
• Pencil
• Ruler
• Colored pencils
• recording worksheet      C:\Documents and Settings\Teacher\My Documents\Data Collection Worksheet.docx 
• Scatter Plots and Line of Best Fit Worksheet:  C:\Documents and Settings\Teacher\My Documents\Line of Best Fit.docx
• individual response devices (if available)
• graphing calculator (if available)

W: Explain to the students that they will be completing a project that will require that they analyze data, make predictions and observations about sports data using the a scatter plot and finding the line of best fit for the data and present this data in report format.

H: Ask introductory questions of the students to present the lesson relating to scatterplots and lines of best fit and their relation to sports.

E:  Question students about the scatterplot and line of best fit.  Present the website and worksheets needed to complete the lesson to the students.  Once the students have collected the data use the Thinkfinity resource to create a scatterplot.

R:  Students will meet in groups to discuss their collected data and students will determine if these results will make sense.  Students will determine if there are any outliers in the data and the effect that these cause on the data.  Students will make a comparison of the data and consider all aspects that affect the data.  Students will prepare to report on the data.

E: Students will individually complete an essay to discuss a series of questions about lines of best fit and scatterplots and the data that they have collected to make predictions about the data.

T:  The teacher will devise a mini quiz to inquire knowledge of the students' understanding of scatterplots and lines of best fit.  Students needing additional assistance will be placed into small groups to receive additional assistance.  The other students will collect data on the March madness basketball tournament for the previous year and create a scatter plot and line of best fit for the data and draw any conclusions that can be reached.

O: The focus of the lesson is to gather bivariate data about one sport and the two different gender teams that play that sport, organize and analyze this data, interpret the application of the data, and present this data in a report format.  Students will after collecting this data design a scatterplot and determine a line of best fit to make determinations about the teams and determine if gender has an impact on performance.

W: "In today's lesson, we are going to gather bivariate data, organize and analyze the data by a scatter plot and a line of best fit, interpret the application of the data to the real-world practical application and present the data in a report format."

H: "How do sports data relate to mathematics? (Some examples are: collection of statistics for points, goals, touchdowns, first place finishes) <allow time for students to respond> Are there displays that express the statistics of basketball into measures of central tendency, scatter plots, and box - and - whiskers plots? (yes, these can appear in sports magazines to show comparison of data) <allow time for students to respond> What is a scatterplot? (a graphical display of data graphed on the coordinate plane showing a relationship between two sets of data) What is a line of best fit? (the line on the scatterplot that best shows the trend in the data) <allow time for students to respond> Today, we will be looking at how NCAA sport's data can be used to draw these types of conclusions and how these displays can allow a person to look at and compare a female team's statistics to a male team's statistics in order to draw conclusions as to which is the better overall team?"

E:  Students will work in small groups and will have background knowledge of the material concepts to be completed.  "What is a scatter plot? (a graphical display of data graphed on the coordinate plane showing a relationship between two sets of data) <Students will provide information> What is a line of best fit? (the line on the scatterplot that best shows the trend in the data) <Students will provide information> "What are the types of correlations that they can have?" (negative correlation, positive correlation, and no correlation) <Students will provide information>  "What is quadratic regression?"  ( using the quadratic equation of best fit as the trend line to display the relationship between two sets of data) <Students will provide information>  "What is cubic regression?" (using the cubic equation of best fit as the trend line to display the relationship in two sets of data) <allow time for students to respond> "Using the website http://www.ncaa.com/statistics/index.html choose a NCAA team for data collection.  Collect data for both the male and female teams for that sport.  Use the data collection worksheet to record these numbers.  Also, select and indicate which category of reporting statistics will be used." 

<NOTE: If this is continuation of either lesson one or lesson one and two or lesson two the data does not need to be recollected.>

 "Once all the data is collected complete the "Scatterplot and Line of Best Fit Worksheet "and graph a scatterplot by using the Thinkfinity resourse for graphing scatterplots which is found at the URL  http://illuminations.nctm.org/ActivityDetail.aspx?ID=146."

R: "Now, look at the collected data and with your group draw determinations as to whether this data makes sense for the particular category of data that is being used (points per game, fouls, errors).  Are there any data items that would qualify to be an outlier for either team?  If so, discuss with your group what effect this will have on the scatterplot and the line of best fit. Also, discuss with your group any conclusions that can be drawn using the scatterplot and line of best fit as to how both teams compare.  Be sure to discuss all aspects that can be considered and be prepared to write an essay on the display of each team and comparsion of the two teams.  Determine whether gender has an impact on the overall performance of the team.  How can scatterplots and lines of best fit be used to make predictions about sports data? How can scatterplots and lines of best fit be used to make predictions about other real world applications? Give examples of these applications and where the applications would be used."

E:  Students will compare these plots as a group. Individually each student will create an essay:

• to discuss which team has the best overall record in the category selected;
• to discuss how each plot describes the data;
• describe if either team has an outlier data and the effect that this item(s) has on the overall data; 
• determine whether gender has an impact on the overall performance of the team;
• tell/show how the scatterplot and line of best fit can be used to make predictions about sports teams;
• identify what real world applications could be predicted using scatterplots and lines of best fit and how could these be used to make predictions using the data.

T: The following strategies will be used to tailor the lesson to each students needs:

Students will use the individual reponse devices to answer questions of a mini-quiz about box and whiskers plots.  Students' responses will be looked at and those students needing additional assistance on this concept will be placed into a small group to receive additional assistance.

Extension: Students will be use the data of the March madness basketball tournament for the previous year to determine the scatterplot and line of best fit for the tournament scores and determine if there is a pattern and any outliers that exist in the scores. 

O: The focus of the lesson is to gather bivariate data about one sport and the two different gender teams that play that sport, organize and analyze this data, interpret the application of the data, and present this data in a report format.  Students will after collecting this data will create a scatterplot and line of best fit to make determinations about the teams and determine if gender has an impact on performance.

Students' progress will be monitored by:

• inspection of the graph and linear regression equation being created;
• pair-share discussion checklists completed daily;
• mini quizzes with questions being answered through the use of interactive response devices with questions being placed on the interactive white board;
• correct usage of vocabulary associated with this section

• NCAA Sports Statistics:  http://www.ncaa.com/statistics/index.html
• Scatter Plots: http://illuminations.nctm.org/ActivityDetail.aspx?ID=146

• recording worksheet      C:\Documents and Settings\Teacher\My Documents\Data Collection Worksheet.docx 
• Scatter Plots and Line of Best Fit Worksheet:  C:\Documents and Settings\Teacher\My Documents\Line of Best Fit.docx