Name of Task: Impact of a Player
Task: From NCTM Illuminations: http://illuminations.nctm.org/LessonDetail.aspx?id=L673
In this activity, students will use the Illuminations Line of Best Fit Activity to plot the data from
two teams during the 2004-05 NBA season. In particular, students will look at the data for total
points and minutes played by each of the starters on the Los Angeles Lakers and Detroit
Pistons. The data suggest that Laker Kobe Bryant is an outlier—he scores more points per
minutes than his teammates, which is part of why some sportswriters have described him as
"selfish." But through further investigation, students will also notice that Piston Ben Wallace is
also an outlier, because he scores fewer points than his teammates.
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Learning Objectives
Students will:
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
Use technology tools to plot data, identify lines of best fit, and detect outliers
Compare the lines of best fit when one element is removed from a data set, and
interpret the results
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Materials
Illuminations Line of Best Fit Activity
Impact of a Superstar Activity Sheet
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Instructional Plan
This lesson gives students an opportunity to identify an outlier within a set of real-life data.
The context for this investigation involves data for the Los Angeles Lakers and Detroit Pistons
for the 2004-05 NBA season. However, you may wish to choose other data sets for use in your
classroom. For geographical reasons, you might want to use teams closer to your school. To
match the interest of students, you may wish to use data regarding players from a different
sport. Or, if your students are generally uninterested in sports, you may wish to use a
completely different set of data.
Using the Illuminations Line of Best Fit Activity, students plot sets of data. Within each of these
sets of data, there is an outlier that students can detect in either of two ways:
1. By visual inspection. A scatterplot of the data will show that some points are not
aligned with the others.
2. By correlation comparison. By removing one player's data at a time, students can
determine which player's data has the greatest impact on the correlation coefficient.
Students can do a visual inspection using paper-and-pencil techniques, but repeatedly
determining the correlation coefficient on a set of data when points are removed can be quite
cumbersome. The use of technology, however, allows for the situation to be explored quickly
and removes the tedium of the calculations. Consequently, it is the second method that will be
covered more thoroughly in this lesson.
Line of Best Fit Activity
Begin the lesson by distributing the Impact of a Superstar activity sheet. The first page of the
activity sheet provides some background information about the teams. The data to be entered
into the Line of Best Fit activity can be found on the second page of the activity sheet. (In
addition, all of the data appears in the Team Data Spreadsheet (Excel), and two columns of data
can be pasted from an Excel spreadsheet into the text box in the Line of Best Fit activity, and
when the Update Plot button is pressed, the points will appear in the scatterplot.)
Impact of a Superstar Activity Sheet
Following the directions on the activity sheet, students will first work with the data for the Los
Angeles Lakers. They will plot the data and then determine the line of best fit for this data. In
particular, they will want to take note of the correlation coefficient (r-value) for the regression
line. Then, one at a time, students will remove one player's data from the set and determine what
effect, if any, the removal of that player's data has on the line of best fit and correlation
coefficient. [For the Lakers, students will notice that the correlation coefficient is 0.75 when the
data for all players is considered. However, when the data for Kobe Bryant is removed, the
r-value increases to 0.95; when the data for any other player is removed, the correlation
coefficient either stays the same or decreases. This indicates that the data for Kobe Bryant might
be an outlier.]
Questions 1-6 on the activity sheet take students step-by-step through the process for removing
one player's data and considering the effect on the correlation coefficient. In Question 7,
however, students are left to conduct a similar experiment on their own using data for the
Detroit Pistons. [In this investigation, students will likely notice that Ben Wallace represents
something of an outlier. When the data of any other player is removed, the r-value does not
change significantly; but when the data for Ben Wallace is removed, the correlation coefficient
increases from r = 0.85 to r = 0.97.]
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Questions for Students
Does it appear that the data for any player from either team represents an outlier?
[It appears that the data for Kobe Bryant represents an outlier for the Lakers, and the data for
Ben Wallace represents an outlier for the Pistons.]
Some sportswriters have accused Kobe Bryant of being a selfish basketball player; that is, they
say he tries to score more than he tries to help his team. Do the results of this investigation
seem to support that accusation? Given that Ben Wallace is also an outlier, could he be
accused of being selfish, too?
[The data suggests that Kobe Bryant scores more points per minute than his teammates.
However, it is difficult to determine if that is a result of selfishness. Perhaps he is just a better
basketball player. On the other hand, Ben Wallace scores fewer points per minute than his
teammates, which would suggest that he is not selfish. The reason he scores fewer points is
that he concentrates on rebounding and blocking shots more than scoring.]
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Assessment Options
1. Collect student work on the Impact of a Superstar activity sheet.
2. Allow students to analyze another set of data using the Illuminations Line of Best Fit
activity. Students should be able to identify any outliers and explain how they know.
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Extensions
1. Allow students to combine the data for the Lakers and the Pistons and consider the
complete set. Are either Kobe Bryant or Ben Wallace outliers in this set? Are both of
them still outliers? How do you know? [The correlation coefficient is 0.77 when all
players are included. When data for both players are removed, the correlation
coefficient increases to 0.96. If either Kobe or Ben are removed, it increases to 0.88
and 0.83, respectively. It could therefore be said, perhaps, that the data for Kobe is
more of an outlier than the data for Ben.]
Alignment to Content Standards:
Alignment to Practice Standards:
Mathematical Goals:
What do you want students to know and understand about mathematics as a result of this lesson?
Prerequisite Knowledge:
What definitions, concepts, or ideas do students
need to know to begin to work on the task?
Accessing Prior Knowledge:
What questions will you ask to help students
access their prior knowledge and relevant life and
cultural experiences?
Task Solutions:
What are all the ways the task can be solved?
Anticipated Student Solutions:
Which of these methods do you think your students
will use?
Anticipating Misconceptions:
What misconceptions might students have? What errors might students make?
Resources/Tools:
What resources or tools will students have to use in their work that will give them entry into, and help
them reason through, the task?
Structure:
How will the students work—independently, in small groups, or in pairs—to explore this task? How long
will they work individually or in small groups or pairs? Will students be partnered in a specific way? If
so, in what way?
Questions that Assess and Advance Student Learning:
How will you help a group get started on the task? How will you focus student thinking on the key
mathematical ideas in the task? How will you assess student understanding of key mathematical ideas,
problem-solving strategies, or the representations? How will you advance student understanding of the
mathematical ideas? How will you encourage all students to share their thinking with others or to
assess their understanding of their peers’ ideas?
Reminder: The questions you ask should keep the task at a high level, not push kids toward
a particular solution path, turning the task into an opportunity to practice procedures.
Selection:
Sequencing:
What solution paths do you want to have shared
In what order will the solutions be presented?
during the class discussion?
Why?
Connect:
What specific questions will you ask so that students: Make sense of the mathematical ideas you want
them to learn? Expand on, debate, question, the solutions being shared? Make connections among the
different strategies that are presented? Look for patterns? Begin to form generalizations?
Extensions of the Task:
What will you do tomorrow that will build on this lesson?