Height and Wingspan1
During this lesson students will measure, record and graph the height and wingspan of members
in their class. They will informally model the graph by drawing a line of best fit. Students will
use the equation of their line to make predictions. They will extend their learning by exploring an
additional scatter plot.
Suggested Grade Range: 7th – 8th Grade
Approximate Time: 60 minutes
Common Core State Standards for Mathematics (CA):
CCSS.8.SP
1. Construct and interpret scatter plots for bivariate measurement data to investigate
patterns of association between two quantities. Describe patterns such as clustering,
outliers, positive or negative association, linear association, and nonlinear association.
2. Know that straight lines are widely used to model relationships between two
quantitative variables. For scatter plots that suggest a linear association, informally
fit a straight line, and informally assess the model fit by judging the closeness of the
data points to the line.
Lesson Content Objectives:
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Collect and graph data that suggests a linear association.
Use a line of best fit to model the data and make predictions.
Materials Needed:
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Graph paper
Tape measure (one per partner pair)
Rulers (one per student)
“Scatter Plots and Line of Best Fit” Activity Sheet
References:
Shake It Up with Scatterplots. Retrieved from
http://www.scholastic.com/browse/lessonplan.jsp?id=449.
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An early version of this lesson was adapted and field-tested participants in the California State
University, Long Beach Foundational Level Mathematics/General Science Credential Program.
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Summary of Lesson Sequence:
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Provide students with two scatterplots. Discuss the patterns they notice.
Ask students to measure height and wingspan. Using whole class data, ask students to
graph data and determine a line of best fit.
Instruct students to determine the equation of the line of best fit and use the equation to
make predictions.
Return to the example at the beginning of the lesson to reinforce concepts learned
throughout the lesson.
Assumed Prior Knowledge:
Students should have previous experience taking measurements (in centimeters) using a
tape measure. Students should also have prior knowledge of constructing a graph given a
table and writing a linear equation given two points.
Classroom Set-up:
Students will be asked to work with a partner and small groups for portions of this lesson.
Students will also participate in whole class discussion.
Lesson Description:
Introduction
Provide students with the “Scatter Plots and Line of Best Fit” handout. Mathematicians
often try to find relationships between two quantities. One way this can be done is by
graphing the data to determine if a pattern exists. Ask students to look at the two graphs
at the top of the handout and write down any patterns they notice. After students have
worked independently for a few minutes, ask:
Do you notice a pattern in the graph shown in example 1?
Do you notice a pattern in the graph shown in example 2? What can you say about the
relationship between math and verbal SAT scores?
Discuss with students that the data shown in the graph of the SAT scores suggests a linear
association between the two sets of data. Discuss the difference between a positive and
negative linear association. Ask:
What type of association do you notice in example 2?
Does the graph in example 1 suggest a linear association? Why or why not?
Explain to students that they will return to the SAT scores examples at the end of the
lesson. Ask students to turn their paper over to the side labeled “Height and Wingspan.”
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Introduce Marcus Vitruvius to students. Vitruvius, a Roman writer, architect and
engineer, suggested that a person’s height and wingspan are approximately equal. In this
lesson, students will explore the relationship between height and wingspan to determine
if Vitruvius was correct.
Input and Model
Provide each partner pair with a tape measure. Instruct students to measure the height and
wingspan of each person to the nearest centimeter. Model for students how to accurately
measure height and wingspan. Have students stand against the wall to measure their
height. Have students hold their arms and hands parallel to the floor to get an accurate
wingspan.
Project the table on the overhead. Ask students to record their height and wingspan
measurements in the table on the overhead. Then ask students to record the whole class
data in the table on their handout.
Provide students with an opportunity to graph the data points in their table. Discuss with
the class what an appropriate scale would be given the data. Note: It is important that
they can see a positive linear association between the data points. Because of this, suggest
to students to begin their scales on the x- and y- axes at a specific value (i.e. 140 cm).
Graph the data on the overhead while students create the graph on their own paper. After
students have graphed the data, ask:
Do you notice a pattern in the graph?
Does the pattern suggest a relationship between the two sets of data?
Is there a positive association between the two sets of data? Negative association?
Instruct students to use their ruler to draw a line that best approximates the data points.
Discuss with students why it would not make sense to connect the line with the y-axis
(this point would represent someone with 0 height). Ask:
Do you think Vitruvius’ claim was accurate?
Discuss with students that their informal line of best fit is a way to describe the data, but
does not represent any one person’s data. The line of best fit suggests a typical
relationship between height and wingspan, and as such can be helpful in identifying
outliers. Ask:
Is the line a good model for the data? How closely does it fit the data?
Do you notice any outliers?
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Michael Phelps’ is 6’ 4” tall (approximately 193 cm) but his wingspan is 6’ 7”
(approximately 201 cm). Ask students to graph this data point on their graph.
What can you say about Phelps’ measurements compared to a typical student?
Do you think this affects his swimming performance? How?
Guide Student Through Their Practice
Ask students to pick two points on the line of best fit to use to determine the equation of
the line. Discuss with students that this equation can be used as a mathematical model to
make predictions about height and wingspan. Ask:
What do your variables mean in the context of the data?
Use your equation to predict the wingspan of a person who is 180 cm tall.
Use your equation to predict the height of a person who has a wingspan of 145 cm.
Check for Understanding
The height-wingspan example should clearly show a linear association between the data.
At this point in the lesson, it might be important to reiterate that a straight line should not
be used in every scatter plot. Return to the first graph shown in the lesson (example 1).
Ask:
Would a straight line best represent this data? Why or why not?
Do you think that another line might best represent the data in the graph?
Return to the height and wingspan example. Ask:
What about the pattern of the data suggested that it could be represented by a linear
equation?
According to your equation, what “should” be Michael Phelps’ wingspan?
Does it make sense to substitute 10 cm for the x-value of your equation? 1000 cm?
Negative values?
Independent Practice
Given the graph of math and verbal SAT scores (example 2 from the beginning of the
lesson), ask students to draw a line of best fit. Ask students to determine to points on the
line of best fit that they will use to determine the equation of the line. Students can record
their work on the “Independent Practice” portion of the handout.
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Closure
During this lesson students have explored scatterplots. Students should see that a line of
best fit can informally describe the pattern in scatterplots that suggest a linear association.
While the line of best fit does not represent a particular data point, it does provide a
helpful way to make predictions based on trends in the data.
Suggestions for Differentiation and Extension
• Have students work with a partner. Ask them to choose one scatterplot and line of best fit
to determine the equation of the line. This will allow students who have not yet mastered
determining an equation of a line given two points to work with a partner.
• Provide students with real life data points that suggest a linear association. Ask them to
informally fit a line of best fit and determine an equation of a line. One relevant example
can be for students to explore earnings and unemployment rates by educational
attainment. Data can be found here: http://www.bls.gov/emp/ep_table_001.htm. Have
students graph education attained as years in school (i.e. Bachelor’s degree can be
considered 16 years).
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Scatter Plots and Line of Best Fit
Example 1:
Example 2:
1. Describe the pattern you notice in the data.
Example 1:
Example 2:
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Height and Wingspan
Height
(cm)
Wingspan
(cm)
1. Draw a line that best represents the data.
2. Choose two points on the line and record in the table below.
Height
Wingspan
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3. Determine an equation of the line.
4. What do your variables represent in the context of the data?
5. Use the equation to predict the wingspan of a person who is 180 cm tall.
6. Use your equation to predict the height of a person who has a wingspan of 145 cm.
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Independent Practice
1. Draw a line that best represents the data.
2. Choose two points on the line and record in the table below.
Verbal
Math
3. Determine an equation of the line.
4. What do your variables represent in the context of the data?
5. Use the equation to predict the math SAT score of a student who scored 570 on the verbal
portion of the SAT.
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