Karen Togliatti and Lindsey Herlehy
Curriculum and Professional Development Specialists
Illinois Math and Science Academy
STEM Integration: Statistics is the Connection
Slow Down! Parachute Design
Logistics
NOTES
This lesson is intended for students in grades 8 – 9 in a pre-algebra or an
introductory algebra course. Students will use a hands-on activity to
investigate various parachute designs and their impact on hang time.
Students should be grouped into teams of two to three with a minimum of
ten teams per class. This lesson will require some open space, so a
cafeteria, hallway, or gymnasium would be desirable for testing parachute
designs.
Materials per student:
1 – copy of Student Pages
per team of students:
2 – 30 cm x 30 cm square pieces of plastic tablecloth, or
other material such as plastic garbage bags, paper
napkins, or nylon
2 – 50 cm x 50 cm square pieces of plastic tablecloth, or
other material such as plastic garbage bags, paper
napkins, or nylon
4 – 2 m pieces of nylon bead cord or other string
1 – Pair of scissors
1 – Ruler
4 – Glue dots
1 – Fishing sinker or other small weight
1 – Stopwatch
20 – Sticker dots
½” – Flat steel washers (between 1 and 35 per team)
per class:
3 – Brown bags
4 – Large sheets 1” x 1” grid paper
4 – Pieces of string, yarn or Wikki Stix for trend lines
1 – Balance or scale
1 – Set Station Instructions (printed on 11” x 17” paper)
3 – (optional) ½” PVC parachute drop assists consisting of:
1 – ½” x 10 ft. piece of PVC cut into 2 ft. lengths
3 – ½” PVC non-threaded couplers
1 – ½” PVC T-connector
4 – meters nylon bead cord
Electrical tape
Time: Two to three 50-minute class periods
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
NOTES
Objectives/Standards
The objectives of this lesson are to:
References to Common Core are
adapted from NGA Center/CCSSO ©
Copyright 2010. National Governors
Association Center for Best Practices
and Council of Chief State School
Officers. All rights reserved.
References to Next Generation
Science Standards adapted from
NGSS Lead States. 2013. Next
Generation Science Standards: For
States, By States. Washington, DC:
The National Academies Press
•
•
Build parachutes to test the relationship between canopy size,
suspension line length, and payload weight on the hang time of a
parachute and hypothesize how a parachute reduces the descent
rate of an object. MS-PS2.A, SEP2, SEP3, CCSS.ELA-Literacy.RST.6-8.3
Develop scatter plots to investigate the physical relationships
between a parachute design variable and its effect on rate of
descent. CCSS.Math.Content.8.SP.A.1, CCSS.Math.Content.HSS.ID.B.6.A
CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP4, SEP 4, SEP5
•
Analyze a set of bivariate data to determine if a linear or nonlinear
association exists and the strength of the association.
CCSS.Math.Content.8.SP.A.2
•
Use data to inform decisions about designing a parachute to carry
a given payload at a rate of descent of 1 m/s.
CCSS.Math.Practice.MP3, MS-ETS1-2, MS-ETS1-3, SEP6
•
Use ratios and proportions to scale the 1 m/s parachute design to
a payload equal to a student’s weight. CCSS.Math.Content.7.RP.A,
CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2
•
Investigate the feasibility of the scaled parachute and discuss
other variables that might impact life-size parachute design.
SEP7, CCSS.ELA-Literacy.WHST.6-8.1, CCSS.ELA-Literacy.SL.6-8.1
Introduction
If an object is dropped from a height, it will accelerate towards the ground
due to gravity. However, as the object descends, it encounters air
resistance. When the air resistance pushing up on the object is enough to
balance the downward force of gravity, the object reaches a terminal
velocity. However, the terminal velocity, if reached, is often too great for
the object to safely impact the ground. To slow the rate of descent, a
parachute is often used.
Parachutes work to slow descent primarily by using an aerodynamic
principle known as drag. Drag is the force that opposes gravity and acts on
an object’s weight. A parachute helps reduce the rate of descent by
increasing the air resistance of the falling object. If a parachute design
creates more drag, then the rate of descent will decrease and the “hang
time”, or length of time that the object remains airborne before landing on
the ground, will increase.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
Parachute Canopy
Suspension Lines
Payload
The three main components of a parachute are
the canopy which is usually made from a
material such as nylon, suspension lines which
connect the canopy to the payload, and the
payload which can be attached via a harness or
other straps known as risers.
Many different variables can influence the amount of drag provided by a
parachute. Examples include canopy size, canopy material, canopy shape,
suspension line length, number of suspension lines, payload weight,
presence and amount of holes or vents, number of canopy layers, drop
height, wind, and atmospheric pressure.
The three variables that students will focus on in this activity will be canopy
area, suspension line length, and payload. In general, as the area of the
parachute canopy increases, so does the surface area and the amount of
drag produced. However, there appears to be a point where increasing the
size of the canopy provides no measurable difference in the amount of
drag. Increasing the length of the suspension lines also provides an
increase in drag primarily by increasing the effective surface area of the
canopy (it can “spread out” and fully inflate more easily). Longer
suspension lines also provide more stability to the parachute, but lines that
are too long run the risk of becoming tangled. Finally, for a given
parachute design, increasing the payload weight reduces the amount of
drag. Thus, properly sizing parachutes, especially for human use, is
essential.
Advanced Preparation
This lesson requires advanced planning to prepare materials for three
stations and a challenge activity. You will also need to decide how each
team will collect their common materials that will be used at each station
(i.e., sticker dots, paper clips, scissors, ruler, stopwatch, and glue dots).
You may choose to distribute these items to each station rather than have
students carry them from station to station. Stations should also be in
different areas of the classroom or open space.
For each station, there is a set of instructions to post for students to follow
(available as a download). On index cards or strips of paper, record
different values of each variable to test. Make sure there are enough
values for each team to test a different value.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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NOTES
Slow Down! Parachute Design
NOTES
Recommended ranges of variables are provided below:
Parachute Canopy Area: 25 cm2 ≤ canopy area ≤ 2500 cm2
Suspension Line Lengths: 10 cm ≤ length ≤ 50 cm
Payload Weight: 5 ≤ # washers ≤ 35
Station 1: For this station, you will need to provide pre-cut suspension line
lengths of 40 cm of nylon bead cord. You will need enough for each team
of two to three students to have four suspension lines. Also, provide each
team with a pre-cut 50 cm x 50 cm square of plastic tablecloth or other
canopy material. Students will cut the canopy down from this size.
Station 2: For this station, you will need to provide pre-cut lengths of 2 m
of nylon bead cord. You will need enough for each team of two to three
students to have one length which they will cut into four equal suspension
lines. Also, each team will need a 30 cm x 30 cm square of plastic
tablecloth or other canopy material.
Station 3: For this station, you will need to provide pre-cut suspension line
lengths of 40 cm of nylon bead cord. You will need enough for each team
of two to three students to have four suspension lines. Also, provide each
team with a pre-cut 30 cm x 30 cm square of plastic tablecloth or other
canopy material. A supply of ½” steel flat washers should be placed at this
station.
Challenge Activity: For this part of the activity, student teams will need precut lengths of 2 m of nylon bead cord. They will also each need one 50 cm
x 50 cm square of plastic tablecloth or other canopy materials. One fishing
weight or other weight (between 10 g and 20 g) will also need to be
provided for this activity.
Optional PVC Parachute Drop Assist: If desired, you can construct a device
to drop the parachutes that will not require a balcony or climbing up on
desks or chairs. From a local building supply store, purchase a ½” x 10 ft.
piece of plumbing PVC pipe and cut into 2 ft. sections. Use three nonthreaded ½” couplers to connect four sections. Label the order of the
sections with permanent marker and measure a height of 2 meters from
the ground. Using electrical tape or permanent marker, mark this height on
the pipe. At the top length of pipe, attach a t-connector and another
section of pipe. Thread approximately 4 meters of nylon bead cord through
the horizontal pipe and out the other side of the t-connector. Knot one end
of the thread. Students will use glue dots to connect parachutes to the
knotted end of the string and can raise and release to test.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
Activity
NOTES
This activity will be broken into three parts. The first part will introduce
students to the relationships between canopy size, suspension line length,
and load on the hang time of a parachute. Students will also calculate the
rate of descent for each design using the formula 𝑑𝑑 = 𝑟𝑟𝑟𝑟. In the next part,
students will be challenged to design a parachute for a given load that will
result in a hang time of 2.0 seconds (1 m/s rate of descent). Finally,
students will use their designed parachute’s dimensions to scale up to a
life-size model that will support their individual weight. They will also
discuss the reasonableness of this parachute design. Throughout the
activity, students will be encouraged to investigate potential interactions
between variables. They will also examine the experimental design process
in regards to controlling variables.
Parachute construction for Part I and Part II consists of attaching
suspension lines to each corner of the square canopy by first knotting one
end of each suspension line. Then, the lines are attached by placing a
sticker dot over a length of the suspension line so that the knotted end
holds the suspension line on the parachute canopy. Suspension lines
should be gathered together and knotted to attach a jumbo paper clip.
Part I: All Parachutes are not Equal
Students should be placed in teams of two or three for this activity.
Pass out the student pages and ask one student to read aloud the
information in the shaded box at the top of the first student page. Next,
ask students to complete Step 1 of the procedure. Using the board or
chart paper, record student responses regarding the potential uses of
parachutes. Point out that while Leonardo da Vinci might have made the
first sketch of a parachute, the first human to jump from a height using a
parachute did not happen until about 1797 when André-Jacques Garnerin
jumped from a hydrogen balloon 3,200 feet above Paris (source:
http://www.history.com/this-day-in-history/the-first-parachutist ).
Allow student teams time to complete Step 2 and Step 3, and then provide
each team with scissors, a ruler, 20 sticker dots, 4 glue dots, and a
stopwatch. Indicate to students that they will be recording “hang time,”
which will be defined as the amount of time that elapses between releasing
the parachute from a height of two meters from the bottom of the payload
until the payload first touches the ground.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
NOTES
Now, introduce each station and indicate to student teams that they will be
responsible for creating one parachute at each station. Model the basics
of parachute construction, and show students the locations of the three
stations. Students will conduct three trials of their designed parachute at
each station and calculate the average hang time, in seconds, for each
parachute design.
At each station, post a large piece of 1” x 1” grid paper with first-quadrant
coordinate axes drawn. You may decide to have students determine the
scale of each axis as well as state the independent and dependent
variables to be tested.
Station
Independent Variable
Dependent Variable
1
Canopy Area (cm2)
Hang Time (sec)
2
Suspension Line
Length (cm)
Hang Time (sec)
3
Payload Weight
(number of washers)
Hang Time (sec)
Students will use a sticker dot at each station to record their hang time for
their selected test variable value. Once all station data has been collected,
allow students time to analyze each scatter plot distribution for direction,
form, and strength. Allow time for each team to discuss and note their
observations, and then hold a class discussion. The following prompts may
be used:
•
Why was it important to find the average of three trials for each
experiment? [There are slight differences in recording the start/stop
time for each trial that is run. Using multiple trials for each
experiment allows us to try and control for “operator” differences.]
•
How did your team calculate rate of descent? [Using the formula
𝑑𝑑
𝑑𝑑 = 𝑟𝑟𝑟𝑟, we solved for the variable r by dividing by t. So, 𝑟𝑟 = 𝑡𝑡 . Our
distance is constant at 2 meters, so take 2 and divide by the
average time for three trials to calculate rate of descent in m/s.]
•
How does rate of descent relate to hang time? [Hang time and rate
of descent are inversely proportional. As the hang time increases,
the rate of descent decreases for the constant drop height of two
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
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Slow Down! Parachute Design
meters. Conversely, as the hang time decreases, the rate of
descent increases.]
NOTES
•
What association, if any, did you observe between canopy area and
hang time? [Student responses may vary depending upon data set
collected. In general, students should note that there appears to be
a positive association between canopy area and hang time. In
other words, if the canopy area increases, hang time increases and
rate of descent decreases. Students may also note the presence of
outliers and that the association may not be linear, although this
will become clearer once students add a trend line to the data set.]
•
What association, if any, did you observe between suspension line
length and hang time? [Again, student answers will vary with the
resultant class data set generated. However, students should note
a general positive association between suspension line length and
hang time.]
•
What association, if any, did you observe between payload “weight”
and hang time? [In general, as payload weight increases, the hang
time of the parachute will decrease. There is a negative
association.]
For each of the three graphs, select a volunteer to use string, yarn, or a
Wikki Stix (wax-coated yarn) to follow the trend, or apparent pattern, in the
data. Direct students to use a smooth curve or line and to not play
“connect-the-dots” with the data. Following the addition of the trend lines,
students can complete Step 6 in the procedure. Allow students to discuss
their analysis with a partner as well as travel to other teams to view their
analyses.
Debrief this activity by allowing teams to share their observations regarding
the trends found in the data. Some observations students may note are as
follows:
•
One or more of the data sets may not appear linear. This may be
expected, especially in the scatter plot of canopy area vs. hang time.
While increasing canopy area does result in an increase in hang
time, at some point there will be no appreciable increase in hang
time for a given payload.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
NOTES
•
Some data sets may have points “closer” to the trend line (or curve)
than other points. Ask students what this closeness may indicate in
terms of using an equation based on the trend to model the data.
•
Students may also note that each data point on the graph
represents a different team’s measurement. Differences in
recording the hang times may impact the overall data set. Ask
students why they took three time measurements at each station.
Part II: Parachute Design Challenge
Students should continue in their teams from Part I. Elicit a volunteer to
read the design challenge aloud. Ask students to interpret what a rate of
1 m/s means for this challenge.
Provide students with materials necessary to make one parachute as well
as one “sensor” weight (a fishing weight or other object with a mass
between 10 and 20 grams). Provide a balance or scale for student teams
to measure the mass of the sensor and encourage teams to estimate a
starting canopy area and suspension line length. Encourage them to refer
back to the class scatterplots while creating their designs. If desired, you
may have students justify their designs to you prior to giving them their
materials to build the parachute.
After most teams have indicated that they have successfully completed the
challenge, reconvene the entire class for a discussion using the following
prompts:
•
How did your team initially decide on the canopy size and
suspension line length to test?
•
How did your team make modifications to the design?
•
Which design component (canopy or suspension line) was more
difficult to manipulate? Why?
•
How did you make sure that your design actually descended at
exactly 1 m/s?
•
What might be the consequences of descending too fast? How
about too slow?
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
Each team will generate one data point to add to a class scatter plot of
canopy size (area) vs. suspension line length based upon their individual
parachute designs. Students can decide which variable is the independent
variable and which variable is the dependent variable. They can also
decide upon an appropriate scale for each axis of the graph. Students can
add their sticker dot representing the combination of canopy area and
suspension line length for a 1 m/s rate of descent. After building the
scatter plot, allow student teams time to analyze the data.
To debrief this part of the activity, ask student teams to share their
observations. Depending upon student background knowledge, you may
choose to ask students to try and fit a line to the data and determine the
slope, or rate of change, between canopy area and suspension line length.
This ratio may be used in the following activity to determine the suspension
line length for a scaled canopy area.
Part III: Scale it Up
Students should continue working in their teams from Part I and Part II. In
this part of the activity, allow student teams the freedom to use any
method of their choosing to determine how to “scale up” their model
parachute to a life-size parachute. Some conversion factors are provided,
but the idea here is for students to look at the information they have
gathered and make a realistic determination of the size of a parachute. In
general, students may use ratios to determine the canopy area and then
use the relationship between canopy area and suspension line length to
determine the scaled suspension lines.
Discuss this part of the activity by asking the following questions:
•
How did your team determine the dimensions of the canopy size
and suspension line lengths for a parachute to safely land you on
the ground at a rate of 1 m/s? [Student answers will vary.]
•
Why might your calculations differ from the online calculator?
[Students may note that the online calculator may refer to a
different canopy shape and a different material.]
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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NOTES
Slow Down! Parachute Design
NOTES
Debrief questions:
 How do you think a parachute works to slow down the descent of an
object? [A parachute works to slow down the descent of an object
by using air resistance (drag) to oppose the weight of an object.]
 How would you design an experiment to test the effect of another
variable on the hang time? [Student answers will vary. However,
students should be able to indicate one variable of interest and
should detail how they would control for the effect of other variables
in their design.]
 If a parachute also traveled a distance horizontally, how would that
impact both the hang time and the rate of descent? [Using the
Pythagorean Theorem, students can rationalize that by traveling
horizontally, the effective distance traveled is now greater than the
𝑑𝑑
vertical drop distance. Since 𝑟𝑟 = 𝑡𝑡 , the distance traveled would be
understated if the horizontal travel was neglected. Therefore, since
d is higher, the rate of descent, r, would also increase for a given
time and we would have overstated the hang time.]
 Did the scaled size of the parachute designed to carry your actual
weight seem reasonable? Why or why not? [Student responses will
vary, but a reasonable parachute size for an adult human would be
in the range of 24 – 28 feet across (7 – 9 m). This value is usually
determined for nylon material and a round parachute shape.
Student calculations tend to overstate the canopy area and
suspension line length.]
CONCLUSION:
This lesson is intended to introduce students to the aerodynamic principle
of drag through a mathematical exploration of several variables inherent to
parachute design. This series of activities integrates science, technology,
engineering, and mathematics principles and content into a hands-on,
minds-on investigation for late middle-school and early high-school
students.
According to the Occupational Outreach Quarterly published by the Bureau
of Labor Statistics, the number of STEM career opportunities is expected to
grow by 12% by the year 2022. This equates to approximately 1 million
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
jobs with a projected median salary of $76,000. In addition, there is a
national demand for students with knowledge and skills in statistics to fill
data-intensive jobs. Statistical literacy is fast becoming an essential skill
that all of our students will need to develop.
The teaching of statistics without context denies students the opportunity
to make strong connections between content and real-world situations.
Using real-world data sets or student-generated data sets does come with
risks. In many instances, student-collected data sets may not contain
enough data for any noticeable effects or relationships to show up.
However, if students are only given “clean” data sets, they may never learn
how to effectively decide what to do with a data point that doesn’t seem to
belong. More importantly, student-generated data sets with a compelling
question or challenge that intrigues students may lead to greater student
motivation and interest in the topic.
In addition to the natural connections found between science and data
analysis, opportunities exist to generate and use data to investigate
environmental issues, political situations, and issues of social justice. As
educators, we must be willing to take risks to integrate STEM activities into
our curriculum when opportunities arise.
EXTENSIONS:
 If students are in an introductory algebra course, challenge them to
determine an equation to model the trend in each scatter plot.
Students may use a graphing calculator or online regression tools, such
as those found at http://www.xuru.org/rt/toc.asp to fit a function to a
set of data points. Then, students may use their model to predict hang
time for an independent variable value not experimentally determined
and assess their confidence in the predicted value for hang time.
 For an in-depth look into calculating terminal velocity for a falling object,
there is an online virtual lab at http://concord.org/stemresources/parachute-model . Students will also investigate the
relationship between mass and surface area.
 Engineers can predict drag using the formula below:
𝐶𝐶𝐷𝐷 𝐴𝐴𝑝𝑝 𝜌𝜌𝜌𝜌2
𝐷𝐷 =
2
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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NOTES
Slow Down! Parachute Design
NOTES
Where D is the drag force, CD is the coefficient of drag (experimentally
determined and usually between 0.8 < 𝐶𝐶𝐷𝐷 < 1.2), Ap is the area of the
parachute (formula determined by shape), ρ is a measure of air density
(approximately 1.29 kg/m3 at sea level), and v is the desired descent
rate.
To calculate the area of a parachute, the drag force of the parachute
will be equated with weight:
𝐷𝐷 = 𝑚𝑚𝑚𝑚
where m is the mass of the object, and g is the standard acceleration
due to gravity of 9.8 m/s2.
Allow students to use the formula to calculate the surface area of the
canopy for a desired shape. They may also then solve for the side
length of a square canopy or a radius of a circular canopy.
Visit https://www.grc.nasa.gov/www/K-12/airplane/drageq.html for
more information on the drag equation.
RESOURCES:
Parachutes, Gravity and Air Resistance - Kids Discover. (n.d.). Retrieved
February 19, 2016, from http://www.kidsdiscover.com/teacherresources/
parachutes-gravity-air-resistance/
Science Buddies Staff. (2014, August 5). Parachutes: Does Size Matter?.
Retrieved February 19, 2016 from http://www.sciencebuddies.org/
science-fair-projects/project_ideas/Aero_p017.shtml
Skydiving Science: Does the Size of a Parachute Matter? (n.d.). Retrieved
February 19, 2016, from http://www.scientificamerican.com/article/bringscience-home-parachute/
Woodford, C. (2016, January 23). Parachutes. Retrieved February 19,
2016, from http://www.explainthatstuff.com/how-parachutes-work.html
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
Student Pages
Slow Down! Parachute Design
The first drawing showing a design of a parachute appeared around 1495 and
is credited to Leonardo da Vinci. Since da Vinci’s time, parachute design has
evolved with advances in materials and knowledge of aerodynamics. So, how
does a parachute slow down an object? In this activity, you will investigate this
question and use the knowledge you gain to meet the challenge of designing a
parachute to drop a given object at a rate of 1 m/s. Finally, you will investigate
whether your model design can be scaled to create a life-size parachute to
safely bring you back to the ground.
Part I: All Parachutes are not Equal
Materials per team:
• Materials to complete Part I can be found at each station
Procedure:
1.) With a partner, brainstorm a list of possible uses of parachutes.
Be prepared to share your list with the class.
2.) A simple model of a parachute can be constructed using three main
components: a canopy, suspension lines, and a payload. On the diagram
below, label the three components and then brainstorm a list of variables
that could be manipulated to investigate the “hang time” of a parachute.
Hang time refers to the time it would take the parachute to travel a given
distance through the air until it touches the ground.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
Student Pages
3.) You and your partner will now visit three stations, each of which tests three
different variables’ impact on hang time. At each station, you will be
provided with materials to make a parachute. You will be responsible for
making and testing one parachute design at each station. Three trials will
be conducted at each station to measure the hang time of your parachute,
and you will record your data in the table below. The AVERAGE hang time
calculated will also be recorded as a point on a class scatter plot at each
station. Each parachute will be dropped from a height of two meters. Use
the formula 𝑑𝑑 = 𝑟𝑟𝑟𝑟 to also calculate the rate of descent for each parachute.
4.) Record your data in the table below:
Station 1 – Canopy Area
(30 cm suspension line length; 1 paperclip load)
Trial 1
Trial 2
Trial 3
Rate of
Canopy Area
Average
Hang Time Hang Time Hang Time
Descent
(cm2)
Hang Time
(sec)
(sec)
(sec)
(m/s)
Station 2 – Suspension Line Length
(900 cm2 canopy area; 1 paperclip load)
Suspension
Trial 1
Trial 2
Trial 3
Average
Line Length Hang Time Hang Time Hang Time
Hang Time
(cm)
(sec)
(sec)
(sec)
Rate of
Descent
(m/s)
Station 3 – Payload Weight
(900 cm canopy area; 30 cm suspension line length)
Trial 1
Trial 2
Trial 3
Rate of
Average
Hang
Hang
Hang Time
Descent
# of Washers
Hang Time
Time (sec) Time (sec)
(sec)
(m/s)
2
What additional variables are held constant for all three stations?
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Slow Down! Parachute Design
Student Pages
5.) For each of the tested variables, a class scatter plot has been constructed.
Describe any patterns observed in the individual scatter plots and identify
the association between the variables, if any. Look for the presence of any
unusual patterns or outliers.
Canopy Area vs Hang Time
Suspension Line Length vs Hang Time
Payload Weight vs Hang Time
Share your observations with other teams and record additional information, if
necessary.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
Professional Learning Day; March 4, 2016
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Student Pages
6.) Now, using string or Wikki Stix, identify the trend in the data shown on each
scatter plot, if any. Sketch each scatter plot below and identify the trend as
either linear or nonlinear. Analyze each trend by discussing how closely the
data points “fit” the trend.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
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Slow Down! Parachute Design
Student Pages
Part II: Parachute Design Challenge
Your team has been selected to design a parachute to safely land a critical
sensor inside an area that is not safe for humans. The sensor must descend at
a rate of exactly 1 m/s. Discuss with your partner the potential consequences
of too high a rate of descent as well as too low a rate of descent.
Materials per team:
Canopy Material
Suspension Line string, 2
meters total length
• 1 jumbo paper clip
• 1 metal “sensor”
•
•
•
•
•
•
1 balance or scale (per class)
1 pair scissors
1 ruler
Sticker dots
1.) With a partner, determine the weight of the sensor. ______________
Using data gathered from Part I of the activity, predict a canopy size (area,
in cm2) and suspension line length (in cm) that would produce a descent
rate of 1 m/s for a square parachute with a load weight of one paper clip
and one sensor:
Canopy size: ____________________________________
Suspension Line Length: ________________________
2.) Next, build and test your parachute. Record any modifications that you had
to make and the results of those modifications in the space below:
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Slow Down! Parachute Design
Student Pages
7.) Your class will be building another scatter plot. This time, we will be
investigating the relationship between the suspension line length and the
canopy area for a square parachute that will allow the sensor to fall at a
descent rate of 1 m/s. Sketch the class data below, and interpret what the
scatter plot is “saying” about the association between suspension line
length and canopy area.
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Slow Down! Parachute Design
Student Pages
Part III: Scale it Up
1.) Your next task will be to determine the dimensions of a parachute that will
support your weight. Below is some information that may be helpful when
determining your life-sized parachute.
1 kg = 2.20462 lbs.
1 cm = 0.393701 in
1 m2 = 10 ,000 cm2
Areasquare = (side length)2
With a partner, determine a method for calculating the canopy area and
suspension line length for a parachute that would support your weight. Use
the space below for your calculations:
2.) Visit the website at http://www.rocket-simulator.com/parachute.php and
compare the estimated parachute size to the one you calculated. Why
might there be differences?
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Slow Down! Parachute Design
Student Pages
Discussion Questions
Complete the following questions with a partner. Then, share your answers as a class.
1.) How do you think a parachute works to slow down the descent of an object?
2.) How would you design an experiment to test the effect of another variable on the hang
time?
3.) Did your parachute travel straight down to the ground after it was dropped, or did it
also move horizontally? __________________________________________________
If a parachute also traveled a distance horizontally, how would that impact both the
hang time and the rate of descent? Mathematically justify your response.
4.) Did the scaled size of the parachute designed to carry your actual weight seem
reasonable? _______ Why or why not?
5.) We calculated the size for a life-size parachute based on a rate of descent of 1 m/s
and using a square plastic parachute. What other variables should we consider when
sizing a parachute?
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STEM Integration: Statistics is the Connection
Analyzing Body Temperature
Logistics
NOTES
This lesson is intended for students in Grade 6 as an introduction to
describing data distributions. Students should ideally be grouped into
teams of 4 to promote discussion. A minimum of 24 students is ideally
required in order to get enough data for analysis. Extensions to seventhgrade and eighth-grade standards are also provided.
Materials per student:
1 – Disposable thermometer
1 – Yellow Post-it note pad sheet
1 – Blue or Pink (depending on male/female) Post-it note
pad sheet
per classroom:
1 – Completed number line to post data
1 – Roll blue painter’s tape
Time: One to two 50-minute class periods (if including extension)
Objectives/Standards
The objectives of this lesson are to:
•
•
•
•
•
Create and analyze a data set to investigate the question Is the
normal body temperature of humans 98.6°F? .
CCSS.Math.Content.6.SP.A.1 CCSS.Math.Content.6.SP.A.2
Display the body temperature data using dot plots, histograms,
and box plots. CCSS.Math.Content.6.SP.B.4 CCSS.Math.Practice.MP.5
Discuss the meaning of the variability in the data and brainstorm
possible reasons for observed variability in body temperature
measurements. CCSS.Math.Content.6.SP.A.3
(Extension) Draw informal comparative inferences between body
temperature data from the male population to those of the female
population. CCSS.Math.Content.7.SP.B CCSS.Math.Practice.MP.2
(Extension) Investigate the relationship between body temperature
and heart rate by constructing and interpreting a scatter plot, and
informally fit a line to the data if a linear association is indicated.
CCSS.Math.Content.8.SP.A.1 CCSS.Math.Content.8.SP.A.2 CCSS.Math.Practice.MP.4
Introduction
This lesson will use a student-generated data set to examine the question,
“Is the normal body temperature of humans 98.6°F?” Data will be
collected on the entire group as a whole and will also be collected by
gender using different colored post-it notes.
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References to Common Core are
adapted from NGA Center/CCSSO ©
Copyright 2010. National Governors
Association Center for Best Practices
and Council of Chief State School
Officers. All rights reserved.
Analyzing Body Temperature
NOTES
The historical value for mean body temperature of 98.6°F is attributed to a
19th-century German physician, Carl Wunderlich. Dr. Wunderlich conducted
his experiments on approximately 25,0000 patients at the University of
Leipzig’s medical clinic and established the normal range for body
temperature of 97.2°F – 99.5°F with a mean of 98.6°F. His description
of a range of normal temperatures is often overlooked and the single point
value of 98.6°F is identified as the normal body temperature. Wunderlich
used axillary, or armpit, measurements and was not overly concerned with
precision or calibration of instruments. In the literature, the process used
to analyze the data set was never described and the original data set itself
was never published. Many scientists now consider 98.2°F to be the true
“normal” mean body temperature for humans (Wasserman, et. al. 1992).
However, true to Wunderlich’s original findings there exists a range of
values that are considered normal.
Other contributions Wunderlich made to clinical thermometry have not
been as widely publicized, but he was instrumental in pointing out that
there appear to be oscillations in body temperature throughout the day. He
also believed that women had a slightly higher body temperature than men,
and that older individuals also had a lower body temperature.
Other variables that might impact the body temperature of an individual
include placement of the thermometer (oral, axillary, tympanic, rectal, or
gut (ingested)), circadian rhythms, female menstrual cycles, seasonal
(annual) variations, and variations due to physical fitness (Kelly, 2006).
Activity
Students should be grouped into teams of four students. Prior to the
activity, use cardstock, sentence strips, or other materials to construct a
number line from approximately 96°F to 101°F (scale every 0.2°F). The
length of each tick mark along the number line should be approximately
the width of a standard-size post-it note sheet. Post the number line along
a wall at a height where students have easy access.
Begin this activity by asking students what body temperature is considered
normal. The most common answer from students is the historically held
norm of 98.6°F. Students should then be asked what they believe it would
mean if they had a temperature above this value, or one below this value.
Additional questions to ask students prior to data collection include the
following:
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Analyzing Body Temperature
 Do you think other temperatures besides 98.6°F would also
indicate a normal body temperature?
 At what temperature would you consider a person to be unhealthy?
 What variables might contribute to an individual’s body
temperature?
Pass out one disposable thermometer to each student. Ask students to
describe the scale that they see on the thermometer. Students should
make observations such as the minimum temperature on the thermometer
is 96.0°F, the scale is increasing by 0.2°F, and the maximum temperature
on the scale is 104.8°F. Then, describe the procedure to determine body
temperature using the supplied thermometer below:
 Remove thermometer from wrapper
 Place under tongue as far back as possible and close mouth for 60
seconds
 Remove from mouth. Wait about ten seconds for device to lock in
accuracy (some blue dots may disappear)
 Read temperature indicated by the last blue dot and record using
the marker on both Post-its
 Throw away wrapper and thermometer
Students will use a yellow, Post-it sticky note sheet to record their body
temperature using a marker. Now, allow students to place their sticky note
along the number line at a location that corresponds to their measured
body temperature. Instruct students that if a sticky note is already placed
at their body temperature they are to place their sticky note directly above
the one (or ones) that is already displayed. Upon returning to their seats,
students should record the class data line plot on their student sheets. At
this point, instruct students to record observations about the data set that
is displayed on the wall. Encourage students to use some numeric
observations about the data set as well and to discuss their observations
with the members of their group. Allow time for group discussions, and
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NOTES
Analyzing Body Temperature
NOTES
instruct the groups to make a list of all the observations discussed. Begin
with one group and have a student representative share their list and
record on the board or chart paper. Then, select another group and ask
them to share their list. Check off items that are repeated and add new
observations that are described. Continue until all groups have reported
out and then note the most common observations. Highlight observations
related to the following:




Shape of the overall distribution
An approximate measure of the center of the distribution
The range, or variability, in the data
Interesting or unusual data points within the data set
If no observations lead to the above categories, prompt students to look for
additional observations that highlight shape, center, spread, and outliers.
Next, students will construct a histogram of the data set. Using painter’s
tape, divide the line plot into five “bins” by placing strips of tape just before
each whole-number temperature (96, 97, 98, 99, 100, 101). Ask students
to describe what values each “bin” or section of the number line would
contain. Students should come to an understanding that the first section
represents temperatures from 96°F to just below 97°F; the next section
from 97°F to just below 98°F, etc. Mathematically, they may represent
each section using the notation 96 ≤ x < 97, where x represents the
measured body temperature. Rearrange all the post-its in each bin and
stack into a single bar. Using painter’s tape, place a horizontal piece of
tape at the height of the bar with length equal to the length of the bin.
Then, remove the sticky notes from that bin. Ask students to describe the
meaning of the “bar” that was created. Repeat for the other four bins.
Students will recreate the histogram on their student sheets and will
describe again the shape, center, and spread of the distribution. Students
will also be asked to compare and contrast the histogram to the line plot. A
major goal of this exercise is to allow students to see that individual data
points are “lost” when combined into a histogram. However, with larger
data sets, it may be impractical to look at a line plot since there might be
too much variation to see any meaningful patterns.
Next, arrange the sticky notes along the wall in order from lowest
temperature to highest temperature. Ask students to equally divide the
sticky notes into four equal groups. Depending upon the size of the data
set, students may need to take a sticky note and “rip it in half” to have four
equal groups. Again using painter’s tape, ask students where you should
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Analyzing Body Temperature
place the tape to create four equal groups. Either place the tape between
two sticky notes (indicating that the value of the data will be found by
taking an average of the data values on either side of the tape) or down the
center of a sticky note (indicating that the particular data value is an
“endpoint” for the segments). A sample data set for 10 points 11 points,
and 12 points is shown below:
96.2 96.8 97.2 97.6 97.8 98.2 98.4 98.4 98.8 99.4
96.2 96.8 97.2 97.6 97.8 98.2 98.2 98.4 98.4 98.8 99.4
96.2 96.8 97.2 97.6 97.8 98.2 98.2 98.4 98.4 98.8 99 99.4
These values are used to determine the five-number summary to create a
boxplot. Each of the lines represents a quartile. Quartile 1, or Q1, means
that ¼ or 25% of the data values are below and 75% are above. Quartile
2, or Q2, is also referred to as the median and is the value at which 50% of
the data is found above or below. Quartile 3 (Q3) is the value at which 75%
of the data is below and 25% is above. The minimum value is the smallest
value in the data set, and the maximum value is the largest value in the
data set.
For the above sample data sets, the five number summaries are below:
Min
Q1
Median (Q2)
Q3
Max
96.2
97.2
97.8 + 98.2
2
= 98.0
98.4
99.4
96.2
97.2
98.2
98.4
99.4
97.2 + 97.6
2
= 97.4
98.2 + 98.2
2
= 98.2
98.4 + 98.8
2
= 98.6
96.2
99.4
These values are used to construct a boxplot such as the one below for the
first data set:
Body Temperature °F
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NOTES
Analyzing Body Temperature
NOTES
Using the painter’s tape, place equal-length strips of tapes at the
appropriate values of the five-number summary for the data set on the
number line. Then, create the “box” by enclosing the lines between the
first and third quartiles (this is known as the interquartile range, or IQR)
and draw the “whiskers” by extending a line from the minimum value to the
value for Q1 and from Q3 to the maximum.
Following construction, students should use their class data to answer the
question:
Is the mean normal body temperature of humans 98.6°F? What does the
term “mean” imply? What about the median body temperature?
Students can mark the value of 98.6°F on their graphs and justify their
decision based upon their data. Allow student groups to discuss their
individual choices, and come up with a consensus for the group. Then,
debrief each group again recording responses of “yes” or “no” with relevant
justification. Finally, ask students how confident they are with their
decision.
Debrief questions:
 What steps might you take to raise the confidence of your decision?
 What variables might play a role in determining an individual’s
normal body temperature?
 How might you test these variables?
EXTENSION: (Seventh-grade)
To extend this lesson for a seventh-grade classroom, now ask the students
to investigate whether or not gender influenced body temperature. Provide
a pink sticky note for a female student and a blue sticky note for a male
student. Ask students to perform a similar data analysis for these data
sets separately. Challenge students to use appropriate graphs to analyze
whether a difference exists between the body temperatures of the male
students in the class and for the female students in the class. Again, direct
students to write a justification for their decision based upon the data and
to be prepared to share their choices with the class.
At this point, it is appropriate to discuss with students if their results are
representative of the entire population of humans. You may have to direct
them towards the idea that this data is only representative of the class,
since a random sample of all humans of all ages at various times of the
day, etc. was not taken. To get a better idea if the temperature of humans
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Analyzing Body Temperature
is 98.6°F, students can use a published data set to get more
“representative” data.
NOTES
Navigate to http://www.statcrunch.com/app/index.php?dataid=661807.
This data set is entitled “Normal Body Temperature, gender, and Heart
Rate” and is a random sample of 130 observations taken directly from
data found in a 1992 study (Wasserman, Levine, and Mackowiak) that
examined whether the true mean body temperature is 98.6 degrees
Fahrenheit. The first column measures body temperature (°F); the second
column uses the key 1 = male and 2 = female for gender; and the third
column measures heart rate in beats per minute. If the size of the data set
is too large, ask students to randomly “sample” the data set for 25 points
to use in their analysis. Summary information for the body temperature
data set is provided below:
The distribution is
bell-shaped with data
clustered around the value
of 98.3°F. The range of the
data is about 4.5°F. One
value at 100.8°F seems
higher than the rest.
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Analyzing Body Temperature
NOTES
A data set of 130 randomly selected healthy male and female
adults’ body temperature was taken using a disposable
thermometer. The data was taken to investigate the claim that the
mean body temperature for the population is 98.6°F. Our data had
a median temperature of 98.3°F, lower than the “normal” body
temperature, and an interquartile range of 0.9°F which means that
50% of our observations were between Q1 at 97.8°F and Q3 at
98.7°F. The number of observations at or below 98.6°F is
91/130, or about 70%. Two values seemed much lower than the
others according to the boxplot, while one value seemed much
larger than the others, perhaps meaning that the individual had a
fever. Since there were outliers present, the median and IQR were
chosen as measures of center and spread.
Students can generate graphs to use for analysis using various statistical
tools. Directions for using the TI-84 graphing calculator are provided in the
extension pages for the Grade 7 activity.
Students are asked to answer the question of “Is there a significant
difference in body temperature between males and females?” The
following graphs can be generated to use in this discussion:
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Analyzing Body Temperature
EXTENSION: (Eighth-grade)
To extend this lesson for eighth-graders, students can now use the data set
from http://www.statcrunch.com/app/index.php?dataid=661807 to
investigate whether there is an association between body temperature and
heart rate. Students may form a hypothesis by thinking about a time when
they had a fever. Do they recall having a higher heart rate (pulse) while
they were ill? Students can use the data to construct a scatter plot and
then can informally fit a line to the data. Students should realize that the
weakness of the association in the data makes the using the line for
predictions subject to error.
Regression line: BEATS = 2.44*TEMP – 166.3
CAUTION: Students can’t use the above graph to determine the y-intercept
of the line since the scales do not begin at zero. In this problem, the yintercept has no real-world meaning (a body temperature of zero degrees F
has a heart rate of -166.3 beats per minute) However, students can
interpret the slope of the line to mean “for every one degree increase in
body temperature, the value of heart rate increases by approximately 2.44
beats per minute.”
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NOTES
Analyzing Body Temperature
NOTES
Engineering Design Challenge:
Below are some ideas for incorporating and engineering design challenge
into the activity. The goal for students here would be to develop a
proposed solution and analyze the feasibility of each design.
•
Design a temperature scale to determine “normal” body
temperature.
•
Design a temperature sensor using everyday items that will record
an increase in temperature from a “normal” value.
Conclusion
This lesson is intended to allow students to generate data and use
statistical techniques to investigate the question of whether the true mean
“normal” body temperature of humans is 98.6°F. Opportunities arise
during this lesson to introduce many statistical ideas and generate good
discussion of the idea of a central value, variability, outliers, significance,
sampling techniques, and experimental design. With NGSS Practice
Standards focusing on Analyzing & Interpreting Data and Using
Mathematics and Computational Thinking the connection between
statistics and mathematics and science is brought to the forefront. The
NGSS standards require key tools from the Common Core Math Standards
to be integrated into science instructional materials and assessments. In
addition, CC Math Practices MP.2 (Reason abstractly and quantitatively) ,
MP.4 (Model with mathematics), and MP.5 (Use appropriate tools
strategically) are key mathematical practices found integrated into the
NGSS standards.
Resources
Kelly, G. (2006). Body Temperature Variability (Part 1): A Review of the
History of Body Temperature and its Variability Due to Site Selection,
Biological Rhythms, Fitness, and Aging. Alternative Medicine Review, 11(4),
278-293.
Mackowiak, P., Wasserman, S., & Levine, M. (1992). A Critical Appraisal of
98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and
Other Legacies of Carl Reinhold August Wunderlich. Journal of the
American Medical Association, 268, 1578-1580.
Shoemaker, A. (1996). What's Normal? - Temperature, Gender, and Heart
Rate. Journal of Statistics Education, 4(2).
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Analyzing Body Temperature
Student Pages
Analyzing Body Temperatures
Dr. Carl Wunderlich, a 19th-century physician, is credited with establishing the
“normal” average body temperature of 98.6°F. Wunderlich used armpit
temperature measurements on approximately 25,000 patients at the
University of Liepzig’s medical clinic in Germany. This value for “normal” body
temperature is still widely accepted today.
Problem:
Is the average healthy body temperature for humans actually 98.6°F?
Materials:
• One disposable thermometer
• One yellow sticky note sheet
• A dark-colored marker
Procedure:
Look at the disposable thermometer you were given and write down any
observations on the thermometer below. Be prepared to share your
observations with your group.
Use the following procedure to record your body temperature.
 Remove thermometer from wrapper
 Place under tongue as far back as possible and close mouth for 60 seconds
 Remove from mouth. Wait about ten seconds for device to lock in accuracy (some
blue dots may disappear)
 Read temperature indicated by the last blue dot
and record using the marker on both sticky notes
 Throw away wrapper and thermometer
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Analyzing Body Temperature
Student Pages
Follow your teacher’s instructions to add your yellow sticky note to the data set
for the class. When all data points have been added, record the data on the
line plot below. What symbol can you use to indicate an individual data point?
Describe the data set above in as much detail as you can. What are the
interesting features of the data set?
Discuss your observations with your group and record additional information
that your group discovers about the data set.
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Analyzing Body Temperature
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Now, create a histogram of the data following your teacher’s instructions. How
does the histogram compare to the line plot?
Finally, create a boxplot of the data following your teacher’s instructions. What
might be a possible reason to use a boxplot?
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Analyzing Body Temperature
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Based upon your data, do you believe that the normal body temperature of
humans is 98.6°F? Use your data to justify your decision. You may want to
mark this temperature on your graphs to help you make a decision. Once your
team has written their responses, share with your group.
How confident are you with your decision?
What additional variables might change an individual’s “normal” body
temperature?
How could you test these variables?
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Analyzing Body Temperature
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Analyzing Body Temperature by Gender
The “normal” human body temperature is historically 98.6 F. In this activity,
you will be investigating the effect that gender may have on the normal body
temperature of human. Using a published set of data, you can use the
statistical features of a graphing calculator to analyze a larger data set.
Problem:
Is there a difference between males and females in normal healthy body
temperature?
Materials:
•
•
•
•
One disposable thermometer
One pink or blue sticky note sheet
A dark-colored marker
One TI-84 graphing calculator
Procedure:
Look at the disposable thermometer you were given and write down any
observations on the thermometer below. Be prepared to share your
observations with your partner.
Use the following procedure to record your body temperature.
 Remove thermometer from wrapper
 Place under tongue as far back as possible and close mouth for 60 seconds
 Remove from mouth. Wait about ten seconds for device to lock in accuracy (some
blue dots may disappear)
 Read temperature indicated by the last blue dot
and record using the marker on both sticky notes
 Throw away wrapper and thermometer
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Analyzing Body Temperature
Student Pages
Using the pink (for female) and blue (for male) sticky notes, add your data to
the class line plots as was done in the previous activity. Using the class data,
create two line plots. Use the data to justify if you believe that there is a
difference between male and female body temperatures.
Use the number line below to create another data display.
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Analyzing Body Temperature
Student Pages
Why did you choose this display?
Based upon your data, is there a significant difference between males and
females in Normal Temperature? Justify your answer.
For larger data sets, statistical software is often used to generate graphs and
perform calculations of basic statistical measures such as the mean and the
median. In this part of the activity, you will use a graphing calculator to analyze a
set of data which is derived from a dataset published in 1992 in the Journal of the
American Medical Association. This dataset randomly selected 130 adults over
the age of 18 and recorded body temperature, gender, and heart rate. The
temperature and gender information has been reproduced for you in the table at
the end of the activity sheets.
1. Using the graphing calculator, be sure to clear the memory of any pre-entered data
and programs by performing the following keystrokes:
2. Using your graphing calculator, enter the “MALE” temperature data in L1 column of
the calculator and “FEMALE” temperature data into L2 column of your calculator
following the steps below:
a) Press
to enter the editor of the calculator.
b) Using the arrow keys, place the cursor
under the L1 column of the calculator and enter the
MALE data (all 65 numbers)by using the [ENTER] key
or down arrow after each entry.
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Analyzing Body Temperature
Student Pages
As you enter the data, the line at the bottom of the display screen will show which
data point you are entering. For example, in the screen shot
below, we are entering the fifth MALE data point, so the display
reads L1(5) = 97.1. After pressing [ENTER] or the down arrow,
the calculator will index to the next data point. In this way, you
can keep track of your location in the data table.
c) Arrow to the right under column L2 and enter the 65 FEMALE
data values.
OPTIONAL: Working as partners, one student could enter the MALE data into L1 and
another student could enter the FEMALE data into L2 using a different calculator.
3. Press
and select 1: Plot1. Then, press [ENTER] to turn the plot “ON”
and select the Boxplot option as shown below using the arrow keys and [ENTER]:
Press
to view a boxplot of the MALE data. Pressing the [TRACE] key
and the arrows will allow you to see various points along the boxplot.
Describe the graph in the space below:
For the FEMALE data, Press
and select
2: Plot2. Then, press [ENTER] to turn the plot “ON” and select the
Boxplot option as before, but change the Xlist to L2 by pressing
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Analyzing Body Temperature
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4. Turn off Plot1 by pressing [2nd][STAT PLOT] and selecting Plot1. Arrow to OFF and
press [ENTER]. Then press
to view a boxplot of the FEMALE data.
Pressing the [TRACE] key and the arrows will allow you to see various points along the
boxplot. Describe the graph in the space below:
5. Now, turn on both Plot1 and Plot2. Use the boxplots to answer the question:
Is there a difference between males and females in normal healthy body
temperature?
6. How does the result from the random data set compare to the class data
for male and female temperature differences?
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
IMSA Professional Learning Day; March 4, 2016
39
Analyzing Body Temperature
Student Pages
Source: http://www.statcrunch.com/app/index.php?dataid=661807
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Male Body
Temperature
L1
96.3
96.7
96.9
97
97.1
97.1
97.1
97.2
97.3
97.4
97.4
97.4
97.4
97.5
97.5
97.6
97.6
97.6
97.7
97.8
97.8
97.8
97.8
97.9
97.9
98
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98
98.1
98.1
Male Body
Temperature
L1
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98.2
98.2
98.2
98.2
98.3
98.3
98.4
98.4
98.4
98.4
98.5
98.5
98.6
98.6
98.6
98.6
98.6
98.6
98.7
98.7
98.8
98.8
98.8
98.9
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99.1
99.2
99.3
99.4
99.5
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Female Body
Temperature
L2
96.4
96.7
96.8
97.2
97.2
97.4
97.6
97.7
97.7
97.8
97.8
97.8
97.9
97.9
97.9
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98
98
98
98
98.1
98.2
98.2
98.2
98.2
98.2
98.2
98.3
98.3
98.3
98.4
98.4
98.4
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
IMSA Professional Learning Day; March 4, 2016
Female Body
Temperature
L2
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98.4
98.4
98.5
98.6
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98.6
98.7
98.7
98.7
98.7
98.7
98.7
98.8
98.8
98.8
98.8
98.8
98.8
98.8
98.9
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99.1
99.1
99.2
99.2
99.3
99.4
99.9
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100.8
40
Analyzing Body Temperature
Student Pages
EIGHTH-GRADE EXTENSION:
To investigate a larger data set, navigate
to http://www.statcrunch.com/app/index.php?dataid=661807 .
What do you think the heading at the top of the columns represent?
Create a display for the data to answer a statistical question of your choice on a
sheet of graph paper. Examples of some questions you might use the data set
to explore are as follows:
 Is the true mean of the population really 98.6 degrees Fahrenheit?
 What is an acceptable range of “normal” body temperatures?
 At what temperature should we consider someone’s temperature to be
abnormal? In other words, when are they sick?
 Is there a significant difference between males and females body
temperature in the sample data?
 Is there an association between body temperature and heart rate?
Following your data analysis, write a conclusion to the question you analyzed in
the space below.
STEM Integration: Statistics is the Connection Karen Togliatti and Lindsey Herlehy
IMSA Professional Learning Day; March 4, 2016
41