Linear Functions and Mathematical Modeling
Project Overview
This RWLO describes a lesson plan that instructs students on how to create a simple x – y
scatter graph which can be used to find the linear correlation between the boiling point of
water and altitude. Graphs will be constructed by hand with graph paper and pen.
CIESE’s International Boiling Point Project data base will be used as the source for all
data sets. Students will be required to graph the boiling point of water as a function of
altitude, then the graph will be analyzed to determine the best linear fit of the data.
Students will be asked to calculate the linear equation that describes this relationship.
The linear equation will then be used to predict boiling points at different altitudes which
can be compared to known or measured values.
This RWLO assumes that students have the prerequisite knowledge required to construct
a simple x – y scatter plot. Students should also be capable of recognizing a correlation
between plotted variables.
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Student Learning Objectives
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Students will be able to create an x – y scatter graph that is properly labeled,
scaled, and plotted.
Students will be able to draw and determine the line of best fit to the data set.
Students will derive the linear equation for the data.
Students will use the linear equation to predict the boiling point at other altitudes.
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Procedure
Time: 50 minutes
Materials: Graph paper, ruler, and pen
Background
 This RWLO describes a lesson plan that instructs students on how to create a
simple x – y scatter graph which can be used to find the linear correlation between
the boiling point of water and altitude. Each student will be assigned to a group
for this exercise. The members of the group will obtain their data for the exercise
as a collaborative unit, but each member of the group will submit their own
completed assignment. The raw data will be downloaded from a collaborative
Web site created by CIESE called the International Boiling Point Project.
Students will be required to graph the boiling point of water as a function of
altitude, then the graph will be analyzed to determine the best linear fit of the
data. Students will be asked to calculate the linear equation that describes this
relationship. The linear equation will then be used to predict boiling points at
different altitudes which can be compared to known or measured values. Students
will be asked to write a summary of their findings based on the data analysis.
 This RWLO assumes that students have the prerequisite knowledge required to
construct a simple x – y scatter plot. Students should also be capable of
recognizing a correlation between plotted variables.
Implementation: This RWLO can be used as a classroom exercise or initiated in the
classroom and completed as a homework activity in order to demonstrate the learning
objectives. Each student will be assigned to a group for this exercise. The members of
the group will obtain their data for the exercise as a collaborative unit. Each member of
the group will submit their own graph and a summary report. The summary will include
the derived linear equation and two calculations using of the equation to find the boiling
point of water at a specific altitude. One calculation should be completed using the
altitude of the classroom.
Steps:
 Assemble the students into their assigned groups. Supply each student with a
piece of graph paper and a ruler. Also supply each student with the reference
handout: Graphical Analyses.
 Describe all necessary information concerning the International Boiling Point
Project (IBPP) and provide the students with its Web address
(http://www.k12science.org/curriculum/boilproj/pastprojects.html).
 Distribute and review the Assignment Handout.
 Discuss how the class will complete the activity. This will be depend on whether
the activity is entirely in-class or partially used as a homework assignment.
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Provide class time for each group to choose and download a data file from the
International Boiling Point Project. All members of the same group must use the
identical data file.
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Content Material
Background: This RWLO describes a lesson plan that instructs students on how to
create a simple x – y scatter graph which can be used to find the linear correlation
between the boiling point of water and altitude. Each student will be assigned to a group
for this exercise. The members of the group will obtain their data for the exercise as a
collaborative unit, but each member of the group will submit his or her own completed
assignment. The raw data will be downloaded from a collaborative Web site created by
CIESE called the International Boiling Point Project. Students will be required to graph
the boiling point of water as a function of altitude, then the graph will be analyzed to
determine the best linear fit of the data.
Student Directions
 Assemble into your assigned group at a computer connected to the Internet and
access the International Boiling Point Project Web-site at
(http://www.k12science.org/curriculum/boilproj/pastprojects.html). Search the
project data by clicking on the PC user file data links. Once your group has found
a data file, send enough copies to the printer so every group member has one.
 Read the Assignment Handout provided by your instructor.
 Obtain a piece of graph paper and a ruler from the instructor if it hasn’t been
provided.
 Read the Graphical Analyses handout provided.
 Complete the assignment.
Additional Resources
 Back-up Web-site for the International Boiling Point Project data:
http://www.k12science2.org/curriculum/boilproj/pastprojects.html
 Web-site that contains directions on how to use its search engine to obtain altitude
data: www.topozone.com
This Web address contains altitude information obtained for a 1997 expedition up Mt.
Everest. There is some reference data on the boiling point of water at various elevations.
http://www.pbs.org/wgbh/nova/everest/expeditions/97/mail/2phys.html
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Assessment
Each of the bullets in the Assignment Handout can be used for assessment based on the
following rubric.
Graph: [5 total points]
 Prepare an x-y scatter graph plot of the boiling point of water verses altitude.
Preparation of the graph will be scored as follows:
5 pts = All of the requirements listed below have been fulfilled.
a) The independent and dependent variable is chosen correctly and plotted on the
appropriate axis.
b) The axes scale are appropriate for the data plotted. The scale uses the correct
number of place holders provided by the original data table.
c) Each axes are labeled or titled. The graph is given a title.
d) All appropriate units are provided in parentheses near the axis label.
e) The data points are presented correctly.
4 pts = Four of the five requirements have been fulfilled.
3 pts = Three of the five requirements have been fulfilled.
2 pts = Two of the five requirements have been fulfilled.
1 pts = One of the five requirements has been fulfilled.
0 pts = None of the requirements have been fulfilled.
Analyze the Graph: [10 total points]
 Analyze the graph. Based on your observations can you identify the linear
relationship between the two variables plotted in the graph? If so, draw the trend
line which best correlates to this relationship. Derive the linear equation for the
line. Include all calculations necessary to derive this equation.
Analysis of the graph will be scored as:
10 pts = All of the requirements listed below have been included.
a) A trend line is drawn on the graph.
b) The trend line has been created with a straight edge.
c) The position of the trend line indicates that the student has interpreted the results
correctly.
d) The student has reported the equation for the line.
e) The y – intercept is reported correctly.
f) The correct number of place holders and units are reported for the y – intercept.
g) The calculation for the slope of the line is included.
h) The slope of the line is calculated correctly.
i) The correct number of place holders and units are reported for the slope.
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j) The linear equation is correct.
Each missing requirement results in the loss of one point.
Student Calculations: [5 total points]
 Use the linear equation to calculate the boiling point of water at your classroom’s
altitude. Show all your work.
 Use the equation to calculate the boiling point at some other altitude. Show all
your work.
Application of the linear equation will be scored as:
5 pts = All of the requirements listed below have been fulfilled.
a) The linear equation used in the calculation is provided.
b) The two altitudes used to solve for the boiling point are provided.
c) The altitude is substituted into the linear equation as the x variable.
d) An example calculation is included.
e) The calculation is solved correctly.
4 pts = Four of the five requirements have been fulfilled.
3 pts = Three of the five requirements have been fulfilled.
2 pts = Two of the five requirements have been fulfilled.
1 pts = One of the five requirements has been fulfilled.
0 pts = None of the requirements have been fulfilled.
Student Summary: [10 total points]
 Summarize your findings. Do the boiling point temperatures acquired from your
linear equation compare to the known value of the boiling point at each chosen
altitude? Explain.
Analysis of the summary statement is scored as:
10 pts = All of the requirements listed below have been included.
a) The summary is clearly developed and complete.
b) The statement is written in complete sentences.
c) The student has included a known value for the boiling point at a chosen altitude.
d) The student has included the reference from which the known value of the boiling
point was obtained.
e) The student has provided convincing arguments based on their comparative data
analysis.
8 pts = Four of the five requirements have been included
6 pts = Three of the five requirements have been included.
4 pts = Two of the five requirements have been included.
2 pts = One of the five requirements has been included.
0 pts = None of the requirements have been included.
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Links to Course Competencies
This RWLO can be used in many different math courses or a physical science course.
The RWLO is best suited for intermediate algebra courses. Upon completion of this
RWLO the following list of competencies shall be met.
 Students will be able to apply the process of mathematical modeling to realworld applications.
 Students will represent data sets graphically and explore the interrelationships
of these representations.
 Students will be able to analyze graphs to identify linear trends and
relationships between the plotted variables.
 Students will be able to derive a linear equation from graphical data.
 Students will be able to solve a linear equation in an application problem.
 Students will communicate inferences and convincing arguments that are
based on data analysis.
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Supplementary Resources
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The International Boiling Point Project Web site contains background information
about the collaborative project, both new and archived data, and many
supplemental links.
There is a Back-up site for the International Boiling Point Project.
This resource provides the linear equation for the relationship between altitude
and boiling point.
A Web-based calculator is supplied to allow calculation of the boiling point for
specific altitudes.
This Web-site contains directions on how to use its search engine to obtain
altitude data: www.topozone.com
This Web address contains altitude information obtained for a 1997 expedition up
Mt. Everest. There is some reference data on the boiling point of water at various
elevations.
http://www.pbs.org/wgbh/nova/everest/expeditions/97/mail/2phys.html
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Recommendations
Implementation:
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This RWLO can be used in either a math or physical science course to graphically
demonstrate the linear correlation between two variables of a data set. The design
of the RWLO requires students to work cooperatively in a group to identify and
download a data file which each student will use, independent of the other group
members, to complete the RWLO. Use approximately 5 minutes to describe the
activity.
Print out all the required materials referenced in the content material section of
this RWLO. This includes: a piece of graph paper, an assignment handout, and a
graphical analysis handout per student.
Back up:
 If the primary Web site for the International Boiling Point Project is unavailable,
the back up site is:
http://www.k12science2.org/curriculum/boilproj/pastprojects.html
As a precaution, print at least one copy of a data file from the International Boiling Point
Project in case the Internet becomes inaccessible.
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