LINEAR FUNCTIONS AND MATHEMATICAL MODELING PROJECT OVERVIEW THIS RWLO

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Math RWLO Template Title Placeholder

LINEAR FUNCTIONS AND MATHEMATICAL MODELING PROJECT OVERVIEW THIS RWLO


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.







Student Learning Objectives





Procedure


Time: 50 minutes


Materials: Graph paper, ruler, and pen


Background


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:







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


Additional Resources

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



Assessment



Each of the bullets in the Assignment Handout can be used for assessment based on the following rubric.


Graph: [5 total points]


Preparation of the graph will be scored as follows:

5 pts = All of the requirements listed below have been fulfilled.

  1. The independent and dependent variable is chosen correctly and plotted on the appropriate axis.

  2. The axes scale are appropriate for the data plotted. The scale uses the correct number of place holders provided by the original data table.

  3. Each axes are labeled or titled. The graph is given a title.

  4. All appropriate units are provided in parentheses near the axis label.

  5. 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]


Analysis of the graph will be scored as:

10 pts = All of the requirements listed below have been included.

Each missing requirement results in the loss of one point.


Student Calculations: [5 total points]

Application of the linear equation will be scored as:

5 pts = All of the requirements listed below have been fulfilled.

  1. The linear equation used in the calculation is provided.

  2. The two altitudes used to solve for the boiling point are provided.

  3. The altitude is substituted into the linear equation as the x variable.

  4. An example calculation is included.

  5. 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]


Analysis of the summary statement is scored as:

10 pts = All of the requirements listed below have been included.


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.



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.






Supplementary Resources





Recommendations



Implementation:



Back up:

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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