75 Word Abstract

Using Temperature Conversations to Model Linear Equations in College Algebra

John Taylor, Florida State College @ Jacksonville

And

Sharon Sweet, Brevard Community College

Instead of using the Reference Points of boiling and freezing points of water in Fahrenheit and Celsius, the student creates a unique set of reference points by using the student’s body weight (or desired weight) as the boiling point of water and the student’s age (or desired age) as the freezing point of water.  The student creates at least five sets of data points utilizing the web site:

http://www.lsua.info/mathworkshop1/frametemp2.html

The values for this new temperature scale are recorded in a data table and the student can plot the unique linear equation which identifiers a different slope of the line. The equation developed is in the form of:

oY = y/x (oX + RPx) - RPy

The presenters will demonstrate this web site and describe how and why they use this site in the College algebra and introductory chemistry courses.

Long Abstract only for the program committee:

Several years ago one of the presenters was at a Summer Mathematic Workshop at Duke University for the purpose of developing interactive math programs for teaching College Algebra and Calculus.  One of the “innovative” problems  for a first lab assignment in a college algebra course,  was the student observed a bank sign flashing the time and temperature in both Fahrenheit and Celsius at five different times of the day.  From this data, the student was to plot the five data points to examine a curve generated.  The data plot is a straight line and the result was a linear equation in the form of y= mx + b.

However, this presenter many years ago had been teaching in his chemistry classes temperature conversion in Fahrenheit and Celsius using  a very unique formula versus the traditional:

oF = 9/5 oC  + 32        or         oC = 5/9 (oF - 32)

These unique formulas which utilize the same order of operation are:

oF = 9/5 (oC + 40 ) - 40        or         oC = 5/9 (oF + 40)  - 40

This workshop participant suggested to the group, that every middle school student has converted Fahrenheit to Celsius and vice versa and had used the traditional formulas above so that the discovery of the linear equation through data modeling was already known.   Instead, this presenter developed a web site  for the workshop participants, which gives each student in the class a unique set of data which would develop in a different unique linear equation.  The web site is:

http://www.lsua.info/mathworkshop1/frametemp2.html

Instead of using the Reference points of boiling and freezing points of water in Fahrenheit and Celsius, the student creates a unique set of reference points of the student’s body weight (or desired weight) is the boiling point of water and the student’s age (or desired age) as the freezing point of water with the condition that the body weight must be a number greater than the age.  The values for this new temperature scale are recorded in a data table and the student can plot the unique linear equation which identifiers a different slope of the line. The equation developed is in the form of:

oY = y/x (oX + RPx) - RPy

The presenters will demonstrate this web site and describe how and why they use this site in the College algebra and introductory chemistry courses.