Joint Critical Thinking Project via Modeling Linear Functions Using Temperature Conversion Scales Abstract:  At FSCJ exercises are being developed to demonstrate critical thinking ability of the students. This project is a joint effort to compare students in both College Alegbra and Chemistry classes. The functional relationship between the Fahrenheit and Celsius Temperature scales are derived using the corresponding boiling and freezing points of water. In this project students each create a unique Temperature scale using the student’s body weight and the student’s age as the boiling and freezing points of water respectively. This “student” scale is then compared to the Fahrenheit and Celsius scales. The resulting functions are graphed and compared. We will illustrate this on the webpage: http://www.lsua.info/mathworkshop1/frametemp2.html Complete Description: At FSCJ exercises are being developed to demonstrate critical thinking ability of the students in all of the general education classes. Cognitive scientists define “critical thinking” as mental activity associated with these types of thinking: a. applying reasoning; b. making decisions; c. problem solving. This critical thinking project is a joint effort to compare students in both College Algebra and Chemistry classes. During the first weeks of a beginning or first semester of college chemistry classes temperature scales are introduced as part of measurement. America still lives with the out dated Fahrenheit scale while most of the world uses the Celsius scale developed as the centigrade scale in the metric system of measurement. Most textbooks demonstrate a graphic comparing three thermometers: Fahrenheit, Celsius, and Kelvin. Then conversion formulas are shown to calculate the corresponding temperature on one thermometer from a temperature on another thermometer. During the first weeks in a College Algebra Class linear equations are introduced. Graphing linear data, the students sees the y=mx+b relationship. At an AMA summer math workshop at Duke University, the participants were developing discovering learning projects to introduce college algebra topics. The first project had a bank sign flashing current temperatures, Fahrenheit and Celsius. Five data points were given for the temperatures at five different times of day. Graphing the data the student discovers that converting one temperature to another is a linear function: F = 1.8C + 32 or C=0.556(F-32). It was pointed out by the presenters that every science student from the fifth or sixth grades and above has seen the conversion formulas in one form or another. One of the best web sites discussing temperature conversions is: http://www.mathsisfun.com/temperature-conversion.html   In addition to the standard textbook formulas, this site has several alternative formulas, one using the +40/-40 process which is by far the best formula for non-mathematical students to use because the conversion from F to C and C to F uses the same order of operation: Add, multiple, then subtract. The functional relationship between the Fahrenheit and Celsius Temperature scales are derived using the corresponding boiling and freezing points of water. However, to make the college algebra project more interesting, the presenters developed a web site so that the each student creates a unique Temperature scale using the student’s body weight and the student’s age as the boiling and freezing points of water respectively. This “student” scale is then compared to the Fahrenheit and Celsius scales. The resulting functions are graphed and compared. Each student’s linear equation is a unique formula to convert Student to Fahrenheit and Student to Celsius. If you Google “temperature conversions” you find about 68 millions web pages. However, the unique webpage developed by the presenters which generates the data points is: http://www.fscj.me/mathworkshop1/frametemp2.html