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 Algebra 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 The actual project handout follows on the next several pages:

CHM 1025C/MAC 1105: Critical Thinking Exercise

By definition:
Learning -  the acquisition of knowledge or skill.

Teaching – the action  of a person who is showing or helping a person to learn.

Cognitive scientist define “critical thinking” as mental activity associated with these types of thinking:
a. applying reasoning
b. making decisions
c. problem solving

In the CHM 1025C Corwin  textbook used at Florida State College @ Jacksonville , critical thinking is introduced within the context of chemical principles. In CHM 1025C and the Corwin text critical thinking  is undertaken specifically in the chapter vignette and end-of-chapter self-tests, and generally in unit analysis problem solving.

In the CHM 2045C MvMurry’s  textbook used by the instructor at North Campus, critical thinking is not introduced or discussed.

At FSCJ we have been addressing “Institutional Effectiveness”(I.E)  across the curriculum. The faculty is developing district wide exercises to assess learning outcomes. For chemistry (CHM 1025C) the science council/cluster feels we need to pursue under our course goals and objectives the following outcomes:

FSCJ CHM 1025C Official Learning Outcomes:

1.      Explain and apply major concepts in general chemistry

2.      Demonstrate knowledge of scientific method

3.      Interpret scientific models such as formulas, graphs, tables and schematics, draw inferences from them and recognize their limitations.

4.      Demonstrate problem solving methods in situations that are encountered outside of the classroom

The following lab exercise addresses all four of the above, especially #3:

Lab Assignment #12:

CHM 1025C Students: Read Corwin’s Section 2.9: Temperature  The above images from Chapter 2 of the CHM 1025C Corwin textbook(page 51) or the below image from Chapter 1 McMurry’s CHM 2045 textbook (page 13) demonstrate equivalent temperatures on the Fahrenheit and Celsius scales with ice water and boiling water. The third thermometer compares to Kelvin Temperatures to Fahrenheit and Celsius temperatures. McMurry just shows the 3 thermometers.

CHM 2045C Students: Read McMurry’s Section 1.8: Temperature Go to the temperature conversion web site: http://www.lsua.info/mathworkshop1/frametemp2.html

1. Setup the Student’s theoretical temperature scale with the following parameters:

A. The Freezing Point of water is Your Age or Your desired Age.  (Prof Taylor 50oT)(Ms Sweet 30oS)

B. The Boiling Point of water is your body weight or desired body weight (Prof Taylor 250oT)(Sweet 120oS)

1.  Fill in the table below/next page with your parameters to make oX (Student): (Professor Taylor’s normal body temperature is the normal 98.6 oF, Professor Bessman 96.8 oF, and Ms Sweet 97.3 oF.
2.  If your normal body temperature is not 98.6 then fill in you Fahrenheit temperature and calculate the blanks across the line of the table for at least 5 points from +250oF to -150oF

Table of Equivalent Temperatures:

 Temperature oF Temp. oC Temp. K Temp. oT Temp. oS Temp. oX (Fahrenheit) (Celsius) (Kevin) (Taylor) (Sweet) (Student) 250 121 394 298 139.0 212 100 373 250 120.0 158 70 343 190 93.0 104 40 313 130 66.0 98.6 37.0 310.0 124.0 63.3 97.3 36.3 309.3 122.6 62.7 96.8 36.0 309.0 122 62.4 81 27 300 104 54.5 77 25 298 100 52.5 75 24 297 98 51.5 68 20 293 90 48.0 50 10 283 70 39.0 32 0 273 50 30.0 14 -10 263 10 21.0 0 -18 255 1 14.0 -4 -20 253 -2 12.0 -22 -30 243 -14 3.0 -28 -33.3 240 -17 0.0 -40 -40 233 -26 -6.0 -58 -50 223 -33 -15.0 -76 -60 213 -50 -24.0 -130 -90 183 -86 -51.0 -148 -100 173 -98 -60.0

1. Using a rectangular piece of graph paper, set up a graph plotting Fahrenheit versus Celsius so that vertical axis is Fahrenheit ranging from 250 down to -150 and the horizontal axis is -100 on the left and 125 on the right.
a. Describe the line or curve generated by this data:

b. If the plot is a line, then what is the slope of the line and the Y intercept and the X intercept.

c.  Write the equation for the line.(Do you remember the equation of a straight line from
algebra?)

d. If the plot is a curve, can you write the equation of the curve?

1.  Now plot Celsius versus Kelvin on a rectangular coordinate graph. If Kelvin is the y axis and Celsius is the x axis, where should the data point (0,273) be located?
1. what is the y axis intercept? What is the slope of the line?
2. Is there an easier way to find the slope of the line by looking at the data?
3. At what temperature Celsius would Kelvin equal zero?

1. In the Corwin  textbook on page 50 and in the McMurry textbook on page 13 we refer to temperature on the Fahrenheit and Celsius scales as degree F (oF) and degree C (oC), but in Kelvin temperature, temperatures are referred as Kelvin units (not oK – degrees Kelvin) (the word scale is actually incorrect)?  Why?

1.  Now plot Celsius versus Student and Fahrenheit versus Student using separate graphs. On the oC vs oF graph, examining the data do you notice that: -40 oF = -40 oC. On your two Student graph plots is there a temperature where    oS = oC    or   oS = oF?

1.  Algebraically is there away to determine if there is a temperature on the Taylor Scale, the Sweet Scale, or the Student Scale when that temperature equals a temperature on either the Celsius or Fahrenheit scale? If so, on a separate piece of paper show the calculations for each (up to six).

1. Algebraically is there away to determine if there is a temperature on the Celsius Scale when that temperature equals a temperature on the Kelvin scale?Why?

Sample Graph Paper Fahrenheit versus Celsius          Name:________________________ Fahrenheit versus Celsius          Name:________________________ Kelvin versus Celsius          Name:________________________ Kelvin versus Celsius          Name:________________________ Fahrenheit versus Student          Name:________________________ Fahrenheit versus Student          Name:________________________ Celsius versus Student               Name:________________________ Celsius versus Student               Name:________________________ 