Intermath | Workshop Support

 Write-up

Title
Temperature Comparisons

Problem Statement
Collect temperatures measured in both Fahrenheit and Celsius so that you have 10 data points at least 10 Celsius degrees apart. Plot Fahrenheit vs. Celsius. Is this graph best described as a linear, exponential, or quadratic relationship? Explain your reasoning.

Problem setup

This investigation requests that we sample temperature relationships between Celsius and Fahrenheit. We are restricted to a minimum of 10 sample sets at least 10 degrees Celsius apart. We are then asked to plot the points and attempt to determine if they are linear, exponential, or quadratic.

Plans to Solve/Investigate the Problem

I will use Excel and an online metric to Fahrenheit conversion calculator to solve this problem. Using the conversion calculator, I will translate Celsius temperatures using 100 as the upper range, -100 as the lower range, and 10 as the interval. I will then place both Celsius and Fahrenheit data points into an Excel Chart. Upon completion, I will graph the points using a scatter plot, and come up with an equation using the trendline feature of Excel. If my R=1, then this formula will be exact.

Investigation/Exploration of the Problem

I created the excel spreadsheets as detailed above. I followed my procedural instructions, and ascertained that indeed my R=1 and my formula for converting Celsius to Fahrenheit is “y = 1.8 x + 32”. See Excel Spreadsheet below:

 Celsius Fahrenheit 100 212 90 194 80 176 70 158 60 140 50 122 40 104 30 86 20 68 10 50 0 32 -10 14 -20 -4 -30 -22 -40 -40 -50 -58 -60 -76 -70 -94 -80 -112 -90 -130 -100 -148

Extensions of the Problem

A possible extension would be to begin with Fahrenheit measurement and convert into Celsius. I will use the same procedure, and see what my results are. I theorize that there should be a converse relationship with my two equations.

 Fahrenheit Celsius 100 37.77778 90 32.22222 80 26.66667 70 21.11111 60 15.55556 50 10 40 4.444444 30 1.111111 20 -6.66667 10 -12.2222 0 -17.7778 -10 -23.3333 -20 -28.8889 -30 -34.4444 -40 -40 -50 -45.5556 -60 -51.1111 -70 -56.6667 -80 -62.2222 -90 -67.7778 -100 -73.3333

As seen in the sheet above, we do have an equation – “y = 0.5564x - 17.672”, but our R value in just a bit

below 1 (R2 = 0.9998). I would make the assumption that this is due to rounding. (Probably why we were instructed to begin with Celsius.

Author & Contact
Jim Taylor
jtaylor1@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
http://www.onlineconversion.com/temperature.htm

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