Hello to all! The sun god smiled upon us on March 20, 2007 and gave the only 45-minutes of sunshine that existed that entire week at precisely the time we needed to make our "local noon" shadow measurements! Our math class began with totally overcast skies and a threat of rain. Fifteen minutes later (and only twenty minutes before our exact local noon), the sun began to peek out of the clouds. Grabbing paper, meter sticks, duct tape and pencils, we ran out of the building and measuring commenced!! However, the wind god was less benevolent to us . . . . papers and meter stick-holders flew everywhere . . . . there was only one group who successfully kept their can in one place for the entire measurement period. Therefore, the measurements of that group were the ones our whole class used.

Shadow measures secured, we headed back to the classroom and constructed similar triangles to reflect the measurements we gathered outside. We used both trig. (good ol’ Chief SOH-CAH-TOA) and a protractor to measure the sun angle. We concluded trig. was the more accurate route to go and used a measure of 43-degrees for our sun angle. Each group’s assignment was to use the data from the class at Lake County Intermediate School in Leadville, Colorado (my daughter is their teacher!!!), Mohammad Noorizadeh’s class from Neishabour Students’ Research House in Khorasan, Iran, and one school of each individual student’s choice from the list to calculate the circumference and percentage of error.

#1: It took us a few calculations to determine the correct north-south difference between our locations. We first used door-to-door measurements and got circumference measures to be four- to five-times what it should have been. When we discovered and corrected our mistake, we felt a lot better about the results!

#2: Using my "accurate" group’s measurements and the calculations of the Leadville group, we determined the circumference of the earth to be 24,840miles or 39,960km. Our percentage of error differed if we used the circumference measured around the equator or the circumference measured going through the poles. Equitorial percentage of error for both kilometers and miles came out to be just slightly more than 0.2%. Percentage of error using the circumference measured going through the poles came out to be slightly less than 0.08% (both kilometers and miles)!!! WE WERE AMAZED!!!!

Calculations with the Iranian school’s measurements did not result in as small of a percentage of error in calculation as when using the Leadville school’s measurements. The individual choices of partner schools of each student were almost all less than a 1% error of measure with each student.

#3: What would we do differently next time? Try to move the Vernal Equinox to a date when the temperature is more likely to be above freezing!!

Summary: What an enjoyable activity! The whole project led to great discussions about geography, politics, places to vacation, and occasionally, math!!! As I stated in my letter of introduction, my class consists of high school special needs students who have struggled with mathematics classes throughout their entire school life. To watch them help each other construct similar triangles, consult trig tables, argue about whether to use sine, cosine, or tangent and then calculate percentage of error was amazing!! I have never been so proud of them!!!

When we first calculated our percentage of error, I was certain we had made mistakes. We kept re-calculating and re-calculating and eventually convinced ourselves that the measures really did produce that accurate of an estimate of the earth’s circumference! It took me some time to have the kids understand that they should be really impressed with their work . . . but, eventually, I think they came to understand what an amazing feat it was!!! It was also a good lesson for them to watch how I (and a few fellow math teachers at my school) tried to figure out our error of computing the north-south difference in miles/km. We didn’t realize why we were making the error at first and my kids saw how the "experts(!)" also make mistakes, work backwards to find their mistake, and start all over again. This was also a valuable lesson learned from this activity.

On a personal note . . . . I was really excited to do this project with my daughter. This is my final year of teaching and it was really fun to work with my daughter on a "professional" level even though we are half a continent apart from each other. My kids were excited, too . . . . they took it to be a "competition" between mom-and-daughter!

Thank you, Dr. Charischak, and all participating schools, for allowing us to become involved in this project. It was really great to see my students "get into" math and realize they possess the skills to compete with "regular" kids from around the world and, in some cases, even produce more accurate results. They did not feel like they were in "watered down, dummy math class" with this project and that was a great, great thing to see!!!

Debbie Morgan (of Morgan’s Marauders)