
School's Report Gallery Fall, 2006
School: A. R. Gould, South Portland, Maine Final Report

Summary: The class enjoyed the project. It was great to get outside on a sunny day. We learned alot about the relationship between the earth and the sun. We were particularly surprise at how quickly the shadow location changed as we were measuring it. We were also surprised that our measurements were accurate enough to calculate the earth's circumference so accurately. Students expressed that it was satisfying "to use math to solve an actual problem".

Data Recorded: Friday, September 22, 2006 Site: Basketball court, apshalt surface Equipment: Gnomon was constructed using a onemeterlong dowel mounted through a wooden base (15" x 3.5" x 1.5"). The base of the meterstick dowel was flush with whatever surface the gnomon rested upon.
 Compass
 Chart paper
 Pencils
 Watch

Here are some photos and diagrams:

a
Observations: 
Students visited the site early in the morning of September 22nd to check weather conditions, view the site layoout to determine the best location for the gnomon, and to take measurements of the shadow positions (at 10 minute intervals) for practice and to experience taking such measurements (determining where the shadow ended, umbra and penumbra, etc.) 
We talked about the the concept of solar noon and took information from the U.S. Naval Observatory website that displayed the sun's altitude and azimuth minutebyminute throughout the day. We decided that we would make measurements every minute beginning at 12:20 PM local time and continue marking readings through 12:40. We began taking measurements at 12:25 PM. After the first few measurements, we realized that the location of the gnomon would soon fall under the shadow of the basketball backboard located to the south of the gnomon. We moved the gnomon and the recording sheet and used a compass to maintain the same orientation of the recording sheet. From 12:25 to 12:33, we recorded shadow lenghts that varied from 96.4 cm to 96.9 cm. We believe that the variation was due to the subjective element of determining the end of the shadow as the light becomes diffuse at the end of the shadow.
Based upon a shadow length of 96.4 cm and a gnomon length of 100 cm, we constructed a scale rightangle triangle. Using a protractor, we determined that the shadow angle was 43 degees (the same as our latitude). Using the pizzaslice analogy, an angle of 43 degrees represented 1 slice of the 8.37 slices that made the entire pie (360 degrees). By taking the equator (shadow angle 0 degrees) as our reference point, we estimated the distance from the equator on a NorthSouth line to be 4,779 km. To make that calculation, we used a conversion factor of 111 km for ever degree of latitude. (We learned that from a fifithgrade student's final report .) Fram the data we calculated the circumference of the earth as being 39,950 km. That is within 0.1% of the actual value. Top

School: Bright Beginnings Chandler, Arizona, USA
From: Baca's Brats with Brains Email: dbaca@bbsschool.org Date: Wednesday, 27 September 2006 15:53:22 Subject: Success! Teacher: Debbie Baca Class: 5th Grade My students were fascinated with the premise of using a shadow to find the circumference of the Earth. Despite having read the story, they didn’t really understand how it worked, but they accepted that it could. I went through the preliminary activities and saved the big “Ah ha!” connection until the end. They thought that was the coolest “science thing” they’d ever learned. SUMMARY OF ACTIVITIES: I read the story and we did the “paper folding” activity (slightly modified). We reviewed terminology (circumference, latitude, longitude, angles, etc.). We had to make sure we could measure to the nearest mm and write it as a decimal. The students also got a crash course in using a protractor and measuring angles, as their exposure prior to this was simplistic and minimal. After completing the shadow measurements we discussed how to find the Sun’s angle. I edged them to the idea that making a “scale model” triangle was better than drawing a “life size” triangle. We divided each measurement by 10 to do this (we ended up with our two “sides” being 10 cm and 6.23 cm). Once we used our measurements to find the circumference, the students went on a quest to find out if they were accurate, or, at least, reasonable. They were, and were quite proud! HIGHLIGHTS: We started building our devices early, as I added an extra “problem solving” activity of figuring out how to do it without just using a meter stick (and make sure it still measured 100cm in the end!). We decided to recycle our newspapers and roll them up to make the “stick.” I would definitely do that again. We had to battle wind on the day of our measurements, so I’m glad we did a “test run” earlier in the morning. This made the students realize that their devices were not strong enough to keep steady in the wind. So, we scrapped math for the day and did another problem solving period of howtokeepthemupright. Their solutions were amazingly successful. WHAT I’D DO DIFFERENTLY: The newspaper rolls they made their devices out of tended to bend after much use and preliminary testing. The only thing I would change about the way I conducted this project is that I would warn the students in advance of the likelihood of this happening and have them better prepared to correct (or keep it from) happening. CONCLUSIONS: We learned about troubleshooting, teamwork, and how creative people can be without the advantages of modern technology! My students enjoyed knowing that although there were more mathematicallyadvanced ways to complete this project, we were able to do it in simpler, fifthgrade ways. I am looking forward to next year! Top

School: Princess Anne Middle School, Virginia Beach, VA Final Report
Here's our data: Used 12.125" rulers. Shadow average length: 9.104" Central Angle Calculated: 36.901 degrees Circumference Calculated: 24,662.7 Error only 240 miles from actual circumference. Jeff Goldstein, teacher Princess Anne Middle School Virginia Beach, VA Mathematics Teacher School: 4275325 x 72004 voice mail My website: http://www.jeffgold.net 

