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School's
Report
Gallery
Fall,
2006
School:
A. R. Gould, South Portland, Maine
Final
Report
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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".
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Data Recorded: Friday, September 22, 2006
Site: Basketball court, apshalt surface
Equipment:
Gnomon was constructed using a one-meter-long dowel mounted through a
wooden base (15" x 3.5" x 1.5"). The base of the meter-stick dowel was
flush with whatever surface the gnomon rested upon.
- Compass
- Chart paper
- Pencils
- Watch
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Here
are some photos and diagrams:
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a
Observations:
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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 minute-by-minute 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 right-angle triangle. Using a protractor, we
determined that the shadow angle was 43 degees (the same as our
latitude).
Using the pizza-slice 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 North-South 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 fifith-grade
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.
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School:
Bright Beginnings
Chandler, Arizona, USA
From: Baca's Brats with Brains
E-mail: dbaca@bbs-school.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 how-to-keep-them-upright.
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 trouble-shooting, teamwork, and how creative people
can be without the advantages of modern technology! My students enjoyed
knowing that although there were more mathematically-advanced ways to
complete this project, we were able to do it in simpler, fifth-grade
ways.
I am looking forward to next year!
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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:
427-5325 x 72004 voice mail
My website: http://www.jeffgold.net
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