Fall 2008

1. Registration opens! By registering for this project, you agree to complete all of the activities listed below by the established deadlines. Detailed Lesson Plans are located in the Teacher Guide.

2. Project Begins! Write the Class Letter of Introduction and submit it to the Discussion Area by September 10 th.

3. Learn about the project. A variety of detailed lesson ideas are located in the Teacher Guide.

4. Complete shadow measurements by September 28th and enter your measurement data at the Project Data website.

5. Do your circumference calculations by October 5th. See Teacher Guide for details.

6.  Write and submit a Final Report by October 12th. See instructions for final report.
Welcome!

Project Overview: Noon Day
Dates: Biannually during the months of March & September

Spring
Time Frame: March 7th – April 11th
Target Measurement week(s): March 17-28

Fall
Time Frame: September 7th – October 11th
Target Measurement week(s): September 17-28

Purpose: To recreate the remarkable measurement of the circumference of the earth that was done over 2000 years ago. Using only simple tools such as rulers, protractors, and meter sticks, students will measure shadows cast by a meter stick at different locations on the earth.

Subjects: Mathematics (geometry, ratios, scale drawing, measurement, introduction to trigonometry (optional)), science, social studies, geography & history.

Summary: Over 2,000 years ago Eratosthenes made a remarkably accurate measurement of the earth's circumference. This project requires collaboration of students in places at different latitudes of the earth to make some simple measurements, share data, use a spreadsheet to make comparisons, and then replicate and share their results. Here is a summary of the steps involved in making the measurements:

1. At least two sites must collaborate whose latitudes (north-south distance) are different enough to give a significant difference in measurements.

2. On the given date students will conduct their measurements outdoor at high noon, local time.

3. Using a standard meter stick each team of students will:

a) lay out a piece of paper flat on the ground

b) hold the meter stick perfectly vertical. (It may be taped to a metal book end, set in sand inside a liter plastic bottle, etc.)

c) mark on the paper the end of the shadow at one minute intervals over a ten to twenty minute period.

d) several measurements should be made by several different students or teams of students the more the better.

e) measure the length of the shadow cast by the meter stick to the nearest centimeter and these measurements will then be analyzed by the students.

f) using statistical computations the class should arrive at what they feel is the length of the shadow cast at local noon (which should be the time of the shortest shadow).

4. This length of the shadow at local high noon and the date on which the measurement is taken will be posted on the Web.

5. This data along with the latitude for each site is enough information to use a simple proportion to make a fairly accurate calculation of the Earth's circumference as determined by each pair of sites.

Number of participants: unlimited

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Week 1: September 10th - 17th
"Setting the Stage" Activities. In addition to completing your letters of introduction and in order to prepare your students for the measurements that will take place later in the month, you might start off by making them more aware of shadows and the "stories they tell." For example:

 Activity: Shadow Stories Have your students look at a shadow (like the one on the right.) Have them describe what a shadow does over the course of a day (from sunrise to sunset.) Make a graph to tell the shadow's story.   See Making a Shadow Plot in the Northern Hemisphere for details. Related questions:  When is the sun directly overhead? What happens to the length of the shadow at that time? Is there any time when the sun would be directly overhead and NOT cast a shadow?

Other questions to ponder

• Do you think ancient man thought the earth was round or flat?
• Let's say you belonged to the "Flat Earth Society." What arguments would you make for the earth being flat?
• What arguments would you give if you were a member of the "Earth is Round" Club?

• Interesting sidebar: One of the myths that James Loewen debunked in his book "Lies my Teacher Told Me - Everything Your American History Textbook got Wrong" (p. 45-48) is that most people at the time of Columbus' voyages thought the earth was flat. Columbus was not so daring, nor did his crew want to mutiny because they feared they would drop off the edge of the earth. The truth is that most people around 1492 believed the earth was round. Historians give credit to Washington Irving's biography of Columbus in 1828 for starting the myth. He had an account of how Columbus had to convince his investors of the spherical nature of the earth. Pure fiction.
Introducing the project to your students

Imagine that you are living over 2000 years ago and you are convinced that the earth is round. How would you go about measuring it? One way would be to start walking in one direction and keep track of how far you go. If the earth is round as you believe, eventually you should return to where you started. Do you think anyone actually contemplated trying this back then? Why or why not? What would be some of the obstacles?

Another method would be to drill a hole to the "other side" of the earth and measure the distance. Once you knew that distance, could you determine how round the earth is? Is there a relationship between the distance around a circle (circumference) and the distance through the center of the circle (diameter)? (You might try one of the activities at http://arcytech.org/java/pi/ to see if you can discover a relationship between the circumference of a circle and its diameter.*) Unfortunately, digging a hole through the center of the earth is just as out of the question as circumnavigating the globe by foot.

This brings me to someone named Eratosthenes who was born 2000 years ago in Cyrene, a town in northern Africa. He actually found out how round the earth is by doing an experiment. His idea was to think of the earth as an orange cut in half. The cross section is divided into wedges just like pizza slices.

Week 2 & 3: March 17th - 28th
Doing the Measurements

• You should try to get your measurement done no later than by the end of week 3. Our target is to do the measurements as close to the Equinox as possible but anytime during this two week span will be fine. (The margin of error is very small if done in this time period.) See http://en.wikipedia.org/wiki/autumnal_equinox for details.
• Since you need a sunny day for shadow measuring, we suggest you check your weather forecast and pick a day when you will most likely have sun.
• Do the measurement when the sun is highest in the sky (at your local noon time.)

Week 4: October 1st - 4th
Analyzing the Data, Determining the Circumference and reporting your results

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Week 5: October 7th - 11th
Reflections and Final Report

Other Notes

• We encourage you to participate in this project as much as possible. We are interested in your methods, strategies, anecdotes, and wild ideas. Please share your experiences with us in the discussion area.
• What makes this project so special is that this is a collaboration. I am eager to make this project work for you as best as possible and to learn from our collective experiences so we can keep on improving it.
*More about "pi" can be found here.

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