Around the World: Surprise! (Part 1)

Back in the late 90's I worked with The Math Forum Problems of the Week. (POWs) Specifically I worked on the Trig/Calculus POW
and the Discrete Math POW.  Submissions came in from around the globe and I enjoyed seeing the variety of methods students used to solve the problems. There was even one time when a student used calculus to prove she found the minimum number of moves needed to solve the discrete math problem for that week!

This past week I was on spring break and I pulled out a wonderful GeoPOW problem from my files.  I plan to use it on Monday, because we often miss students on the first day back from spring break due to families extending their spring break.  Rather than having several students miss new material, I thought it would be fun to look at this surprising problem.  In the GeoPOW files, this problem was called "All Around the World".

Imagine that the Earth is a perfect sphere*, and that a metal wire is snugly wrapped around its equator. Now imagine that we cut this wire in one spot and splice in an additional 100 meters of wire.  We take up the slack by using posts to raise the wire an equal distance all the way around the Earth.  How high above the surface of the earth will the wire be?

*many students are surprised to learn that the earth is not a perfect sphere*

Collaboration is a big part of learning math in my classroom; students will work on this problem in groups.  After each group gives me an explanation that convinces me that they have the correct answer (Note: The answer is about 15.9 meters.), the group will reach into a hat and pull out a slip of paper that will have one of the following items written on it: basketball, moon, Jupiter, beach ball or Mars.  The groups will then repeat the problem that they just did with the Earth, but with their new spherical object.  After students have finished the problem, they will go to the tinyurl written at the front of the room to enter data into the following form:

After students click the Submit button, they will see the message "We will review the results from the class shortly."  The surprise will come when I turn off the AV Mute button on my projector and we see the results at the same time!  Come back for part 2 of this blog when I share how the lesson went and my students' reactions.  But before then, do the math and predict why my students will be surprised.