Quick synopsis of current lesson: As part of map and math studies the students draw lines of latitude and longitude on a grapefruit to represent a globe. Then they are challenged to flatten out the globe to make a map. The globe (skin of grapefruit) gets torn and distorted. Class discussion about how representing 3 dimensions in 2 dimensions causes distortion. We discuss different map projections.
Next step is to challenge them to “draw” a cube. (Use overhead to shine through clear plastic cube to create image on board.) I ask if anyone could do it. Almost always they say that they have. Then we discuss properties of a cube (angles 90 degrees, sides equal). Their drawings don’t fit that description. They figure out they have not successfully drawn a cube. (Impossible). (Thanks to Carl Sagan for parts of this lesson.)
We then discuss dimensions. We try to construct hypercubes (or at least the shadow of a tesseract) using straws. These hang from the ceiling.
HELP NEEDED: For 5th graders. It would be great to have the help of someone with a higher math or physics background to supplement my explanations and provide perspective. It’s possible that the models are not being done correctly because of the limits of my highest level of physics which was 12th grade. I explain that when we look at our drawings in 2 dimensions of cubes, we can pretty well “get” what a real cube looks like. But when we look at our tesseracts, I don’t “get” what it would really look like. My premise is that a mathematician or physicist might be able to make the leap. One of my students with exceptional ability might someday be able to SEE what I can’t. The purpose of the lesson is to inspire and feed the wonder that young children have.

Students already love these lessons. I believe I could benefit from working with someone who has a higher level of understanding of this material. Help could be via Skype (we are actually well set up for advanced video conferencing at my school beyond Skype.) Class visit would be great too. Help could be concrete in construction of models, or just motivational helping children to connect with the world of science that awaits them later in their education, or perhaps connections that I haven’t conceived yet.

My students are 10-11 years old, 5th graders. Deerfield School, is in the Millburn Township Public Schools, in Short Hills, New Jersey. Although not a so-called “gifted” class. All students are “gifted” and capable of much more than we require of them. You will be amazed at how high a level of understanding these children are capable of, prior to the educational system wearing them down.

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