Geometry Summary

Monday - Friday, July 4 - 8, 2005

Tuesday, July 5, 2005

Ginny, David, Judy, Kelly, Josue, and Melissa are working on lessons concerning similarity and changes of scale, and how these affect surface area and volume.

Darryl Yong (from Harvey Mudd) has joined our working group, and has taken to working with Mike, Theresa and Jim in their study of 3-dimensional solids. We have a feeling that Darryl's addition will cause quite an uproar in the group!

Wednesday, July 6, 2005

Judy and David completed their rough draft/outline of their part of the larger

similarity project. They are going to work on incorporating some of the principles of the 11 o'clock hour to make their lesson more "open."

Josue and Melissa continued to work on and to learn how to use Cabri 3D. They have been working of making 3-dimensional models of the Cuisenaire rods.

Thursday, July 7 2005

We started out with Steve extending his five minute short by leading the group in a construction of a tetrahedron using Cabri 3D. The focus was on how the thought processes of constructing things in three dimensions is very different from those in two dimensions.

Mike, Theresa, Darryl and Jim continue to have too much fun. They are focused on three polyhedra that are constructed with equilateral triangles: A tetrahedron, an octahedron, and a hexahedron. They are working to construct an algorithm that can be used to determine which nets can be folded up into these polyhedra.

Some of the questions they are exploring are:

• Refer to the polyiamonds make with 6 equilateral triangles at http://mathworld.wolfram.com/Polyiamond.html. Which of these nets would fold to make a hexahedron?
• Find as many nets as you can for your model. (Geometer's Sketchpad® could be used to create these nets.)
• Using one of the nets you found, see how many different ways you could color the net so that each face is a different color.
• Using one of the nets you found, see what the minimum number of colors you would need if each face that shares an edge is a different color.

Ginny and Kelly have turned in some preliminary resources. They have constructed TASK CARDS that lead students in a simple open investigation of how changed in scale change the surface area and volume. They are using Cuisenaire rods to drive their investigations. Their task cards are designed to foster cooperative skills.

Melissa and Josue are working on a student introduction to Cabri 3D that will lead students to build Cuisenaire models. They have learned to use the software by building the very same shapes, so they are getting their "learning" down on paper so students will benefit.

David is working on vocabulary and teacher notes for the unit. Judy is working on revising their activities from their rough draft. Judy also found http://www.printfreegraphpaper.com and http://www.mathematicshelpcentral.com to be a good resources for getting graph paper for their project.

Friday, July 08, 2005

Today we presented our rough drafts of their projects.

Jim's glasses broke today, so he is wearing his prescription sunglasses during the presentations. He looks like a movie star.

The first group is using Cuisenaire rods to study changes of scale, surface area, and volume.

• Judy presented her introductory lesson "Double the Dimensions - Double the Volume or Double the Surface Area?" The purpose is to investigate the relationships of the volumes of rectangular prisms when the dimensions are changed by different factors.
• Ginny and Kelly presented their cooperative investigation into the changes of scale. The key to their project are cooperative task cards. The goal is for students to communicate in four different ways the relationship between surface area and volume when dimensions are doubled.
• Josue and Melissa shared their Cabri 3D sketches. They are creating a student tutorial that will introduce students to the software by having them construct Cuisenaire rod models. Melissa will "field test" the tutorial on her unsuspecting room mate.

The second group is studying nets.

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