## Investigating Geometry Summary

### Monday - Friday, July 9 - 13, 2007

Monday
Transformation tools in GSP were reviewed as a full class. This was done through the context of constructing a square using reflections and rotations. Individuals were then encouraged to team up with others to pursue a project (either as a continuation of last weeks mini projects or a new project) for the remaining working group time.

Tuesday
Teams met and formulated the details of their project.

Wednesday
Working groups did not meet today.

Thursday
Teams continued to work on their projects.

Friday
Groups discussed the progress of their projects to the full group (see below). Jim and Art also illustrated some sample Geometry projects from past years.

Sketchpad Beginner's Group (Jill, Deb, Caroline, Mary): The members of this group have little to no background in using Geometer's Sketchpad so Art introduced them to the basics. First, they practiced using each of the tools and then moved on to constructions, transformations, measuring, and graphing. The second day, they worked on conic sections by constructing parabolas, circles, ellipses, and hyperbolas including their loci.

Transformations in GSP (Ralph): Ralph is focusing on the basics of transformations since they are included in his state standards and he never was taught them while he was in school. He is creating hands-on scripts for his students to use with GSP.

Non-Euclidean Geometry (Philip): Philip has been toying with a program entitled "WinGeom" in a non-Euclidean model. He has also offered to help other groups with their projects.

Circle Inversion (Chris and Bill): Chris and Bill are creating a series of tools in GSP that allow the user to invert objects into and out of a circle. They will also be focusing on the different constructions that could be used to make these tools and analyze the strengths and weaknesses of these constructions.

Volume Decomposition (Rey and Josue): Similar to breaking a parallelogram into two triangles to find the area formula for a triangle, Ray and Josue are using Cabri 3-D to have a visual model of how the volume formula for a pyramid can be constructed from that of a prism.

Transformations Using Quilt Squares (Deb and Mary): Deb is using GSP to show how reflections and rotations can be used to create different quilt squares at the elementary level.

Sketchpad Tutorials (Rob): Rob is writing a sequence of scripts for students to use with GSP including right triangle trigonometry and circle theorems.

Trigonometry and Bees (Mario): Mario is using GSP to visually support a pre-existing "bee" unit on the perimeter/area of regular polygons using trigonometry.

Wasted Farmland Problem Solving (Kim): Inspired by a lesson study, Kim wants to use GSP to allow students to study composite area problems (e.g. circle inscribed in a square)

Bicycle Sprockets (Rich): Rich wants to use the construction and animation features of GSP to show how the sprockets in a bicycle work.

Centers of Balance (Carla): Carla has been studying how the centers of balance (both based on area and vertices) can be constructed for irregular polygons in GSP.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.