Park City Mathematics Institute
Geometry
Project Abstracts

Drafts of Project Files (password required)

Polyomino Group
Marcia Bollwage, Stephanie Ruprecht, Nicholas Salvatore

Students will explore properties of polyominos to enhance their understanding of geometric and algebraic concepts that are taught in most traditional curricula. The students will identify relationships between changes to linear measures and the geometric properties of polyominos through exploration, data collection, and graphical representation.

Star Polygons - An Exploration of Polygon Properties
Tony Anderson, Mary Andrews, Ellie Schweber
The concepts explored in the project include the some of the interior angle measures of polygons and the relationships betweens the sums of the measures and the number of sides in the polygon. This will be done by having students use star polygons to expand their understanding of various properties of polygons. An interactive applet and the Geometer's Sketchpad will be used as tools in this exploration.
Incorporating the Geometer's Sketchpad into the Connected Mathematics Program Perimeter, Area, Surface Area and Volume
Christina Dubal, Alicia Garza, and Cheryl Myers

The middle school geometry concept explored in this project will focus on measurement, a difficult concept for students across the nation. In these problems, sixth grade students work on constant-area with changing-perimeter, and constant-perimeter with changing-area. In addition, problems will be modified to meet the standards for the 7th and 8th grade levels to include surface area and volume. Students are provided with problem situations to investigate using the Geometer's Sketchpad. Lesson investigations are reinforced through Covering and Surrounding, Comparing and Scaling, and Filling and Wrapping from the Connected Mathematics Program. The purpose of this project is to integrate technology, using Geometer's Sketchpad, into a middle school mathematics curriculum.

Constructing Single Image Stereograms
Bill Schultheis and Jennifer Friends
This activity demonstrates the connection between geometry and depth perception in binocular vision. Students use properties of similar triangles to construct single-image stereograms: images in 2 dimensions, that when properly focused upon, appear fully 3-dimensional.

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© 2001 - 2014 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. 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.