Park City Mathematics Institute
Investigating Geometry
Project Abstract

Drafts of Project Files (password required)

Exploring Similarity Through Geometer's Sketchpad, Snap and GeoGebra
Tina Cardone*, Allison Krasnow, Rina Martinez
This project is a study of how three different types of software can be used to investigate similarity. We start with an introductory lesson where the students use pencil and paper to explore and define similarity. The students continue to discover coordinate rules for similarity using either Geometer's Sketchpad or Snap. Students plot multiple polygons and decide if they are similar, as well as build their own figure similar to a given one. In Snap students use trial and error to discover the exterior angles of polygons, while in Sketchpad they construct the similar figures and measure the angles. GeoGebra is the software used for a final unit project on similarity. Students use indirect measurement to find the height of a tall object (in this case, the Campanile at the UC Berkeley campus). They model their measurement method on GeoGebra to determine which measurements they'll need to make when they go out in the field. Students compare their results and the class discusses which measurement techniques are most accurate.
Basic Trigonometric Functions Introduction
Marakina Allen, Lauren Burton*, Becky Vega
Through an activity measuring side lengths and angles, students will compare and recognize ratios of a right triangle to introduce the basic trig functions sine, cosine, and tangent.
Developing Spatial Reasoning Through Drawing, Manipulatives, and Dynamic Software
Barbara Lynch, Josephine Relaford-Doyle, Katherine Williams*
This introduction to spatial reasoning in first-semester geometry consists of lessons, class activities, and two projects. In class activities students build on prior knowledge of points, lines, and planes and use manipulatives and dynamic software to explore spatial relationships between these undefined terms. The points, lines, planes final project requires students to justify their answers to a series of always/sometimes/never statements by providing real-world evidence and abstract drawings. In the other final project student model real-world objects with orthographic drawings. As a result of these projects students will have a deep understanding of undefined terms in geometry and will be able to represent three-dimensional objects using two-dimensional drawings.

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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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.