## Investigating Geometry Summary

### Monday - Friday, July 3 - 7, 2006

This week, our small groups defined and made progress on their projects, with the goal of creating activities and tools that are useful and usable by teachers.

Project Topic: Teacher's Guide to Geometer's Sketchpad
Nagwa Fayed and Jason Yates

Nagwa and Jason initially struggled to find a project to meet their needs. Based on their own experiences, they decided to create a guide to instruct teachers to use Geometer's Sketchpad. Next week, they will present examples of the topics covered in the guide. Their current goal is to help teachers prepare a lesson on slopes of lines in the coordinate plane. They are planning to extend this lesson to cover additional topics, such as parallel and perpendicular lines.

Project Topic: A Guide to Classic Geometric Constructions
Juan Esparza and Josue Martinez

Basic geometric constructions are often left out of geometry courses because of time constraints. This project consists of a series of constructions that will help the students see the building steps as they happen. The instructor can control the speed and sequence in which the steps of the constructions appear. The seven constructions were created in two different Sketchpad documents in order to finish more quickly; the group is in the final stages of joining the files and working out the bugs. The final project should be completed by Thursday.

Project Topic: Connecting Algebraic and Graphical Representations of Linear Functions
Peter Colino, Jerry Pascher, Sendhil Revuluri, and Miguel Torres

Last week, we began creating a set of tools to allow students to visualize the connections between parameter values and graph behavior for several families of functions (including linear, quadratic, and trigonometric functions as well as several conic sections). This week we narrowed our focus to linear functions and created a unit plan focused on connecting the behavior of the graph of a line with parameter values, the coordinates of specific points, and ultimately the algebraic slope-intercept form. We have completed lesson sketches for a four- or five-day series and are currently working on creating detailed student and teacher resources and adjusting our Sketchpad tools to fit the final lessons.

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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.