Park City Mathematics Institute Investigating Geometry Project Abstracts Drafts of Project Files (password required)
Geometry Constructions: Bridging the Gap
Juan Esparza* and Josué Martinez

Basic geometric constructions are often left out during the school year 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 will have the ability to control the speed and sequence the constructions appear. These constructions are widely used in any standard geometry text. However, in the Prentice Hall Geometry book, the seven constructions are covered in two different chapters, four constructions in Chapter 1 and three in Chapter 7 and in the Key Curriculum Discovering Geometry book, it is found in chapter 3. They will be introduced at the beginning of the year and will be covered more in depth at the appropriate time.

A Tool for Teachers: Constructing Lessons Using Geometer's Sketchpad
Nagwa Fayed, Jason Yates*

This is a manual for teachers to use in presenting professional development workshops for their colleagues. The presentation focuses on introducing teachers to Geometer's Sketchpad using lessons appropriate for Algebra and Geometry. The manual begins by exploring several basic functions of the program and gradually shifts into more intermediate and advanced skills. The first lesson develops the concept of slopes of lines in a coordinate plane.

Sliding Into Linear Functions: Connecting algebraic and graphical representations
Peter Colino, Jerry Pascher, Sendhil Revuluri*, Miguel Torres

Linear relationships are a central theme in a student's first algebra experience. We have created a set of dynamic graphing tools to help students discover connections between graphical and algebraic representations of linear relationships. Using these tools, students can vary the values of slope and y-intercept in a given equation, and investigate the influences on the graph. As they complete the set of activities associated with these tools, students will:

• articulate the influences of slope and y-intercept on the graph of a line
• connect the graph of a linear function with a table of values
• define slope by discovering patterns in the table and graph; and
• understand the y-intercept, leading to the slope-intercept form of the equation of a line.

Besides the tools, activities, and worksheets for linear functions, this project also includes more dynamic graphing tools allowing students to experiment with quadratic, trigonometric, conic, and other families of functions in various forms. These tools allow teachers to demonstrate, and students to experiment with, the effects of changes in the parameters associated with each family of functions (vertex, period, amplitude, etc.), leading to a more thorough understanding of the connections between the algebraic and graphical representations of these families of functions.

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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.