Monday - Friday, July 19-23, 2004
Jim brought in some graph paper (from Staples): www.meadweb.com It has space for graphs as well as tables and writing. Jim led us through some examples of parametric functions using graph paper, acting out, physical models, and technology. Connie and Joyce helped with the graphing calculator part. Connie recently attended a one week TI-84 workshop. Jim asked us to describe if and how parametric equations were used in our classroom. Marta uses graphing calculators and parametrics with her Integrated III class. Kelley, Sean, and Joyce use parametrics some in Pre-Calculus mostly at the end of the year. Joyce and Connie have also worked with parametric equations in AP Calculus.
Functions Group Project Specifications
Parabolas: From introduction to sophistication or the basics and beyond.
Celeste, Marta, Lynda and Donna plan to develop activities and lessons to foster understanding of parabolas from physical models, tables, graphs, and equations. They also plan to work with transformations of equations for parabolas from tables, graphs, pictures, equations, and use of technology. Rani will examine geometric transformations using matrices.
Seth and Kelley are creating a lesson to generate parabolas in an unusual way using three points, ratios, and tangent lines. The lesson will be developed using Geometer's Sketchpad software.
Connie and Joyce are working on preparing introductory parametric activities using parabolas generated from physical models. Graphing calculators and Sketchpad will also be used to further develop the understanding of parametrics.
Thursday and Friday
Group members have been working of their projects and learning a lot about Sketchpad in the process. As of Friday, here is the status of the projects:
Project 1: Lynda, Kelley, Seth, and Connie are generating parabolas using various physical models and generating the equation for the function using technology.
Project 2: Donna, Marta, and Celeste are working on a lesson plan with a new twist on the well used and loved chess board problem. This will be a lesson involving generating ordered pairs, graphing the pairs, and deriving equations from the data. They will be focusing on various payment schemes (traditional doubling scheme, a linear sequence such as 1, 3, 5, 7, 9, ... which would be added up for a running total, squaring each entry such as 1, 4, 9, 16, 25, etc.). Students will be comparing the various schemes and learning about various kinds of functions, their similarities and differences. Sketchpad was helpful in creating a chess game board for the lesson.
Project 3: Rani is creating a unit lesson examining transformations of graphs (rotations and reflections) from patty paper physical models to sketchpad to multiplying using matrices. Jim has had some suggestions for Rani and connections between her project and parabolas and functions.
Joyce and Jim are providing resources and help where needed.
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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.