## Visualizing Functions Summary

### Monday - Friday, July 6 - 10, 2009

We spent one day doing a paper--folding activity that created the various conic sections--matching a single point with points along a line created a parabola; matching a point within a circle with points along the circle created an ellipse; and matching a point outside a circle with points along the circle created a hyperbola. We then looked at how each of these conic sections could be constructed using The Geometer's Sketchpad, which required looking at the way each is defined.

The remainder of our time this week has been spent working within our smaller groups on our projects:

Maura, Meghan, Akemi, and Jet are creating a series of lessons that use pattern growth to visualize linear functions. Students will collect data as images change by measuring perimeter, area, and rates of change. The goal of the project is for students to visualize linear functions in multiple representations, beginning with a pattern and constructing the corresponding table, graph, and equation.

Seth, Louis, and Hillary are developing a 1-2 day lesson that introduces the topic of functions. The goal is to help students gain a deeper understanding of what a function actually is and what the purpose of functions are, specifically in their predictive capabilities. The concepts of domain and range, and having a distinct output for each input will be included.

Felipe and Kym are putting together an activity that focuses on linear functions that are restricted in their domain and range to fit the contours of an image.

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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.