Park City Mathematics Institute Visualizing Functions Project Abstract Drafts of Project Files (password required)
Introduction to Functions
Hillary Stone*, Lou Shoe, Seth Leavitt
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.

Looking for Patterns
Meghan Fenton*, Maura Cassidy, Akemi Kashiwada, Jet Warr
This series of lessons introduces students to linear functions using pattern growth. By analyzing the changing perimeter of consecutive images, students will be able to visualize linear functions in a pattern and throughout the course of the lessons, in a table, graph, and equation. The goal of the unit is that students be able to move between the corresponding representations of a linear function. The sequence of patterns will address y-intercept, rate of change, parallel lines, domain and range, and independent and dependent variables.

Applications of Piece-wise Linear Functions
Kym Riggins*, Felipe Rico
The purpose of this lesson is for students to develop the concept and understand the applications of piece-wise functions. The task includes students replicating the contour of the wing of a bird from a given picture to which a coordinate system has been attached. Students model the curve of the wing by first using two points along the bird's wing which will yield one linear equation and a very raw approximation to the true shape of the wing. This is improved by requiring three points (yielding two lines), four points, up to a maximum of 7 points. Once students have defined functions for the points they've selected, a discussion takes place in regards to the appropriate domain for these functions so that a graphing calculator can be programmed to graph a precise sequence of lines that will adjust to the contour of the bird's wing.

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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.