- 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.