Functions Abound

by Shelly Rogers

Introduction Concept Map Project Calendar Lesson Plans Letter to Parents Assessments Resources Modifications Grant

Description: Throughout this project the students will spend several days studying specific types of functions. For instance, there will be a class period completely devoted to the parabola. Initially, the teacher will guide the students to form a connection between linear functions, studied the day before, and a parabola in order that the students can build upon their prior knowledge. The students will then use a software program called Gizmo to explore the parabola; the program is designed to help students conceptualize the cause and effect relationship of changing certain aspects of a parent function and the resulting manipulated function. Afterwards, the students will be given images that consist predominately of parabolic outlines and instructed to recreate the images using Graphmatica, another software program. The rest of the period will be spent in discussion and presentation of the images that they recreated. The class periods devoted to the other types of functions will proceed similarly. Upon completing the class periods designated for the study of particular types of functions, the students will spend the remaining project days searching for images around them that can be recreated using many of the different types of functions. They will collect these images using the digital cameras, so that they can be saved on the computers and so that the students will then have the images with them while they use the Gizmo and Graphmatica programs to do the image-reconstructions. For the final assignment, the students will be required to find an image that they especially like and follow the same process as before in order to reconstruct it using functions. Throughout the unit the students will generate a portfolio of their recreated images, notes as to how they constructed their images, and reflections on what they learned during the process, particularly of how they learned to manipulate functions. To conclude the Functions Abound Project, the students will present their portfolios to their fellow classmates. To accompany the students’ work, one day during the project, a guest speaker will discuss his or her career with the students and explain how the use of functions is relevant within their occupation. Through this speaker and the students’ experiences relating functions to real-world images, the students will see mathematics in a different light. They will understand that math is intrinsic within their lives. They will also tangibly learn math, rather than trying to learn about functions and the manipulations of functions through an often distant and un-relatable textbook.