Students are given a worksheet of line graphs, most of which represent functions and a few of which don’t. The challenge is for students to figure out how to move relative to a motion detector so as to recreate each of the graphs.
Students discover through their interaction with the motion detector that they are able to kinesthetically approximate only the graphs of mathematical functions. Based on these observations, students are able to deduce the definition for a function and use this knowledge for future mathematical problem solving.
Given a graph, students will be able to define and identify a mathematical function.
Students will be able to construct a mathematical function represented in a graph and be able to explain why it is a mathematical function.
Students will be able to create a written “story” that explains a given graph of a function.
Mathematics, Pre-algebra and Algebra, 6th – 9th grades
Patterns, Relations, and Functions:
distinguish between linear and nonlinear functions given graphic examples
describe and use variables in a contextual situation
analyze functions of one variable by investigating rates of change
interpret representations of functions of two variables
draw reasonable conclusions about a situation being modeled
approximate and interpret rates of change from graphical data
Problem Solving strand:
monitor and reflect on the process of mathematical problem solving
build new mathematical knowledge through problem solving
Lesson can be extended and integrated into writing and literature lessons.
Change over time
Patterns and trends
Structure generates behavior
Temporal and spatial boundaries
Computer (or graphing calculator) connected to the motion detector
Motion detector software installed on the computer to graph the distance of a person from the motion detector over time OR the “hiker” program input into the graphing calculator to plot incoming data
Computer projector or overhead projector connected to a graphic calculator with display pad
Copies of the handouts for each student
Overhead transparency of the distance examples sheet
1-2 hours; Allow for more time if students are not familiar with graphing or with the equations d=rt and y = mx + b.