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Creating Functions with Motion

Overview:

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.

Lesson Objectives

Curriculum Context

Systems Concepts

  • 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

 

Algebra strand: 

  • 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

  • Accumulations

  • Interdependencies

  • Structure generates behavior

  • Temporal and spatial boundaries


Materials

Time

Systems Tools

  • Motion detector

  • 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.

  • Behavior-over-time graphs

 

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