Park City Mathematics Institute
Visualizing Functions

Sinusoid Curve Fitting with Fathom
by Matt Bracher, Cascade Christian High School, Puyallup, Washington

    Activity Guide: MS Word || PDF
    Teacher Guide: MS Word || PDF
    Fathom Document: Fathom || Fathon zipped
    Student Worksheet: MS Word || PDF

This is a Fathom 2 classroom activity.

This activity is for students to explore the effects of the amplitude, period, phase shift, and midline on the graph of a sinusoid by manipulating those parameters until its graph matches the one Fathom generates.

Intended for high school math classes exploring the graphs of sinusoids.

    Computer with Fathom 2
    sinusoid_curve_fitting.ftm file
    Student Activity Guide
    Student Worksheet

Familiarity with sine and cosine functions and graphing in general. This activity can be used either as a discovery lesson, where students are familiar only with the basic graphs of sine and cosine, or as a reinforcement of more advanced material.

The students will become familiar with the effects of changing the amplitude, period, phase shift, and midline on the graph of a sinusoid. They will then describe, in words, the effect of each.

If the activity is being used as a discovery lesson, then the students can simply explore what effects the four sliders have.

If being used as reinforcement, where students have already covered the material, then it can be used in a pre- and post-test situation. Quiz the students on writing the equations of several graphs, score and return the quizzes, let the students explore the effects of the four sliders in Fathom, and then follow with another quiz. The latter results will hopefully show improvement where there were earlier errors.

The activity can also be used for remediation with students who are having trouble mastering the equation of a sinusoid.

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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.