case 1

Worksheet 4, Clip 1, Discussion of Bug on Fan, 3:13

In this video the teacher initates a discussion about worksheet 4.

Worksheet 4, Clip 2, Discussion of Rate of Change of Sine Function

In this video the teacher uses the Motion of a Fly Applet to initate a discussion about the rate of change of the sine function.

Worksheet 4, Clip 3, Discussion of Rate of Change of Cosine Function I, 3:01

In this video the teacher uses the Motion of a Fly Applet to initate a discussion about the rate of change of the cosine function

Worksheet 4, Clip 4, Discussion of Rate of Change of Cosine Function II, 2:29

In this video the teacher uses the Motion of a Fly GSP to discuss what happens when there is a negative change in amount.

Worksheet 4, Clip 3, Discussion of Rate of Change of Cosine Function I, 3:01

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  • The teacher has the students identify how the outputs of the cosine function are changing in order to create the graph for the cosine function. In order to help the students conceptualize what is going on, the teacher reminds them that the input to the cosine function is the arclength and the output is the horizontal distance from the center.
  • He then uses the applet to help the students analyze how the outputs change for equal changes of input (arc length). He has the students attend to what happens to the change in horizontal distance as he moves the applet by a set number of radians. This helps the students understand the concavity of the graph for the cosine function.