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 2, Discussion of Rate of Change of Sine Function
The teacher begins by reminding students what they are dealing with when discussing rate of change. It is important to review this concept, either as a teacher or it can be asked of the students.
The teacher follows by having the students identify how the outputs of the sine function are changing in order to create the graph for the sine function. In order to help the students conceptualize what is going on, the teacher reminds them that the input to the sine function is the arclength and the output is the vertical height.
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 vertical distance as he moves the applet by a set number of radians. This helps the students understand the concavity of the graph for the sine function.