In this clip the class is discussion how to create the algebraic representation for a trig function with a period that is NOT 2π.
Worksheet 10, Clip 1, Student Presentation of Problem 4, 3:47
The students are creating a function for the first graph and come up with 2.5sin(2π/3*x), which is incorrect. The students have no problem justifiying the amplitude or that it is a sine function, but their argument for the sine function is incorrect.
They are using the period as part of the argument. The instructor realizes this and as opposed to giving them the correct answer begins a discussion.
The students realize it is the period, but the instructor must help them make the connection between the period and the argument of the sine function. He does this by revisiting the notion of period they had come to as a class.
He also records important student statements on the board, which denotes them as meaningful. He finally uses the example of sin(θ) versus sin(5θ) and how that affects the period. By revisiting a problem they had previously worked in class the students were able to see their misconception.