case 1

Worksheet 8, Clip 1, Page 2 Discussion, Part I, 3:23

In this clip the teacher is using function examples to make sense of periodicity.

Worksheet 8, Clip 2, Page 2 Discussion, Part II, 1:11

In this clip the teacher places the graphs on the board to facilitate a class discussion.

Worksheet 8, Clip 3, Page 3 Discussion, 1:40

In this clip the teacher leads a discussion about how the period changes when the argument of cosine is changed.

Worksheet 8, Clip 1, Page 2 Discussion, Part I, 3:23

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  • In this example he uses the context of rate to focus on the relationship between time and the argument of sine which is in radians. This allows the students to reason about period in a familiar context. Note how he has the students give the number of radians for 1 second and for 1/10th of a second for part d.
  • He decomposes each operation for the students by rephrasing their answers as "1/10th of 2 radians" and "1/100 of 2 radians". This will help them identify the two functions that make up this composition.
  • After this discussion the teacher uses a trig function, has the students create the composition of the two functions, then place their graphs up on the board so he can formalize periods.
  • Note that the teacher makes teh students justify their answers and makes their thinking observable to the other students.