Reflection: High Expectations Generalizing the Sine Function - Section 4: Generalizing the Function

 

In an ideal world, I'd probably have each of my students play around with GeoGebra or a Desmos file individually to "discover" the various transformations of the sine function.  But it's not an ideal world, and my students don't have access to computers or tablets in class.

In this case, I do what I think is the next best thing: I lead a guided investigation with a computer and projector.  I ask the questions, and the students tell me what to try.  As they make suggestions, I always ask them to explain what they think is going to happen first.  The class often has some good laughs when things don't go quite the way they were expecting!  Gradually, the students zero in on the correct algebraic changes to effect the desired changes in the graph.

Most importantly, however, I'm concerned with why these algebraic changes lead to these particular graphical changes.  Why does a constant coefficient affect the amplitude but not the period?  Why does addition of a constant within the argument shift the graph left, but not affect the period or amplitude? Why? Why?

In a lesson like this, my job is to ask questions.  Sometimes the questions are designed to guide the students toward making the correct adjustments, and sometimes they are designed to guide them to an explanation.  In any case, remember that this is not a lecture, and it is not simply a "how-to" guide - it's a student investigation into causes.

  It's Not Just "How-To"
  High Expectations: It's Not Just "How-To"
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Generalizing the Sine Function

Unit 9: Trigonometric Functions
Lesson 4 of 8

Objective: SWBAT choose trigonometric functions to model periodic phenomena. SWBAT interpret the results of the mathematical model in context.

Big Idea: Based on their modeling experience, the general sine function is quick and easy to define.

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