Objectives: To recognize the effect of various shifts on the period, amplitude and midline of a sin function.
Preliminaries/Lead-In: I will probably begin this activity with a discussion of what it means to be a function again (given an input we attach an output) and then explain that sin is just a name for a function with a specific rule for attaching an output to an input. We begin by thinking of this rule graphically and we use Mathematica to see that. I might then graph the SIn function in mathematica together as a class and begin the activity from there.
Suggested Procedures: I would let them work 1-4 mostly by themselves checking in with them to make sure they are using Mathematica ok to get the sine function up and also checking in that they realize that sin(x-4) is the same as f(x-4) etc. If I remember correctly they have some trouble jumping to thinking about sin as just any other function where it's defined with a graph. Then I will check the table in 3 together with them as a class after they have had a chance to graph them all in Mathematica. And again after 5 I will check with them to make sure they are getting everything ok.... In general I expect only to spend one day on this - however if I have time and they seem to be struggling I may end up taking a little longer.
Wrap-Up/Take-Away:
Possible Homework: I probably won't leave any of this to homework - I'll have to see how they are doing - at most Q5 but even that I think I want them to do all of this in class.
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