Finishing Up Sine and Cosine Graphs

So last week we started graphing sine and cosine in class.
Day 1:  Filled out a chart of values, noticed things, used Desmos to see what different transformations did.  (I wrote about it here.)

Day 2:  Whiteboards... such a nice easy to way to see who "gets" it!

Day 3:  The kids picked up this picture (after taking a short weekly Algebra review quiz):

I found this in a Sports Illustrated almost two years ago and kept it (and was actually able to find it last week when I wanted to!  That's a miracle in itself.).  On the board, I wrote: "If Jay Cutler's maximum was 100% and minimum was 0%, write an equation that models his week."  I'm sure I could've come up with a much better lead but I was stumped... if you have any ideas please let me know!  It was a more interesting way of picking out the transformations and putting them together to write an equation than a randomly generated graph would've been.  

We decided to use cosine with an amplitude of 50, vertical shift of 50, period of 6 days (I gave them dates for those maximum values that were 6 days apart) and applied a horizontal shift of 0.  But after writing that equation, I told them that, Oops - the graph actually starts with that first point which was two days before the maximum.  So then we had to incorporate that horizontal shift.

It was pretty fun (I thought).  Then I gave them an assignment to write equations for 4 graphs on their own.  

Day 4:  (Today)  So now we're applying their equation writing skills. I put together a list of 10 different cities' average normal maximum temperatures (found on noaa.gov). They have to plot these values on a grid and come up with an equation that models that city.  They also have to do it for Cincinnati so that we can compare the two.  

Day 5:  (Tomorrow) We're going to use my new bff Desmos to check people's models.  I'm going to have them plot the data points and enter the equation that was generated by their classmate.  Then I think I'll have them set up an equation with sliders (all you do is enter something like a cos (bx + c) + d  and you'll be given the option to set up sliders) to have them try and fit an equation.  Or something like that.... I'm still trying to refine my ideas.

So what's up for Wednesday?  Tangent and reciprocal graphs.