Wednesday, November 28, 2012

What do you notice?

Today in Precalc we started graphing sine and cosine curves.  I gave them these charts to fill out all of the sine, cosine, and tangent values of our favorite unit circle angles.  Then I handed out Sam's  @ultrarawr's awesome graph paper (which I stole while "eavesdropping" on twitter) and had them graph their results.

Then I asked...
What do you notice?

It was fun to hear their observations. They started out a little slow (I don't think they're ever asked anything like this without there being a "right" answer) but after a few non-mathy things they jumped into odd/even, zeros, and maxima.

This was an easy segue into the "correct" terminology of amplitude and period, and the transformations followed from there.

Oh, and it was soooo nice to have the kids make a prediction on what a value would do to the graph (like a vertical translation) and then show it using the Desmos calculator.  Love their sliders!


  1. Thank you so much for sharing. I am a fourth-year math teacher. I have been looking for a graphing tool with sliders like the one you showed. None of the ones I found worked as well for me as this one does.

  2. Glad to help! I've been really happy with how easy Desmos is to use... and how much it shows!

  3. Kristen - thanks for the shout out!
    Ms. Poag - so happy to have you on board :) Here are a few slider resources to help get you started:
    video -
    and our user guide -

    If you have any questions we're happy to help. Shoot us an email at

    Happy graphing,
    Team Desmos

  4. Great lesson! Do your kids know the values of the trig functions for their favorite unit circle angles, did they calculate them, or what?

    Loving that this lesson successfully pulls together so many great Twitter Math Teacher ideas.

  5. Thanks Megan!

    The kids filled out a chart with all of the unit circle sin & cos values. Of course, I encouraged them to not use their unit circle and I'm sure some did that, but I recall seeing lots of circles out too.