Riemann Sums Foldable

Riemann Sums Foldable

Biorhythms

This is another activity we did to reinforce trig graphs.  It was fun, the kids loved it, and I did it on Digital Learning Day, so that was a plus!  I originally only planned on doing it in my Pre-Calculus classes, but my AP Calculus kids heard about it and insisted on doing it during their class, too!

*UPDATE - the day after we did this was the first day of the Winter Olympics, so I had my students chart the biorhythms for several different athletes. We're going to monitor how those athletes perform during the Olympics and compare their actual performances with their biorhythms.

Biorhythms Activity

Here's Shaun White's biorhythms for February 2014.  The red line marks the day he got 4th in the half pipe.

Ferris Wheel Math

I'm having my students relate what they've learned about amplitude, period, phase shift and vertical shift to a real world scenario involving ferris wheels.  I started  by having them read chapter 15 of the book, The Joy of X which I've blogged about before.  It's a chapter about the ubiquitousness (is that a word?) of the sine curve.  It's a great read!  We then focused in on the example of the Ferris wheel that he gives in the chapter.  I started by working through the first problem on the worksheet with them.  I then turned them loose to do the card match and work the second problem.  The conversations they had and the observations they made were amazing!  And I love love love the card match - it really forces them to see the connection between the graphs, the equations, and the descriptions of the Ferris wheels.  One of the graphs doesn't have a matching equation, so they have to write that equation themselves, and two of the descriptions get used twice, which brings up a great conversation about how that can happen.  I loved this activity!

Ferris Wheel Activity

Note - I didn't realize that the problem was in meters, so on the last question you can either ask them for meters/min and km/hr or you can have them change meters to feet in the problem.  Sorry about that!

Ferris Wheel Card Match

Basic Integration Rule Foldables

Foldables I made for Basic Integration rules.  I had a mistake on the power rule, but I fixed it in the digital file posted below.  Before I gave them these, I had them intuitively find the integrals of some basic functions.  They were able to figure the power rule out on their own, which was awesome!

Basic Integration Rules Foldable
Trig Integration Rules Foldable

Graphs of Sine and Cosine Foldables

Foldables I made for graphing Sine and Cosine.  I'm not completely happy with them, so I'm sure I'll modify them for next year.  I'd like to add a description of what amplitude, period, phase shift, and vertical shift actually are in terms of how they're represented on a graph, not just how to find them from an equation.

Graphs of Sine and Cosine Foldable

Translating Sine and Cosine Foldable

Function Behavior Card Match for AP Calculus AB

I love these card matching/sorting activities! The discussions that go on between students as they try to figure things out are amazing! This one has students match up four sets of cards. When they're done, they have 8 sets containing 4 cards each - 1 function graph, 1 derivative graph, 1 function description, and 1 derivative description. It's a great activity to reinforce the vocabulary and basic concepts associated with functions behavior. I like to use it before I introduce the algebraic approach of the First Derivative Test.
Function Behavior Card Sort Activity

Function Behavior Foldables for AP Calculus AB

We're starting Function Analysis in my AP Calculus AB class.  Here are a few foldables that I came up with to help students keep things straight.  I've included links to the PDF's below.

Increasing/Decreasing Foldable

Concavity Foldable

Max/Min and POI Foldable