Euclid's Algorithm

This tool for visualizing of Euclid's algorithm (programmed by Jason Davies) comes from Underground Mathematics. Fawn Nguyen has written a fabulous narrative on how she used it as a notice-and-wonder activity with her sixth graders. What she did would work just as well with high school students. All you need to get started are two positive whole numbers.

Snail's Trail Quilt Square

I created this GeoGebra applet based on a quilt square pattern to use in a precalculus class as a visual introduction to the sum of an infinite geometric series. A nice accompaniment is this applet from Irina Boyadzhiev. I also created a Desmos activity with a focus on asking questions which incorporates these two applets.

Visualizing radians

Sam Shah shared a GeoGebra applet created by a colleage of his which does a beautiful job of demonstrating what a radian is. He wrote about it here. I made minor modifications, mostly so that the word radian doesn't actually appear. Here's that slightly modified version.

Exponential Models Card Sort

Thanks to the ever-innovative-and-tuned-in-to-what-teachers-would-love-to-have Desmos team, I've created an online version of a card sort that I originally developed in paper form to help precalculus students think carefully about the meaning of the parameters in various forms of exponential equations. See this blog post for more detail on the context in which I use this.

Introduction to Point-Slope Form

I created this Desmos activity to help students understand point-slope form of a linear equation, both how it relates to the equation for calculating the slope between two points and why it might be useful even if you're already good at slope-intercept form. It also introduces the idea of calling the change in x by the name h.

Evaluating Inverse Trig Expressions

I created this applet on GeoGebraTube to help students practice evaluating inverse trig functions of special angles by visualizing both the unit circle and the graph of the inverse trig function.

Variation on John Golden's GeoGebra Ferris Wheel

I love John Golden's GeoGebra Ferris Wheel, which he's written about here and I've written about here. I also love how GeoGebraTube makes it so easy to start with the great work of someone else and create a variation on it. Here's my variation on John's creation for a user who's slightly more experienced with transformations and with sine and cosine functions. Rather than asking the user to come up with parameters for a given function, it requires the user to come up with the whole function. I also added the option to hide the actual function so that the user could begin by thinking about what it would look like.

We had a great discussion in precalculus class today based on a single randomly generated wheel. We went wherever student questions and answers took us and ended up covering lots of ground. The particularly interesting stuff from my perspective came when those who saw the graph as a shifted sine wave were fighting it out with those who saw it as a shifted cosine wave and those who saw it as a flipped cosine wave. Finally lots of people were seeing lots of ways that they might write an equation for a sinusoidal wave. At the very end of class we generated a new wheel and everyone tried to write a function to go along with it. Class was over and people were pleading, "Please--try my equation!"