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.

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.

Finding Equations of Polynomial and Rational Functions

I created this activity with Desmos. Graphs of several polynomial and rational functions are provided. The goal is to find the equation of each. It's self-checking in that when you type in the right equation your graph will match the given graph.

Observe and Ask

This simple Desmos sketch is designed to elicit observations and questions that will lead naturally to an introduction of the ideas of domain and range and an exploration of power functions. I show it to a class without any explanation and as I move the a-slider I ask for questions (which I write on the board, but don't answer). If students want the k-slider moved or if they want to see a particular value of a or k, I oblige. Eventually I ask students to begin trying to answer some of the questions and see where that takes us.

Puzzle

Can you figure out how the p and q sliders control the lines? To check your answer, try typing in equations of the lines (in terms of p and q) in the blank rows underneath the sliders and see if the lines that your equations produce match the lines that are already there. (When you've found something that works--but not before, that's cheating!--you can scroll down to rows below the blank ones to see if your equations are the same as the ones that were actually used to produce the lines.)