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.

Compass and Straightedge Construction Challenges

Ancient Greek Geometry from Nico Disseldorp's Science vs. Magic is a simple but elegant applet which gives compass and straightedge constructions the feel of a game. You start with two points and are given a list of things to construct, along with the number of steps in which you ought to be able to complete each construction. Click on two points and you create a line segment between them. Click one point and drag and you get a circle centered at that point. You score when you complete each construction, and score more when you do it within the number of steps prescribed. The first task is Proposition 1 of Book 1 of Euclid's Elements. The applet works equally well on a tablet or a standard computer.