Category Archives: Math Software

Surprise, Surprise: Tangent Circles Produce an Ellipse

This will be the first in an occasional series of posts that offer interactive Web Sketchpad models for drawing conic sections. My interest in conic sections dates back to the mid 1990s, when I authored Exploring Conic Sections with The Geometer's Sketchpad for Key Curriculum Press . You can read more about it in … Continue Reading ››

Iteration in the Complex Plane

The cover story of the April 2014 issue of Mathematics Teacher is on "Iteration in the Complex Plane", by Robin S. O'Dell. It sounds like pretty advanced mathematics, but is surprisingly accessible with The Geometer's Sketchpad. It's all based on the surprising principle that you can multiply two complex numbers very easily if … Continue Reading ››

Simultaneous Equations in Elementary School? You Bet!

Algebra classes devote considerable time to equations in a single variable before solving multiple equations in two or more unknowns. But just because elementary-age students are not familiar with algebraic symbolism doesn't mean they can't solve simultaneous equations, too! The mathematician and educator W. W. Sawyer makes a compelling argument … Continue Reading ››

Arranging Addends Puzzles

Arranging Addends is an interactive puzzle that I designed on a long bus ride through Alaska. The goal of the puzzle is to arrange the circles and the six numbers (1, 2, 4, 8, 16, and 32) so that three conditions are met simultaneously: The sum of the numbers in the green circle is 21, … Continue Reading ››

Discovering the Angle Sum and Difference Identities

In my Advanced Methods class at Penn’s Graduate School of Education, my students are working in groups to create shared lesson plans using an inquiry approach. For a number of reasons it can be challenging for these pre-service teachers to identify appropriate topics for student inquiry, but sometimes the brainstorming they do turns into something … Continue Reading ››

Wait for a Date

Consider the following probability question: Two friends arrange for a lunch date between 12:00 and 1:00. A week later, however, neither of them remembers the exact meeting time. As a result, each person arrives at a random time between 12:00 and 1:00 and waits exactly 10 minutes for the other person. When the 10 minutes have passed, … Continue Reading ››

Discovery by Dragging

A few days ago I led a webinar on the Common Core and Sketchpad for Sketchpad beginners, and I showed four Sketchpad activities aligned with both the Content Standards and the Standards for Mathematical Practice. I mixed it up a bit by showing two … Continue Reading ››