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 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 ››

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 ››

Yesterday, I led a webinar that demonstrated how Sketchpad and Web Sketchpad can be a powerful tools for exploring Common Core algebra topics. My examples included solving for unknowns with a pan balance, exploring the slopes of lines, maximizing the area of a fixed-perimeter rectangle, and graphing trigonometric functions. I touched only briefly on each example during the … Continue Reading ››

Today's guest post is from Marta Venturini, a PhD student in Mathematics Education at Simon Fraser University under a "Cotutelle Agreement" with the University of Bologna, where she's a PhD student in Mathematics. While looking for some tasks that would be suitable for Sketchpad, I found the “dog leash” problem in a March 2007 Continue Reading ››

It started with an unassuming bunny that hopped along a number line. In 2011, our team at KCP Technologies released Sketchpad Explorer for the iPad, making it possible for teachers and students to interact with desktop Sketchpad models on their iPads. We were thrilled to bring the iPad’s … Continue Reading ››

Harry Parker died this summer, two weeks after coaching the Harvard rowing team to yet another sweep of all four races (varsity, JV, freshmen, and spares) against Yale and two days after accompanying his 1980 Olympic … Continue Reading ››

Four years ago, my colleague Scott Steketee and I began brainstorming new Sketchpad activities for a National Science Foundation grant called Dynamic Number. Our goal was to use Sketchpad to make ideas from number, operation, early algebra, and algebra come alive through interactive models that emphasized conceptual understanding. Continue Reading ››

As a fourth-grader in 1977, I had a love-hate relationship with my Addison-Wesley textbook. Its contents overflowed with arithmetic problems, but every so often an entertaining brainteaser appeared to break the monotony of drill practice. These puzzles were clearly marked: Each appeared in a box set aside from the main text and featured a bespectacled … Continue Reading ››