*AB*and

*CD*of a circle intersect at point

*P,*then the product

*AP · PB*is equal to the product

*CP · PD*. You can see an illustration of this theorem in the Web Sketchpad model below. Drag points … Continue Reading ››

The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords *AB* and *CD* of a circle intersect at point *P,* then the product *AP · PB* is equal to the product *CP · PD*. You can see an illustration of this theorem in the Web Sketchpad model below. Drag points … Continue Reading ››

In years past, my colleagues and I at Key Curriculum conducted Sketchpad professional development workshops for teachers. One of our favorite activities challenged participants to construct a rhombus in as many different ways as possible. This assignment invariably led to great discussions because there are a multitude of ways to build a rhombus, and each method highlights its … Continue Reading ››

In a blog post last year, I introduced my Arranging Addends puzzle. Take a look at the websketch below, built with Web Sketchpad. 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 … Continue Reading ››

Several weeks ago, my friend Martin shared the following probability puzzle with me: *Two points are chosen independently and at a random on a stick. The stick is broken at those points to form three smaller sticks. What is the probability these three sticks can form a triangle?*
This is a classic problem, dating back to … Continue Reading ››

Did you know that aside from being a source of news, *The New York Times* is also the place to get your weekly fix of mathematics? Their online Numberplay column features some very clever math puzzles. Last year, in fact, our blog featured a Numberplay puzzle about a flying squirrel-frog from former Key Curriculum … Continue Reading ››

The origins of this week's Web Sketchpad model date back to the Connected Geometry curriculum from the mid 1990s. I was one of the co-authors of the curriculum, working at Education Development Center with a wonderful team of math educators (Al Cuoco, Paul Goldenberg, and June Mark, … Continue Reading ››

Simultaneous equations belong in elementary-school mathematics curricula. That's been my mantra for many years, and I want to examine it now in the context of an interactive Web Sketchpad activity.
When I say that elementary-age students should encounter simultaneous equations, I don't mean that they should be instructed in the standard algebraic procedure for solving pairs of equations … Continue Reading ››

For this year’s Pi Day post, I thought I’d continue our Web Sketchpad (WSP) construction theme. But rather than adapting the visualizations from last year’s Pi Day post to the new construction capabilities, I decided to take a different approach. Some time ago, I built a set of custom tools for … Continue Reading ››

Dan Meyer has posted a number of "What Can You Do With This?" activities on his blog. (Activities is probably too prescriptive a word; they're more in the nature of prompts for student thinking, noticing, and wondering.) One of the first was the image below, which he made by superimposing frames from a … Continue Reading ››