The Math Education Blog
MAY 2026 UPDATE: Using Claude AI, I’ve rebuilt the Hidden Polygons websketch presented here. The new puzzle offers a greater variety of hidden shapes (equilateral triangles, rhombi, rectangles, square, regular pentagons and hexagons) and a simpler user interface for identifying the shapes. Check it out! Take a look at the two groups of shapes below....
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...
A little over a year ago, the Museum of Mathematics opened in the heart of New York City. One of my favorite exhibits at the museum is the Human Tree. When you stand in front of the Human Tree screen and wave, your arms are replaced by images of your body. This structure repeats, with more...
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...
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 Kangourou...
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 multitouch technology to Sketchpad, but sensed that there...
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. Scott and I had lots of help....
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...
Tomoko Fuse is a Japanese origami artist whose designs are highly geometric. A Google search for her origami models reveals a plethora of boxes and intricate three-dimensional structures, many of which are folded from multiple sheets of paper and then assembled together. As an avid origami folder, I’ve always admired Fuse’s work. But nothing prepared...
In a recent blog post, Karen Greenhaus describes how it’s possible to construct familiar corporate logos using Sketchpad. You might start with a rhombus, for example, and then reflect it twice to obtain the Mitsubishi logo. Karen’s post got me thinking about other creative uses of transformations with Sketchpad. In particular, Sketchpad 5 allows you to...