Pi Day 2022 is now over, but I'm still thinking about a tweet from 10-K Diver: Take two random numbers X and Y between 0 and 1. What is the probability that the integer nearest to X/Y is even? The answer—spoiler ahead—is (5 – π)/4. (You can run my Web Sketchpad … Continue Reading ››
Category Archives: Geometry
A Paper Folding Investigation from Connected Geometry
In a prior post, I shared some good news: The Connected Geometry high-school curriculum authored by Education Development Center (EDC) is now available for free. I could easily devote every future blog post to a tasty Connected Geometry morsel, but I'll restrict myself to just a few. The investigation … Continue Reading ››
Connected Geometry
It's that time of year when we start seeing "best of" lists for books, movies, music and the like. In that spirit, but stretching way beyond the past year, some of my favorite geometry textbooks include Geometry: Seeing, Doing, Understanding (Harold Jacobs), Discovering Geometry (Michael Serra), and Geometry: A Transformation … Continue Reading ››
Symmetry Challenges
In his article Simply Symmetric, Michael de Villiers observes that symmetry is a powerful but often overlooked tool for formulating proofs:
Most primary geometry curricula around the world introduce the concept of line symmetry fairly early, and sometimes also that of rotational, translational and glide reflective symmetry. … Continue Reading ››
The Swimming Pool Problem
In a prior blog post, I presented an uncommon method for solving the well-known Burning Tent problem. My solution, modeled on the approach in the Connected Geometry curriculum, used a dynamic ellipse to pinpoint the optimal solution. Now, I'd like to offer a related problem from Connected Geometry where … Continue Reading ››
Introducing Web Sketchpad at the 2021 NCTM Annual Meeting
A Follow-Up to the Interior Angle Sum
This post is a follow-up to Sarah Stephens' guest post of a week ago, in which she described a lesson using embodied cognition to help students make sense of the interior angle sum theorem for triangles, not just as an abstract concept, but as a property grounded in their concrete physical experiences.
The Interior Angle Sum: An Embodied Investigation
[This guest post by Sarah Stephens, a senior at Pennsylvania State University, describes a lesson she created as part of her Senior Honors Thesis on leveraging embodied cognition to help students develop abstract mathematical concepts.]
As a soon-to-be classroom mathematics teacher, I have taken special interest in the field of … Continue Reading ››
Protect the Sheep
A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.
Constructing the Pi-Petal Rose
When I was introduced to radian measure in high school, I knew just one thing: How to convert between radians and degrees. Had you asked me to illustrate a radian on a circle or to explain why radian measure was useful, I would have been stumped.
In this post, I'll describe a Web Sketchpad activity … Continue Reading ››