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 ››

# Tag Archives: Web Sketchpad

# 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 ››

# 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 ››

# Introducing Web Sketchpad at the 2021 NCTM Annual Meeting

NCTM’s Virtual 2021 Annual Meeting ran from April 21 through May 1, and in Session 299 Daniel Scher, Karen Hollebrands, and I presented an on-demand video workshop to introduce Web Sketchpad (WSP). Even if you weren't able to attend the conference, you can still take … Continue Reading ››

# 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.

# Protect the Sheep

A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.

# Adding and Subtracting Fractions on a Number Line

This brief post offers the Web Sketchpad fraction model below (and here) for adding and subtracting fractions on a number line.

The video below explains how to use the model.

# A Plethora of Hyperbola Constructions

In my prior blog posts, I've presented methods for constructing ellipses and parabolas using both Web Sketchpad and paper folding. Now it's time for me to finally turn my attention to hyperbolas.

All of the Web Sketchpad models below (and here) are based on the distance definition of a hyperbola: the set of … Continue Reading ››

# 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 ››

# Tweaking the Expanding Circle Construction

In last month's blog post, I described a parabola construction technique dating back to the work of Persian polymath Ibn Sina (c. 970 – 1037). After I published the post, my colleague Scott noted that my construction could be more robust to allow for parabolas that are downward facing as well as upward facing. … Continue Reading ››