# 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.

# The Perimeter Problem

At a recent meeting of mathematics content coaches (many from the organization Reimagined) we investigated the following problem:  What is the perimeter of the polygon below?

It appears at first that there isn't enough information to solve the problem. Indeed, the lengths of only three of the polygon's … Continue Reading ››

# Pythagoras Plugged In

The title of this post is a nod to the Sketchpad activity module Pythagoras Plugged In by Dan Bennett. Dan's book contains 18 visual, interactive proofs of the Pythagorean Theorem. And there are more:  The Pythagorean Proposition, published in 1928 by Elisha Scott Loomis, contains over 350 proofs, 255  of which are geometric. Wow!

I revisited the … Continue Reading ››

# A Mathematical Mystery Story with Web Sketchpad

Several years ago, I wrote a blog post about the value that students derive from writing mathematics with Sketchpad. The post included an example of a simple Logo iteration, easily implemented in Sketchpad, that produces some very complex and interesting shapes depending on the values of several input parameters. In the … Continue Reading ››

# Exploring Tessellations with Web Sketchpad

Metamorphosis is a New York-based company that offers professional content coaching to transform the mindset and practice of both teachers and administrators. I recently had the pleasure to collaborate with Metamorphosis staff members Toni Cameron and Kara Levin as well as mathematics coach Ariel Dlugasch from P.S. 276 in a coaching learning community that brought … Continue Reading ››

# Dilation Games: Assessment That’s Fun

March 2023 UPDATE: If the dilation games below whet your appetite for challenges based on transformations, check out these Reflection and Rotation games as well.

What does dilation feel like?

I recently had the opportunity to work with a group of students who were testing activities that treat geometric transformations as functions (what … Continue Reading ››

# Constructing an Ellipse with Web Sketchpad Tools

In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip's path as you pull the pencil around the taut string. Guaranteeing that the traced … Continue Reading ››

# Hello Spring!

Today's blog post features a sketch from Anna Nguyen, who's a 9th grade student. Anna observes, "Math is one of my favorite subjects. I'm not a genius or the smartest in my class, but I do enjoy dealing with letters and numbers, which is also why I like chemistry. I think GSP is the most … Continue Reading ››