In how many ways can you use dynamic geometry software to build a rhombus that stays a rhombus when its vertices are dragged? This challenge, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties … Continue Reading ››

# Category Archives: Math Software

# Euclid Walks the Plank

Using Web Sketchpad, students construct a boardwalk path of equal-length planks to explore the key concepts behind Euclid’s Proposition 1.

# A Triple Number Line Model for Visualizing Solutions to Equations

In Algebra 1, I was the king of solving for *x*. Algebraic manipulation was fun and satisfying, and I was good at it. But my confidence was shaken when I encountered a test question of the variety 4*x* + 5 = 4*x* – 3. After subtracting 4*x* from both sides, I was … Continue Reading ››

# Exploring Scaled Polygons

Below are some common methods that geometry curricula offer for constructing scaled polygons:

- Place a polygon on the coordinate plane, pick the origin as the center of dilation, scale each vertex by some specified amount by using its coordinates, and then connect the scaled vertices.

# Injecting Surprise Into the Triangle Midline Theorem

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 ››

# 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 ››

# The Polar-Cartesian Connection

The Web Sketchpad model below (and here) shows the function *f(θ)* = 1 – cos 2*θ* in both Cartesian and polar form. For each graph, the independent variable appears as a red bar that corresponds to a particular value of *x* (for Cartesian) or *θ* (for polar). The red bar has … Continue Reading ››

# The Cowgirl Problem

In a previous post, I described two different approaches to solving the Burning Tent optimization problem. Now I'd like to offer a related problem that I assigned many years ago to my pre-service mathematics teachers at New York University.

A cowgirl wants to give her horse some food and … 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 ››

# Race to the Burning Tent

How can you identify a lover of math? Casually mention a burning tent and notice if her first thought is how to minimize her path to a river and then to the tent to douse the flames. Here is a full statement of this classic geometry problem:

*Ah, the great … Continue Reading ››*