*Pythagoras Plugged In*by Dan Bennett. Dan's book contains 18 visual, interactive proofs of the Pythagorean Theorem. And there are more:

*The Pythagorean …*

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If there were an award for 'Mathematical Theorem Most Amenable to a Visual Proof,' the Pythagorean Theorem would surely win. 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 … **Continue Reading ›› *

I began this post on Friday night in Hamburg Germany, near the end of ICME, the quadrennial international math-education conference that's been both exhilarating and exhausting. I’m now finishing it on the airplane headed back home.
As interesting as many of the presentations have been, they've also been … Continue Reading ››

I'm currently attending the 13^{th} International Congress on Mathematics Education (ICME) in Hamburg, Germany, with well over 1000 math educators from around the world. Professor Gabriele Kaiser opened the conference with a statement of solidarity with Turkish mathematics teachers and researchers who at the last minute were unable to attend due to newly imposed government … Continue Reading ››

In a previous post, I described the game Chisla, an app that succeeds in making basic arithmetic both challenging and tense. Given a numerical target, you have just 15 seconds to pick numbers from a list of possible addends that will sum to that value. A target of 10 is no big deal, but when the target escalates … Continue Reading ››

Below is a collection of four interactive number charts that we first introduced in our NSF-funded Dynamic Number project.
Start by asking students to press the four directional arrows and to explore what they do. The right arrow, for example, moves the shaded square to the right, and wraps the square to the next row up when you … Continue Reading ››

Angles are a thorny concept to teach because of the fundamentally different ways in which they can be used and understood. In the article What's Your Angle on Angles?, the authors divide the concept of angle into three main groups: angle-as-figure, angle-as-wedge, and angle-as-turn.
In the Web Sketchpad game below, we focus on angle-as-turn. Given an angle, students enter an estimate … Continue Reading ››

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 article* where … Continue Reading ››

How challenging can single-digit addition be? That's the question I asked myself when my friend Hung suggested that I download Chisla, a mobile game for iOS and Android.
From its description alone, the game seemed suitable for young learners practicing their addition. Take a look at the image below. The game presents you with an array of 25 random digits. … Continue Reading ››

In my recent posts, I've introduced interactive models for comparing fractions and multiplying fractions. To continue the fraction theme, below is a Web Sketchpad model in which the need for equivalent fractions arises naturally through the rules of a game.
The model displays two arrays. Dragging the four points changes the arrays' dimensions. The goal is to drag blue squares into the blue array … Continue Reading ››

In the short two years since we introduced Web Sketchpad in this blog, we've developed lots of websketches and shared them here. As the number has grown, it's become challenging to keep track of them all. Here then is an annotated list of all the elementary-themed Web Sketchpad activities we've offered. The list includes links to our original … Continue Reading ››