*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 ›› *

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 ››

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 ››

Last week, Scott and I attended a fraction symposium at NYU, and it made me realize how long it's been since I've written about our Sketchpad work with fractions. Below is a Web Sketchpad model for displaying and solving fraction multiplication problems. Representing fraction multiplication with an area model is a common approach, but it's challenging to sort … Continue Reading ››

For the past few years, Scott Steketee and I have collaborated with the author team of* Everyday Mathematics *to integrate Web Sketchpad deeply into their curriculum.
As part of that work, I just completed a websketch that nicely mixes practice with logical reasoning. Students are challenged to find a hidden treasure on the coordinate … Continue Reading ››

The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords *AB* and *CD* of a circle intersect at point *P,* then the product *AP · PB* is equal to the product *CP · PD*. You can see an illustration of this theorem in the Web Sketchpad model below. Drag points … Continue Reading ››

In years past, my colleagues and I at Key Curriculum conducted Sketchpad professional development workshops for teachers. One of our favorite activities challenged participants to construct a rhombus in as many different ways as possible. This assignment invariably led to great discussions because there are a multitude of ways to build a rhombus, and each method highlights its … Continue Reading ››

In a prior blog post, I introduced my new puzzle, Arranging Addends, that mixes arithmetic with logical thinking to create an engaging playground for mathematical discovery. Let’s revisit this puzzle and introduce some new variations.
Take a look at the puzzle below (and here), built with Web Sketchpad. Your goal is to arrange the … Continue Reading ››

Several weeks ago, my friend Martin shared the following probability puzzle with me: *Two points are chosen independently and at a random on a stick. The stick is broken at those points to form three smaller sticks. What is the probability these three sticks can form a triangle?*
This is a classic problem, dating back to … Continue Reading ››

Did you know that aside from being a source of news, *The New York Times* is also the place to get your weekly fix of mathematics? Their online Numberplay column features some very clever math puzzles. Last year, in fact, our blog featured a Numberplay puzzle about a flying squirrel-frog from former Key Curriculum … Continue Reading ››