*ABCD*and

*BFGE,*sharing a vertex. Given that

*AE*= 5, what is the length of

*DG?*My first thought was that surely the problem was … Continue Reading ››

Twitter is a great place to find geometry problems. The July 22, 2017 post of xylem presented the image below with two squares, *ABCD* and *BFGE,* sharing a vertex. Given that *AE* = 5, what is the length of *DG?*
My first thought was that surely the problem was … Continue Reading ››

I was delighted that Daniel recently posted our Binomial Multiplication sketches in Web Sketchpad format. I thought about those sketches when I noticed a fairly new myNCTM thread on "When and How do we phase out the body in math education?"
This thread raises a very important question for us as … Continue Reading ››

The four Web Sketchpad activities below from our Dynamic Number project provide a sequenced collection of challenges and games that develop an area model approach to binomial multiplication and factoring. You can click any of the images to open the interactive websketches on a separate page.
**Dynamic Algebra Tiles, Part One**

In the first websketch, students … Continue Reading ››

I've lost track of how many parents have quizzed me as to why the mathematics their children are learning is so different from what they remember in school. "Why must my kids study more than one way to multiply? Isn't memorizing their multiplication facts enough?" is a frequent lament. James Tanton, Mathematician in Residence at the … Continue Reading ››

In my previous post, I wrote about cross number puzzles—puzzles that mix arithmetic and logic to introduce students to place value, commutativity, and the addition and subtraction algorithms.
Now, I'd like to present a variant of cross number puzzles that adds some algebra to the mix. Below (and here on its own page) are … Continue Reading ››

We live in a golden age of number puzzles. Sudoku is probably the most famous of all modern-day number puzzles, but there are many Japanese puzzles that are also gaining popularity, such as KenKen and Menseki Meiro. In this post, I'd like to introduce a number puzzle for young learners that predates … Continue Reading ››

As a longtime Sketchpad fan, one of the most interesting features of Web Sketchpad (WSP) for me is the way its behavior can be customized. WSP makes it possible to add JavaScript to a web page in order to interact directly with objects in the sketch. For instance, a JavaScript function could use the locations … Continue Reading ››

In the interactive websketch below (and here on its own page), *ABCD* is an arbitrary quadrilateral whose midpoints form quadrilateral *EFGH*. Drag any vertex of *ABCD*. What do you notice about *EFGH*?
The midpoint quadrilateral theorem, attributed to the French mathematician Pierre Varignon, is relatively new in the canon of geometry theorems, dating to 1731. Mathematics educator Chris Pritchard … Continue Reading ››

Here is a wonderful geometry problem from Japan: The five triangles below are all isosceles. The quadrilaterals are all rhombi. The shaded quadrilateral is a square. What is the area of the square?
I wondered at first whether the English translation of the problem was correct because with so many side … Continue Reading ››

Last year, I had the pleasure of co-organizing a geometry-focused coaching collaborative led by Metamorphosis, a New York-based organization that offers professional content coaching to transform the mindset and practices of teachers and administrators. I had so much fun that I decided to do it again! My workshop partners were Metamorphosis staffers Toni Cameron, Ariel Dlugasch, … Continue Reading ››