Geometry tends not to receive much love in elementary curricula, and that's a shame. In this post, I'll describe some of my new ideas for using Web Sketchpad to introduce young learners to fundamental properties of circles.

On page 1 of the websketch below (and here), begin by asking students to drag point … Continue Reading ››# Category Archives: Geometry

# A Double Spiral from David Henderson

David Henderson, one of my two Cornell master's thesis advisors, died this past December. I wrote about David in a prior post, and in particular, his approach of asking us to grapple with a small number of rich problems, allowing us to find our own, often non-traditional, … Continue Reading ››

# The Perimeter Problem

When the Metamorphosis team of content coaches meet at their New York office, the day is filled with Qi Gong, video case analysis, good food, and—best of all—a mathematical challenge for everyone to investigate and discuss. These problems are chosen to be accessible across a wide range of grade levels and to allow for a variety … Continue Reading ››

# A Dynamic Approach to Finding Pirate Treasure

In his 1947 book,

*One, Two, Three...Infinity,*physicist George Gamow poses a pirate treasure problem that has since become a classic. Below is my reworded statement of the puzzle.Among a pirate's belongings you find the following note: The island where I buried my treasure contains a single palm tree. Find the tree. From the palm tree, … Continue Reading ››

# The Scaled Maps Problem

Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other.
Believe it or not, you can stick a pin straight through both maps … Continue Reading ››

# Dissecting Rectangles Into Squares

The picture below on the left shows a right triangle

*JML*with altitude*KM*. This altitude is defined as the*geometric mean*of*JK*and*KL*. Using similar triangles, you can prove that*JK*×*KL*=*KM*². Another way to think about this construction is shown below on the right. Start with segments*JK*and … Continue Reading ››# A Geometry Gem from Twitter

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 ››# Enhancing Web Sketchpad

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 ››

# Digging Deep Into Varignon’s Theorem

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 ››# Function Dances at NCTM

At the 2017 NCTM Annual Meeting I was invited to do a short Wednesday-afternoon presentation on Function Dances in the NCTM Networking Lounge. (Here's the handout from the presentation.)
The idea of function dances is to get students (or in this case teachers) moving around, acting as the independent and dependent … Continue Reading ››