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 ››# Tag Archives: Dynamic 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 ››

# What’s New with Web Sketchpad in 2019

For the past five years, Scott and I have featured interactive Web Sketchpad models in nearly all our Sine of the Times blog posts. As much fun as it's been to build "websketches" to share with you, we've really wanted to put the creative power of Web Sketchpad into your hands.
And now, finally, that's possible. Today … 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 ››

# Adding and Subtracting Integers

A recent post on the my NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers.
I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … 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 ››