A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.

# Category Archives: Geometry

# Constructing the Pi-Petal Rose

When I was introduced to radian measure in high school, I knew just one thing: How to convert between radians and degrees. Had you asked me to illustrate a radian on a circle or to explain why radian measure was useful, I would have been stumped.

In this post, I'll describe a Web Sketchpad activity … Continue Reading ››

# The Varied Paths to Constructing a Rhombus

In how many different ways can you build a rhombus that stays a rhombus when its vertices are dragged? This assignment, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties of the quadrilateral.

While the rhombus task works … Continue Reading ››

# Catching Up with New Web Sketchpad Functionality

This past January, we introduced the Web Sketchpad Tool Library and Viewer. The Tool Library is a collection of over 60 mathematical tools for customizing a Web Sketchpad model, making it possible for teachers to decide which tools students have available to them on an activity-by-activity basis. The Viewer is a site … Continue Reading ››

# Circle Tracer Challenges

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 … Continue Reading ››

# A Double Spiral from David Henderson

David Henderson, the author of *Experiencing Geometry*, 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, ways of … 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 ››