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 ››
It appears at first that there isn't enough information to solve the problem. Indeed, the lengths of only three of the polygon's … Continue Reading ››A recent post on an NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers. We wanted to make a visualization tool for students that they could use in multiple ways. The result is the Web Sketchpad model below (and here). Page one focuses on addition while … Continue Reading ››
How much tolerance do you have for puzzlement? When faced with a mathematical conundrum, do you embrace the challenge, or do you feel some trepidation at confronting the unknown?
For many of us, an unfamiliar mathematical task is sure to raise our heart rate a beat or two. As teachers, it’s easy to translate these fears … Continue Reading ››
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 = KM². Another way to think about this construction is shown below on the right. Start with segments JK and … 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 ››