In my last post, I shared some generalities about puzzle creation. Today, I will zero in on the specifics of creating puzzles for the mathematics classroom. I will do this by way of analyzing some examples. Multiple PathsA characteristic of all classrooms is that they are constituted of students whose backgrounds and talents vary widely. … Continue reading Puzzles for the Classroom
I attended the San Francisco Math Teachers' Circle last weekend. It was facilitated by Paul Zeitz. The topic: showing two polygons have equal area by cutting one into pieces, and rearranging them to cover the other one with no gaps or overlaps.The assumption was that the area of a rectangle is length times width. The… Continue reading Scissors Congruence!
I've really enjoyed solving the puzzles in Euclidea, a brilliantly designed app for iOS and Android. The basic format is "given this, construct that". You start with just two tools: a straightedge and a slack compass (i.e. a compass that does not remember the radius it was last set to). As you find useful and… Continue reading Stumped by Euclidea
Prior to the publication of the Common Core State Standards for Math (CCSSM), transformational geometry was rarely seen in geometry courses. It certainly was missing from the one I taught. Still, I have always been interested in this topic, and it provided the backbone of my "Geometry 2" class, a post-Algebra 2 elective which I… Continue reading Transformational Proof
(To search from previous posts on this topic, use the Search box on the right.) I suspect that by far the most common introduction to geometric construction in US classrooms is a presentation by the teacher (or textbook) on various compass and straightedge construction techniques. "This is how you construct a perpendicular bisector. This is… Continue reading More on Geometric Construction
A few weeks ago, I led a workshop on taxicab geometry at the San Jose and Palo Alto Math Teacher Circles. Taxicab geometry is based on redefining distance between two points, with the assumption you can only move horizontally and vertically. So the taxicab distance from the origin to (2, 3) is 5, as you… Continue reading Taxicab geometry
My early forays as a curriculum developer date back to my days as a K-5 math specialist in the 1970's. A key insight of my young self was that activities intended for students were that much more worthwhile if they were also interesting to me. I learned to view with suspicion activities that were boring… Continue reading Polyarcs
Taxicab Geometry I will be leading workshops on taxicab geometry at the AIM Math Teachers Circles next week. Here is the announcement:Please join us for math and dinner with Henri Picciotto (www.mathedpage.org)!The topic will be Taxicab Geometry. Many concepts in geometry depend on the idea of distance: the triangle inequality, the definition of a circle, the value… Continue reading April: in the streets!
At the San Francisco Math Teachers' Circle yesterday (March 4, 2017), we explored four "teacher-level" geoboard problems (All can be adapted for classroom use.) Here is a brief report, including some spoilers, I'm afraid. Pick's Formula It turns out that the area of a geoboard polygon can be figured out by counting the lattice points… Continue reading Geoboard Problems for Teachers
I will offer two workshops this summer (2017), at the Head-Royce School in Oakland, CA. Sign up for either or both! June 26-27: Hands-On Geometry (grades 6-10) June 28-30: Transformational Geometry (grades 8-11) If the times or locations don't work for you, I can offer a workshop for your school or district. Contact me directly.… Continue reading Geometry Boot Camp!