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
Blog
Transformational Proof
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
More on Geometric Construction
(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
Errata
According to Merriam-Webster, the word errata means "errors" in Latin, but it is used in English to mean corrigenda which in Latin means "corrections". So there you have it: errors can be corrected — student errors, teacher errors, and (ahem) curriculum developer errors.My books, great as they are, do contain errors. Some are small errors… Continue reading Errata
Taxicab geometry
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
Polyarcs
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
April: in the streets!
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!
Geoboard Problems for Teachers
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
Calculation
Many students have weak arithmetic skills. Many teachers blame this on calculator use, but it is just as likely that the real reason lies elsewhere. For one thing, the teaching of arithmetic traditionally does not involve developing any understanding, so the learning is shallow and fragile. For another, students correctly feel that mindless arithmetic is… Continue reading Calculation
Geometry Boot Camp!
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!
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