You may be familiar with polyominoes, the figures that can be made by connecting unit squares, edge to edge. For example, these are the tetrominoes, each one made of four unit squares: Polyominoes are an example of polyforms. I discussed polyforms in this article: Geometric Puzzles in the Classroom. In particular, this is where I… Continue reading Polyarcs in the Classroom
Tag: Manipulatives
Lab Gear, the Great Connector
I had the good fortune of mentoring Liz Caffrey for five years, at the very beginning of her teaching career, when she worked at the high school where I chaired the math department. She is now a veteran and talented middle school teacher in the Boston area, but we’ve stayed in touch. In this guest… Continue reading Lab Gear, the Great Connector
Geometric Puzzles Unit
The Geometric Puzzles home page on my website contains many links, and it is organized reasonably well. Still, someone who is not familiar with all these puzzles may need help in turning them into a curriculum unit. This is what I hope to do in this post. (I will try to not duplicate the overview of… Continue reading Geometric Puzzles Unit
Virtual Manipulatives: Part 2
In the previous post, I discussed virtual manipulatives in general, and a particular implementation for algebra, using a Google Drawings representation of the Lab Gear. In this post, I will explore GeoGebra as a platform for virtual manipulatives. Pattern Blocks Virtual pattern blocks are not hard to find on the Web. One good implementation is on the Math… Continue reading Virtual Manipulatives: Part 2
Virtual Manipulatives: Part 1
Learning Tools In 1981, after ten years in K-5, I switched to teaching high school math. In some ways, this felt like starting a whole new career: the math was more involved, the relationship with students less like parenting, and tradition weighed a lot more heavily on the profession. Still, in other ways, teaching is… Continue reading Virtual Manipulatives: Part 1
Sum and Difference of Cubes
Teaching the factoring of the sum of cubes and difference of cubes was not a priority for me in my teaching, and the topic does not seem to be part of the Common Core Standards. However, some people do have to include it in their classes, and as a result the subject occasionally comes up… Continue reading Sum and Difference of Cubes
Wallpaper Symmetry Part 2
This post is a continuation of Wallpaper Symmetry Part 1, which you should read first. Both posts are companions to the Wallpapers Catalog on my website. --------------------------------------------------------------------- A long time ago, in my twenties, I attended a lecture about the mathematics of wallpaper designs. The presenter gave an overview of the entire proof that there are only… Continue reading Wallpaper Symmetry Part 2
Wallpaper Symmetry Part I
While sheltering in place, I decided to use some of my time to complete a project I had been contemplating for a long time: creating a catalog of the 17 wallpaper groups using pattern blocks. It is now live on my website: Wallpapers Catalog. The idea is to provide a bridge between schools, where pattern… Continue reading Wallpaper Symmetry Part I
Asilomar Report: Conic Sections
As my retirement starts to kick in, I no longer attend conferences — except for one: the annual meeting of the California Math Council (Northern Section.) Once again, I had a great day at Asilomar, a beautiful spot near Monterey, right on the Pacific Ocean. Here is my annual report. Conic Sections Figuring out an approach to… Continue reading Asilomar Report: Conic Sections
Learning from Teaching (cont.)
For the second time this summer, I taught a version of my Visual Algebra workshop, this time as part of a summer institute at the Atrium School near Boston. (Earlier in the summer, I did this at Synapse School, in Silicon Valley, and wrote about it here.) Once again, I walked away from the workshop… Continue reading Learning from Teaching (cont.)
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