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 to me and other adults, but supposedly good for children to slog through. Thus started a career-long search for low threshold, high ceiling problems and puzzles. (That way of describing such activities originated in the 1980’s Logo movement, but that is another story.)
Among my first creations were pentomino puzzles whose difficulty spanned the whole range from Kindergarten to adult. (If you don’t know what pentominoes are, visit Geometric Puzzles in the Classroom before reading further.) Those puzzles were collected in books and cards that remained in print for an astounding 30 years or so. Alas, those are no longer available, as they have fallen victims to test prep obsession, to the gobbling up of smaller publishers by mega-corporations, and to the latter’s lack of interest in actual children’s education. If and when time allows, I will make those puzzles available online on my Web site, as I did for the not-unrelated SuperTangram puzzles*.
Anyway, what prompted this post was this message from Meghan, a teacher in Santa Cruz:
I’ve been using your website like crazy this year. I’m teaching Geometry and used your transformation materials, and mixed in a little bit from your Space class. I used many of your puzzle problems to create a presentation project: each group had a different spatial/area puzzle including the polyarcs. One particularly artistic student drew these, which I thought you’d appreciate.
Polyarcs were my own invention, which you can read about here. Here are Aviva’s polyarc creations:
Fun stuff! I’d love to see other student polyarc art! Start them off with this worksheet. (Prerequisites: they need to know how to find the area and perimeter of a circle.)
Back in the day, I used geometric puzzles in my elementary school classes as activities in a weekly “math lab” session, and as menu options for students who finished other work early. The logistical key was that each student had a folder which listed all the options, and where they checked off the puzzles they had successfully solved.
* Alas, I am the only source of plastic supertangrams. If you sell math manipulatives and are interested in selling them, get in touch! Likewise if you want to buy some sets from me.