In a recent post, I mentioned a problem posed in 1917, which remains unsolved and which lends itself to use in K-12 education: Consider an n by n lattice. Is it always possible to choose 2n points in it so that no three points are in a line? Today, I present a related unsolved problem… Continue reading Another "K-12 Unsolved" Problem
A PLC is a Professional Learning Community. In an ideal world, every math department is a PLC,but in reality there are some obstacles to that idea: not all schools give teachers time to dedicate to professional learning not all teachers are interested in professional growth it is not clear what to do in a PLC,… Continue reading Department as PLC
Draw a polygon following grid paper lines. No crossings, no holes — in other words, a polyomino. Now try to inscribe a square in it, with all its vertices at lattice points on the perimeter of the polyomino. Here are two examples: Conjecture: it is impossible to draw a polyomino that does not have… Continue reading Inscribing Geoboard Squares in Polyominoes
In a recent post, I mentioned K-12 Unsolved, the project I’m involved in that aims to publicize 13 unsolved math problems, in the hope that an appropriate version of each problem will find its way into K-12 classrooms. One problem we looked at was posed by Henry Dudeney in 1917. Here is the problem: Consider… Continue reading No Three on a Line
6 March 2024: I sent out my e-newsletter: a summary of the blog posts and changes to my website in the past four months. Subscribe! 24 February 2024: I led a session on “Geometric Puzzles” for the Santa Cruz Math Circle eighth graders. Read about various versions of this workshop (for teachers or students) on… Continue reading News
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
This post is about a problem I learned about at Unsolved K-12, and was reminded of at Integer Sequences K-12. Both conferences were joint meetings of mathematicians and educators, organized by Gord Hamilton. Like several of my favorite problems from those conferences, this problem involved explorations on a lattice. Here is the problem:– You must… Continue reading Ariadne’s String
Last winter, I attended an interesting meeting of mathematicians and math educators in Banff, Canada. Our charge was to compile a list of integer sequences that would offer suitable problems for students (and teachers) at each level from Kindergarten to 12th grade. It was a sequel to 2014’s Unsolved K-12 meeting, and once again was… Continue reading Integer Sequences
If you are familiar with my curricular creations, you know that I often use the geoboard as a microworld to introduce interesting problems and important concepts. This is in line with my call for a tool-rich pedagogy. (A geoboard is a square lattice pegboard on which students use rubber bands to create and investigate geometric… Continue reading Geoboards and Dot Paper
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