When it comes to simultaneous equations, I like to push the bounds of conventional pedagogical wisdom. In an earlier post, I offered a puzzle in which elementary-age students solve for four unknowns given eight equations. Now, I'd like to present a puzzle that might sound even more audacious: Solving for ten unknowns. … Continue Reading ››

The study of multiples and factors is ripe with opportunities to engage students in intriguing mathematical puzzles. In prior posts (When Factoring Gets Personal, and Open the Safe), I've given some examples of what can be done. Now I'd like to introduce you to … Continue Reading ››

A couple of days ago I got an email from my long-time friend Geri, who was spending some quality Sketchpad time with her 12-year-old grandson Niels. Geri emailed me for advice because Neils was having some trouble figuring out how to construct a pentaflake. Neither Geri nor Niels had any idea that I'd never even … Continue Reading ››

We've all seen amazing examples of illusions, but did you know that there is a fertile community of researchers creating new ones? The Best Illusion of the Year contest and website provide a showcase for celebrating illusions. This year's winner for best illusion was created by Christopher D. Blair, Gideon P. … Continue Reading ››

Nathan Dummitt teaches mathematics and statistics at Columbia Preparatory School in New York, NY. He teaches all four years and is interested in sharing low-threshold, high-ceiling activities with his students. — Guest post by Nathan Dummitt I teach Geometry at a high school in New York City, and I like to start the school year … Continue Reading ››

According to Wikipedia, the Brouwer Fixed Point Theorem, named after mathematician and philosopher Luitzen Brouwer, states that "for any continuous function f mapping a compact convex set into itself, there is a point x_{0} such that f(x_{0}) = x_{0}. This is a deep theorem, but one aspect of it is lovely, surprising, and entirely approachable by high-school geometry … Continue Reading ››

In the early 1990s, Danny Vizcaino, a high school student at Monte Vista High School in California, wrote to Key Curriculum Press noting that Sketchpad did not come with a tool to draw an oval. Undaunted by this omission, Danny had built his own oval with the software and shared it with Key's editors. As shown in the interactive … Continue Reading ››

When I was child, I loved to solve the brainteasers in logic puzzle magazines. You probably know the type: Ruth, Phyllis, and Joan each bought a different kind of fruit (orange, apple, pear) and a different vegetable (spinach, kale, carrots) at the supermarket. No one bought both an orange and carrots. Ruth didn't buy an apple or kale. … Continue Reading ››

There are certain topics in mathematics education not appropriate for polite discussion. Number bases other than 10 fit this category well, perhaps because of their association with the maligned "new math" of the 1960s. That's a shame because there is a lot to learn from them, especially when presented as interactive puzzles. Below (and here) are … Continue Reading ››