Early summer is a great time of year in Seattle and Eastern WA, where we’re splitting our time right now. We’ve been pouring energy into a few projects: launching our new game, Prime Climb; supporting Seattle Summer School with curriculum and professional development support; piloting a Math for Love summer camp, which just wrapped up after an excellent week; and …

## Quadrilateral Puzzle

I’ve been immersed in puzzle and lesson creation lately, and I thought I should take advantage and throw some of them out here on the blog. Please take, solve, use in your classrooms or at home, and let me know what you think. If people like the puzzles, I’ll make a point of putting them out here more often. A …

## Pythagorean Theorem Part 1 (Video)

I finally tried my hand at a video explanation of a mathematical idea I like. This is part 1 in a short series on the Pythagorean Theorem. It starts where I’ve always felt the story should start: with the question of how to double the square. What do you think? I’d love feedback, since I’m planning more. What works, what …

## Midpoints of a quadrilateral form a parallelogram

Take any quadrilateral, like this one then mark the midpoints, and connect them up. It sure looks like we’ve built a parallelogram, doesn’t it? The amazing fact here is that no matter what quadrilateral you start with, you always get a parallelogram when you connect the midpoints. This is the kind of result that seems both random and astonishing. You …

## Billiard Balls and Laser Beams: Talk, Slides, and Videos

I had the opportunity to speak at the University of Washington Monthly Math Hour on April 17. Following my talk a six and a half year old named Rebekah gave me this drawing she drew during the talk. The talk, Billiard Balls and Laser Beams, was inspired by the mathematics of reflections (things that bounce off other things), a topic …

## Student Proof: connect a point on a circle to the two endpoints of a diameter, and you to get a right triangle

A few weeks ago a student and I noticed that if connect a point on a circle to the two endpoints of a diameter, you seem to get a right triangle. After working for a bit, we came up with pretty nice proof of why that is, in fact, the case. I told him that if he wrote it up, …