Monique gave us a nice overview of some her **mental math** tricks and tips. I had never really considered thinking of numbers left-to-right before! Monique also talked about *friendly *numbers, and I liked her caution: “What’s friendly to one person isn’t necessarily friendly to another.”

Check out this page for more **mental math** techniques.

Mila showed us some **beautiful geometry problems** that I have taken to calling “intuitive” geometry problems. I have talked about these problems in every one of my classes, from **Sophomore Math Analysis** to **Multivariable Calculus.**

A mathematician friend of mine had a birthday party this weekend, and this was my gift to him:

So far we’ve come up with six different solutions, including one that references **Cavalieri’s Principle**, which I had recently illustrated with CD cases on my website.

Julie shared with us the “**Which Cup Will Roll the Biggest Circle?**” investigation (hat-tip to Dan Meyer). I shared this with a few colleagues, and we all enjoyed exploring the idea and discussing it. There is a lot of commentary and a fully-fleshed out lesson at **Dan Meyer’s blog**: http://blog.mrmeyer.com/?p=4018.

Flannery shared with us here first day of school activity: small groups are given a bunch of polygons that can fit together to make squares. The groups task for everyone to make a square, but there no talking or taking is allowed. A fun team-building activity, and she is looking for more of these types of problems. In addition, Flannery talked about some **math trails** she has created for the students at her school.

Chanel shared three nice activities with us: a quick** trisecting-the-square** problem, a nice **medians and coordinate geometry** activity, and a structured investigation into **elementary graph theory**. All three are nice ideas to have in the repertoire, and nice handouts to have in the desk.

Japheth shared with us a nice structured introduction into how **Cardano** solved the cubic equation. A similar approach, not as cleanly presented, can be found here.

At the end, I talked for about 20 minutes about the ways I use various technologies in and out of the classroom.