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.

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