## 3D Gears Math

SO here is the information for making 3D gears that all fit together. I used Sketchup for the design. All the gear convexities and concavities are 3-inch half-circles.

6-Spoke Gear

12-sided circle

Rotated 7.5 degrees

12-Spoke Gear

24-sided circle

Rotated 15 degrees

24-Spoke Gear

48-sided circle

Rotated 3.75 degrees

Rectangular 14-Spoke Gear

12- by 24-inch rectangle

## 3D Gears

After having discussions with my math peeps, I decided to make gears. From scratch, in Sketchup. Many failures ensued. Thankfully, a Youtube video showed me the light (granted, I had to watch the video about 20 times).

Anyway, the gear ratio works (don’t ask me what that means), and different sizes of gears spin with each other. I even got fancy with irregular shapes (see the long gear) as well as gears with cut-outs (to save filament) and a gear with holes (to create abstract designs a la Spirograph).

## Stairway to Multiples

Different stairwells had different numbers. Brilliant kinesthetic way to learn.

## Water under the Bridge

On the way home from monitoring the NYS math test at 372K, I crossed over the beautiful, retractable Carroll Street bridge that crosses the Gowanus Canal. I saw a whole section of the ground under water. It is the area where there are pulleys that could, in theory, pull the sections of the bridge to the side should a large barge pass through. This patch of ground to the side of the actual canal is usually NOT underwater.

Carroll Street Bridge over the Gowanus Canal

It reminded me of the subway tracks that were under water I wrote about in December 2010 (see “Water under the G” below).

## SWAT

I just finished six weeks of SWAT — Students Will Ace Testing — in preparation for the New York State mathematics test. Everyday in one of two schools, working one-on-one with targeted students. We focused on particular math topics that were discovered to be the most common topics on the tests for the past five years. I hope the students that I worked with did well.

SWAT T Shirt