Sunday, December 18, 2011


Shikaku (四角), which means four corners in Japanese, is a fun puzzle game where you fill a puzzle board with quadrilaterals (squares and rectangles) using the clues on the board. Each quadrilateral must contain only 1 number and have the area given by that number.

It's a fun little game to help students connect area with multiplication (a quadrilateral with area 6 can be 1x6, 2x3, 3x2, or 6x1), discover properties of prime and composite numbers (all prime numbers n can only be drawn with 1xn, or nx1 and no prime number can be drawn as a square), and reasoning (some quadrilaterals will have to be redrawn as you encounter limitations).

Here's a video of me playing this Shikaku puzzle.

You can find more puzzles on the Nikoli Shikaku page.

Note: Shikaku was created by the same folks popularized Sudoku.

(via Breedeen Murray)

UPDATE: Changed "came up with" to "popularized" and added link to wikipedia in comments.

Saturday, December 17, 2011

Speeding Up Audio Podcasts with Winamp and PaceMaker

Here's a time-saving tip for those of you Winamp users who follow more podcasts than you have time to digest. There's a plugin called PaceMaker that allows you to speed up and slow down MP3s without changing pitch. This is useful if you want to listen to podcasts without feeling like you're listening to Alvin and Chipmunks. I first learned of the PaceMaker plugin in college when I was learning to play the guitar. It was helpful to be able to slow down songs so I could get some practice improving finger coordination as I strummed new chords along with the song.

Here's what you need to use it:
  1. If you don't have it, grab a copy of Winamp from the Winamp download page. I usually skip the MP3 bundle that comes with the download.
  2. Install Winamp.
  3. Once Winamp is installed, you'll need to visit the PaceMaker Winamp plugin page and grab a copy of the installer.
  4. Install PaceMaker.
  5. To enable the PaceMaker plugin, go to "Tools" select the "Preferences" menu item.
  6. Scroll down on the left and click on "DSP/Effect" then select the "PaceMaker tempo controller" option in the right pane.
  7. Adjust the tempo to speed up the audio podcast. Then just play your MP3.
I find that for most podcasts +40% is a comfortable pace. This is true if the podcast is on a familiar subject or if it's easy to follow. Some podcasts can be played at even higher tempos but at higher tempos I spend more effort listening carefully to words than paying attention to the discussion.

There's some simple yet useful math in here, but that'll be another post.

Sunday, December 4, 2011

3D Video of Asteroid Vesta

A stereoscopic anaglyph 3D video created by NASA's Dawn Spacecraft.

I think a commenter on Slashdot said it best:
Each time NASA releases images from some distant planet or asteroid, I'm floored. The number of things that have to go right, that have to not fail, millions of miles away, is immense. Kudos to the scientists and engineers who worked on imaging Vesta. Fantastic results!

(via Slashdot)

Thursday, December 1, 2011

Mathy Conversations with Students

I use many non-verbal cues in my classroom. Often, I'll use hand signals or facial expressions to convey my requests/commands to students quietly. The signals and expressions help me avoid interrupting the class just to address a single student when other students are already working.

Today, I gave a student a judgmental look to hint that he wasn't doing what he was supposed to be doing. Usually students just go back to work, but today he decided to point it out.

Jimmy: You always give me that look!
Me feigning innocence: What look?
Jimmy: The one where your eyebrows are like this (student signs the letter v with his hands).
Me acting clueless while giving a subtler version of the expression I gave him: Huh?
Jimmy: Yeah. Your eyebrows look like a V. It's like they're perpendicular.
Me giving my best perpendicular brows: That's impossible! I'll even take a picture and show you that they aren't perpendicular! Eyebrows can't be perpendicular.
Jill: Some girls will draw 90 degree eyebrows using a Sharpie!
Me signing a V on my forehead: Like a 90 degree unibrow?
Jill: No, they draw sharp corners for eyebrows like this (she signals a circumflex).
Me: Are you saying I have a continuous function for an eyebrow?
Jimmy: No, you don't have a unibrow, it's discontinuous.
Jill laughs: Yea. You have a removable discontinuity!
Me laughing at their insight: Because the limit exists! My eyebrows meet from the left and right and it's undefined in the middle.
Me sensing more students getting off-task: Alrighty, back to work!

A spontaneous opportunity like this doesn't come up often which is why I'm mad I missed an opportunity for review here. I should have asked "what would my eyebrows have to look like for there to be a non-removable discontinuity?" instead of hurrying the kids back to work. Maybe someone would have responded with "you just raise one eyebrow so they don't meet in the middle." I need to be more open to opportunities like this one. I love it when students can apply a concept learned in class in unexpected ways. I love the fact that I get to have these conversations at all. I love my job!