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Published on Thursday, April 19, 2012 in , , , , , , ,

I teach quite a few fun mental challenges over in the Mental Gym.

While I teach methods in as simple and straightforward a manner as possible, there isn't always just one approach. In this post, I'll take a look at new approaches to feats in the Mental Gym.

In my tutorial on Squaring 2-Digit Numbers Mentally, I already teach two methods - a mathematical approach, and Jim Wilder's pure memory approach.

NumberSense's approach takes advantage of an algebraic pattern. The number is separated into 2 variables, a being the 10s digit and b being the 1s digit. The problem then becomes (a + b)2, whose expanded form shows how to make the problem easier:

Besides making the squaring of two digit numbers easier, this video also illustrates a good point about algebra. Algebra lets you see patterns of which you may not have been previously aware, and help you see a shorter, and possibly better approach.

Another mathematical challenge I tried to simplify over in the Mental Gym was the unit circle and its associated trigonometric functions.

These lessons are especially handy for students taking trigonometry. Here's a handy approach to memorizing the unit circle, especially useful for tests, that works solely by taking advantage of several simple patterns:

We'll wind up this post by focusing on two of the puzzles.

First, there's the Sudoku. I already link to instructions on Sudoku strategy, but if you find those hard to understand, e-How has a series of excellent instructional videos on the Sudoku-solving techniques that you may find helpful.

In the Towers of Hanoi, the seemingly-simple task of moving disks from 1 peg to another quickly gets complicated. Here's a short, direct tutorial that helps make the solving pattern much clearer:

If you've come across an alternative way of doing any of the feats over in the Mental Gym, I'd love to hear about it in the comments!

### 1 Response to Mental Gym Updates

Jay
7:48 PM

I'm a mental calculator so I'm drawn more to the rapid calculation feats. I really like the Exponential Expressions feat that is explained. You can really get a lot of mileage out of it using it for root extractions based in similar principle to the cube and fifth root feats explained. When I present the exponent feat I ask someone for a single digit number than ask for another. I raise the first number to the second power. I also ask for a number and raise it to its powers in sequence. I race calculators since it's all from memory anyway. I'd like to see more rapid calculation feats and number feats like this one, but as always, great site.

-Jay