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Number Tricks or Number Patterns

October 18, 2013

I love number patterns. There is a beauty in the way our number system works and the patterns that materialize. Sometimes the opportunity presents itself to not only investigate a number pattern but to also have some fun.

When the students entered class today I was sitting quietly at a desk and had a copy of The Proof of Fermat’s Last Theorem on the board. I told the students that we were going to have a look at the 140 page proof and that while it was a long proof I thought it was good if they could see how important that it is to “show your work.” Well this did not really interest a Grade 6 class and frankly I was glad they did not call my bluff as I am not sure I could have explained most of the proof.

Some of the students noticed that I had the app The Amazing Mind Reader on my iPad. They asked me what it was and I told them it was a math trick that I was trying to work out. They were more interested in this than in a 200-year-old problem so I suggested that we may have a few minutes to try to figure it out. After all, “I spent my lunch hour working on it.”

If you have not played the app the premise is pretty simple.  The steps to solving the problem are:

Mind Reader Chart

  1. Pick any two digit number
  2. Add the digits together
  3. Subtract this number from the original number
  4. Find your number on a list with some symbols beside them (see the image to the right)
  5. Amazingly the app will pick the symbol that you have on your mind

The first two times we tried the app the students were amazed that the iPad was able to detect their symbol (I could not resist telling them that this was because the spirit of Steve Jobs was in my iPad). After the second try students tried to work how the iPad was able to do it.

Eventually students were able to explain how the iPad “did it.” This is where Fermat’s Last Theorem comes in as we talked about the importance of begin able to clearly articulate your solution. Over the course of the next 10 minutes we were able to refine their explanations so they made sense. In the end this was likely an even more important lesson than the  identification of the patterns which made it easy to identify the symbols.

As a final note, I asked students to determine if they could extend the pattern to three digit numbers? Four digits?

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