I’ve wrapped up my 1st algebra unit with my 6th graders and I have to say it was an overwhelming success. Student growth from the pre-test about 6 weeks ago to the post-test a few days ago shows a range of 10-50 percentage point gains with an average gain of roughly 30 percentage points.

For many of them, this was their first time actually digging deep into algebra and using it to solve problems. They were able to represent problems verbally, visually, and symbolically. I started on error analysis with them toward the end of the unit. That proved to be a little more difficult than I had hoped, but we still have plenty of time in the year for that.

The culminating activity for them involved having them learn to write secret codes with algebraic equations and functions as an encryption device.

Before jumping into the activity I showed a short clip from “A Beautiful Mind” It was the pentagon scene in which John Nash stares at the wall of code and deciphers it mentally. That isn’t exactly where I was going with the activity but it quickly got me some buy in from a classroom full of pre-teen girls who had never heard of cryptography or used the word encrypt or decrypt a day in their lives.

We began this exercise using simple substitution to “hide” messages. A = 1, B = 2 and so on. They grabbed onto that rather quickly and some of them even made the leap that this was essentially the equation y = x with X being the input position of the letter and y being the encrypted position of the number.

Next, we used one step equation to encrypt and decrypt secret messages. Essentially, if A = 1, B =2, C = 3…we would use the equation 5x = y to encrypt the message. A = 1 became A = 5 and so on. We toyed around with this simple encryption for a day or so and eventually moved up to multi-step equations as encryption and decryption devices.

Finally, we moved into the realm of non-linear functions as encryption devices and the use of tables/grids to decrypt secret messages. This proved to be a little more difficult because developing an equation for the system we used may be about a year away for my 6th graders. This was the most time consuming of all the activities and I witnessed a loss of interest and some burn out on this activity.

I like the idea of using real world application of mathematics beyond using equation to figure out how many people can come to your party, etc.

I have been receiving jokes and little messages from my students in the form of encrypted numeric messages since we concluded the activity and I love it! One disappointment took place yesterday though. We were completing our second review of the last 6 weeks when I witnessed one girl passing a note to another. I was overjoyed for a second because I had hoped that they were using a code to communicate in class. Unfortunately, it was in English and I was able to read it quite easily.

Sigh.

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