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Math Explorations 2012
Shodor > SUCCEED > Workshops > Archive > Math Explorations 2012

At the beginning of the day, Jenny and Alexandra taught the students how to play a game called the Boss Game. The game taught the class about patterns by standing up and sitting down in patterns according to base 2. Not only did the game illustrate how to count numbers in base 2, but it also gave the students a chance to get up and move around! After playing the Boss Game, Jenny introduced the algebraic concept of linear functions. The students used the linear function machine on Shodor's website to experiment with these functions by mathematically "poking and prodding" them and seeing what happens to the function when variables are changed. By using the Data Flyer application, the students were able to visualize changes to these linear functions on the x-y coordinate plane. Next, Alexandra talked with the students about the concept of bases in numbers starting with the base-2 binary system. This proved to be a lot of fun, and built upon what the students had already learned. Eventually the students were able to encode and decode messages using the binary system, and one student was able to present a code for the rest of the class to decode as a group.

After break was over, Alexandra led the class in an exercise with the Clock Arithmetic application. The class had the chance to play with a clock that had an adjustable number of hours on its face to figure out how many rotations would occur over a set number of hours. This taught the students how to discern the number of rotations by dividing by the number of hours selected by the number of hours on the face. Using this knowledge of bases and division, the class began learning about ciphers; tools to encode messages. Starting with simple shifts and replacement patterns, the students learned about Caesar's Cipher and a few other forms of historical encoding. By using simple shift and multiplication ciphers, the class even coded another Shodor intern's name, IAN, to SER. Alexandra and Jenny then challenged the students to come up with their own ciphers and code entire sentences and phrases. Using all of the skills the students had mastered throughout the day, everyone developed a fully functional cipher that could bother encode and decode secret messages.