Creating a Cryptography Unit to Make Math Pop

[Melissa Aviles]

Hello, my name is Melissa Aviles and I am a secondary education student at Aurora University.  I am working on designing a math unit that will really get kids engaged.  I am thinking of doing an introduction to Cryptography using modular, or clock, arithmetic aimed at ninth or tenth graders.  My plan is to begin with an overview of modular forms and to teach the kids the computational aspects of modular arithmetic.  I think that by using real world applications such as calendar and clock counting in my teaching, I can demonstrate to students that they have already been using modular arithmetic.

 

Once the students have gained a basic understanding of the concept and how to manipulate modular expressions, I plan to introduce encrypting and decrpyting.  My final assessment for the unit will probably involve students encrypting messages, possibly using their own codes, and decrypting messages from their classmates.  This topic is a fun way to demonstrate how math can be used outside the classroom while helping kids expand their knowledge of division and remainders.

 

 

I have included some of the resources I have come up with so far. Some sources contain lesson plan outlines.

 

These provide lots of overheads and worksheets for teaching modular arithmetic.

 

I would really appreciate any feedback anyone has on the subject and my ideas. I am still in the early planning stages and would love to hear from you....thanks so much for your help!

 

Melissa

[Michael Paul Goldenberg]

Suggest you look here: http://www.simonsingh.net/The_Code_Book.html and consider downloading the free Code Book on CD rom. Tons of resources and material there.

Also, COMAP'S high school text series, MATHEMATICS: MODELING OUR WORLD introduces linear functions via a unit on cryptography. You might want to check into that as well. Probably parallels some of what you're doing with the Caesar ciphers. As I recall, there is also some work in that unit on matrices for encrypting and decrypting that allows for a useful exploration of matrix inverses and the like.

When I first read THE CODE BOOK about a decade or so ago, I was really impressed with the fact that Charles Babbage broke the Vigenere code (aka ' le chiffre indéchiffrable' or 'unbreakable code'). The thinking he used was mighty slick, and this is where the matrix work above comes into play, in part.

[Melissa Aviles]

Thank you so much for your suggestions - the website is great!

[MariaD]

Challenge the kids to make their codes not breakable by one piece of information (namely, one correspondence between a letter and a letter). This is a more open-ended problem with more room for complexity. Simply using a cyclic cipher is a bit young for high school, though it's a cool start of the unit.

Murderous Maths series have two coding books, but they may be too young, as well.

[Melissa Aviles]

I love the correspondence idea! Thank you so much for your thoughts!

[Melissa Aviles]

Thank you, Dave, for your cross-curriculum idea. This topic would definitely be a great way to teach a little background information on how cryptography was and is used in the real world.