Design a math code to encode and decode messages!

  • You will design a code that uses math to encode and decode messages. You and your team will devise an encoding device that is based on one or more mathematical techniques you know so far. You will create a method for decoding messages and then practice coding and decoding “secret “messages sent with your code.

    • To create a code that involves math… i.e., equations, integers, formulas, patterns, prime numbers, fractions, percents, factors, etc.

    • Each team member will write a report that clearly explains how to encode and decode messages with the team’s method — the math involved, with several different examples … including a set of encoded messages that readers can use to practice your system.

    • The report must be at least 2 pages long, and must include a cover page, a title page, your report, and a bibliography showing all resources used in your research on coding techniques.

    • For each letter, number, or other symbol to be encoded, the code must assign an unique symbol.

    • There must exist a decoding system that the receiver of the message can use to translate the message.

    • The code must be difficult to break!

    • Letter to letter code: This code “shifts” the alphabet a specific number of letters. Here is an example where the shift is 6 letters—

      ABCDEFGHIJKLMNOPQRSTUVWXYX — to

      FGHIJKLMNOPQRSTUVWXYZABCDE

      (For example: to encde the word DOG, write the letters beneath the letters DOG…. the encoded word it ITL…. The decoder must know the shift number 6, or else must try all 25 possible shifts until one yields a sensible message…

    • Remainders: This more sophisticated code is harder to crack. It uses remainders after dividing by 26. First choose a code multiplier, 5 for example. To encode the letter K, note that K is the eleventh number in the alphabet. Multiplying the letter number by 5 (11 × 5 = 55). Divide that by 26 (55 divided by 26 is 2, remainder 3). The remainder 3 tells you to encode the K as the letter C.

    • Research and report on the breaking of the German war code by Alan Turing’s team in England.

    • Research and report on the work of the Navajo code talkers during WWII

    • Research and report on cryptology and methods used to solve cryptograms.

    • Research and report on the Braille system for blind readers.

    • Research and report on the Morse code.