Monday, August 8th, 2011...12:11 pm

Secret Codes with Math

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This activity that I created with my wife, Tanya Chartier, is intended for classroom use. I have used it after performing my Mime-matics mime show that introduces mathematical ideas in classrooms. In particular, college students from Davidson College have traveled with me and led the activity following the presentation. In each case, it has been fun and successful. The picture below to the right is Rose, a math major, leading her group in developing a cheer for their army.

Activity Overview

Facilitator will…

  • Assign student roles and guide them on their parts.
  • Allot a 2 minute time-frame for the armies to determine their cheers.
  • Read or summarize narrative.
  • Play role of Acceleratus within narrative.
  • Present paper with the message to be deciphered while playing Acceleratus.

The class will play the following roles:

  • One student will be Julius Caesar and will be given the corresponding mask (found at bottom of the this post).
  • One student will be General Mathematicus Superfluus and will be given the corresponding mask (also found at the bottom of this post).
  • Half of the class will be the army of Caesar.
  • The other half will be the army of Superfluus.

Student Responsibilities:

  • Caesar and Superfluus will enact the story as it is read.
  • Both armies should propose a brief cheer for their army (2-3 words/grunts e.g. “hu-ha” or a short phrase).
  • When the words “Julius Caesar’s army” or “General Mathematicus Superfluus’ army” are read, the army will cheer their cheer.
  • Superfluus and Caesar are responsible for visually signaling the cheer for his/her army.


We are in the Roman Empire during the reign of Emperor Julius Caesar. A battle rages between Julius Caesar’s army (pause for cheer) and General Mathematicus Superfluus’ army (pause for cheer). Each side is full of brave and valiant soldiers determined to defend homeland and kin. Their leaders are strong (pause), smart (pause), and confident (slight pause for acting).

During the battle, Caesar has immediate need for his currier, Acceleratus. So, he beckons him in a loud voice saying, “——” (facilitator pauses for Caesar to fill in the blank). Acceleratus, light of foot and quick in reflexes, darts through Julius Caesar’s army (pause for cheer). Soon, Acceleratus (played by facilitator) arrives and has a scroll placed in his hand. The young currier will follow a perilous route with the intent of taking the precious message, which contains secret information that could ensure Superfluus’ defeat, to one of Caesar’s generals. With the message in-hand, Acceleratus makes his way back through Julius Caesar’s army (pause for cheer) toward Caesar’s general.

Meanwhile, General Mathematicus Superfluus’ army (pause for cheer) continues its relentless press on Julius Caesar’s army (pause for cheer). In Julius Caesar’s army (pause for cheer) Acceleratus repeatedly asks for the location of the general who is difficult to locate given the chaos. “—-” (facilitator asks for general).

Neither army has taken the advantage but suddenly a possibly fateful turn of events occurs. A soldier in General Mathematicus Superfluus’ army (cheer) catches the currier. (facilitator pauses and waits to be caught by a student). He returns Acceleratus to General Mathematicus Superfluus. The message is opened and its contents read:


Looking deep into the face of currier, Superfluus senses the importance of the note. He knows well of Caesar’s cunningness and believes that the words are somehow a code. But, how does he determine their contents? He tries threatening the currier (pause for possible threat by a creative student). The currier does not divulge the secret. He then decides to entice the currier with a wonderful prize that he might receive as a trade for the true contents of the enclosed code. Superfluus, in a very sly voice, says to the currier, “—————” (pause for student to create something). In time, Superfluus again recalls the wisdom of his foe Julius Caesar, who would never divulge the key to his code to the currier who travels with his message. And so, from General Mathematicus Superfluus’ army (cheer) are called some of the finest who are asked to look carefully at the message to see if they can decipher its hidden message (pause for Superfluus to choose a few people). They work vigorously as the battle rages on.

Transition from Narrative to Lesson

Using the Secret Decoder Ring

The message found during the battle we just enacted was encoded with the Caesar cipher which encoded messages for Julius Caesar and as such bears his name. Let’s learn how to use the cipher and soon decode the message. The key is the decoder ring that we see below.

This cipher is also called the shift cipher since each letter is replaced by a letter some fixed number of positions further down the alphabet. Let’s look at examples of encoding and decoding using our secret decoder ring.

Encoding: (Putting Words into Secret Code)

Let’s encode the letter “G” using a shift of 8. Put your finger over the letter “G” and count 8 letters around the circle which will place your finger on letter “O”. Therefore, the letter “G” becomes, or is encoded as, the letter “O”.

Let’s also encode the letter “X” with a shift of 8. Again, put your finger on the letter “X” and count clock-wise around the circle 8 letters. Your finger should land on the letter “F”.

Encoding a word is the same process but simply takes a bit longer. Let’s use a shift of 5. Then the word:




Decoding: (Putting Secret Codes into Words)

Given the amount of the shift, called the key, we simply count counter-clockwise around the circle. For example, let’s decode the letter “D” with a shift of 9. Put your finger on the letter “D” and count 9 letters counter-clockwise. Your finger should land on the letter “U”.

Using a shift of 7, then the letters:


decode to be the word:


We are now ready to decode the message taken from Caesar’s currier. Suppose, I slip and tell you the key is 3. Now determine the secret message and what strategy might unfold for the armies!

Below, you see the images of Caesar and Superfluus.

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