Spy Game

Abstract

Students will learn about modular arithmetic in order to decipher encrypted messages.

Objectives

Upon completion of this lesson, students will:

• learn about modular arithmetic

Student Prerequisites

• Technological: Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser for experimenting with the activities

Teacher Preparation

• access to a browser
• paper
• pencil
• scissors

Lesson Outline

1. Focus and Review

   • Have a clock drawn on the board with hands aligned as if it were 12:00.
   • Ask the students according to the clock on the board what time it would be in:
     • 3 hours
     • 8 hours
     • 13 hours
     • 28 hours
     • 334 hours
   • Ask students to think about the answers for a moment. See if they can recognize a pattern that might make it easier to calculate an answer for the "What time will it be in 334 hours question?"

2. Objectives

   • Students will demonstrate their ability to use modular math by deciphering several encrypted codes.

3. Teacher Input

   • Explain to the students that an easy way to calculate what time it will be in x number of hours is to divide x by the number of hours on the face of the clock (the mod), take the remainder, and count that far on the clock.
   • Introduce this method in writing. For example: 334 mod 12.
   • As a class, calculate:
     • 36 mod 6
     • 53 mod 8
     • 420 mod 22
     Show how they can check their answers using the Clock Arithmetic Applet
   • Explain the term multiplier.
   • Explain how to decode a message if they are given the multiplier.

4. Guided Practice

   • Have the students convert the alphabet into numbers setting A=0, B=1, C=2, etc.
   • Tell the students to write a short sentence about themselves that they won't mind someone else reading.
   • Have the students convert the letters in their sentence to numbers using the alphabet numbers they just calculated.
   • Explain the term shift.
   • Have the students shift their numbers by 5 and convert their list back into letters.
   • Explain that their sentences should now look like a bunch of letters.
   • Have the students swap messages and try to decode them using their current knowledge.

5. Independent Practice

   • Have the students pair up and open the Caesar's Cipher applet.
   • Have each student use the computer to encrypt a message by changing the constant value.
   • Tell the students to swap messages with someone else in the class.
   • Instruct the students to decode the message they received from their classmate.
   • Now, have the students encrypt a message using a multiplier.
   • Have the students swap messages and decode the message they receive.
   • Explain that the messages you are about to pass out have been intercepted from a company that has discovered the fountain of youth and that the encrypted messages will lead them to the fountain.
   • Hand out several messages for the students to decipher.
   • Have the pairs of students work to decipher the codes.
   • In order to ensure that each partner is doing an equivalent amount of work require that each student must be responsible for deciphering at least 3 messages.

6. Closure

   • Once the first group has finished give the class 10 more minutes to work on completing deciphering their messages
   • Review vocabulary
   • Ask several groups to share their ciphers and solutions with the class

Suggested Follow-Up

You may wish to follow-up with the Caesar Cipher 2 activity.