Students will learn how to do modular math and use it to decipher encrypted messages.

Understand patterns, relations, and functions

• represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;

• recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

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

• Encrypted codes for the students to decipher.

• Access to a browser
• paper
• pencil
• scissors

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. Guided Practice
• 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.
• Have students calculate:
  • 36 mod 6
  • 53 mod 8
  • 420 mod 22
• Tell the students to check their answers by using the Clock Applet.
• 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.

4. Teacher Input
• Explain to the students how to decipher an encrypted message if they are given the shift.
• Explain the term multiplier.
• Explain how to decode a message if they are given the multiplier.

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.
• Instruct the groups to take turns playing with the Caesar's Cipher 2 applet recording the original message, the encrypted message, and the correct shift and multiplier.
• Decipher each of the fountain of youth messages with the class to review how to properly decode messages with a shift and or a multiplier.