Robert M. Scher (rscher@dimacs.rutgers.edu)

New York City School Chancellor's theme of "literacy" was implement in math class with a term project in cryptography. Each student was asked to either:

1. do a research paper on cryptography, or

2. invent a code. write a secret message in code. provide a decryption of the message.

Two math fun days were introduced. Cryptologoy puzzles were both handed out and described on the chalk board (hand out attached). Codes covered were:

1. Caesar cipher

2. Rotating grill

3. Rail fence

4. Matrix crypt

5. Pig-pen

6. Columnar transposition

**Cryptography supplemental lessons to graphing linear equations**

Pre-requisite lessons

1. Basic graphing

2. Graphing equations

3. Graphing by slope-intercept method

4. Inverse equations

*Aim: How do we use coding with linear equations?*

__Do Now__

Decode this "secret" message:

x= 23, 8, 1, 20, 19 13, 25 12, 9, 14, 5 ? y= ?

Use the "decoding" equation y= x

x= # on circle

y= # secret letter

__Handout__: "coding circle" ditto

*Example for discussion*

Try this secret message:

PDWK LV IXQ

Discuss the "secret coding" equation

y= x+3

Find the decoding equation by solving for x

Decoding equation

x= y-3

**Practice**

1. If y= 2x+3 is encoding, what is the decoding equation?

**Class Activity**

1. Each student writes a 25 letter coded message using a simple

y= x+a equation where

-6 __<__ a __<__ 6

Give each student a different number. Work in pairs coding and decoding.

**Topics Covered**

Equations

Graphing

Evaluating

*Aim: How to use graphing to find a secret in a linear equation.*

__Do Now__

1. Write the equation of the line through points (-3, 3) and (3, 21)

2. Graph the equation.

__Handout__: Graph paper

Have students number the y axis from 0 to 26. Place the letters A through Z along the y axis beginning with A=1 through Z=26.

There are 2 sets of secret equations:

1. y= x+2 | 1. 15x+18 | |

2. y= 19x+3 | 2. 4x+9 | |

3. y= 9x+1 | 3. 14x+1 | |

4. y= 19x+1 | 4. 20x+5 | |

5. y= 9x+19 | 5. 9x+19 | |

6. y= 24x | 6. 25x |

Students work in pairs. Each pair of students is given 6 papers numbered A1-A6 or B1-B6. Each paper has a pair of points. Students are told to:
1. Write the equation in y =mx+b form

2. Graph the equation

3. Decode the message as follows:
"M" number of A1 is first letter of message. "B" number is second letter of message, etc. Use the y axis to convert #'s to letters.

Use these pairs of points as possible values:

A1 | (0, 2)(3. 5) | B1 | (-1, 3)(0, 18) | |

A2 | (-1, -16)(0, 3) | B2 | (1, 13)(-1, 5) | |

A3 | (-2, 1)(-3, -8) | B3 | (0, 1)(1, 15) | |

A4 | (0, 1)(1, 20) | B4 | (-1, -15)(0, 5) | |

A5 | (-1, 10)(0, 19) | B5 | (-1, 10)(-2, 1) | |

A6 | (1, 24)(0, 0) | B6 | (1, 25)(0, 0) |

Secret messages decode as follows:

A: "Abscissa is x"

B: "Ordinate is y"