ETE 501 Technology Strand7777777John Doe
An intro to Cryptography
1)Subject: Mathematics
2)Topic: Cryptography
3)Grade level: 10
4)Number of students: 25
5)Number of lessons in topic: 3
6)Lesson number: 1
7)Title of current lesson: How to encode text
8)Objective: To introduce students to the topic of cryptography – the art of cipher writing, its foundation in mathematics and its importance in the world.
9)Estimated time: 40 minutes
10)Technology used: MS Word to create handouts
11)Activities: First, I will arrange students into groups in a manner that promotes appropriate interaction among classmates that do not usually engage each other. To calm the chatter that I know will inevitably form from this transition (conflict resolution strategy), I will read part of the first chapter from “The Code Book” by Simon Singh. This section is an introduction to the circumstances preceding the execution of Mary Queen of Scots in 1586. I will ask students to pay attention to what the conflict of the story hinges on. My intent is to get students interested and motivated for the lesson on ciphers. I will tell them that this is the lesson topic and that we will be creating our own ciphers and decoding those of our classmates over the next few lessons.
I will briefly review handling remainders with division of whole numbers, leading into the topic of modular (or clock) arithmetic. I will do several examples using time (mod 12), prompting students for input on the outcomes of examples to get them thinking about how to do the problems. I will give them Cryptography Handout No. 1, which has 26 examples using 26 as the modulus. I will explain that this is the formula for encoding text, so it is important that if they are having problems they need to tell me now. I will have them split up the problems to make this task go more quickly, and then have them work on their individual parts alone. I will circulate around the room to make sure everyone in each group knows how to do the problems, checking off students names from a class roster as I go (so I can assess their individual work). After a moment, I will have them share answers within their groups. Then I will have each student give an answer orally (assuming there are not more than 26 students in the class). The answers to this worksheet can be used to make a cipher alphabet. Students will keep these worksheets as a reference for their notes.
After the lesson, students will be asked to write a paragraph about what they think the outcome of the introduction of the case of Mary Queen of Scots will be. I will tell them I also want to know what they could use cryptography for. Students will encode these paragraphs in the next class.
12)Procedure: The use of MS Word will be as described above for the handouts.
13)Samples: The first sample is an Excel handout from lesson 2, the second sample is the handout from lesson 1.
Cryptography Handout No. 2Alphabet / Percent Frequency / This chart and table will help you to analyze
encoded messages by using a bit of statistics.
A / 1 / 8 / Letters in any written language have a certain
B / 2 / 1.5 / frequency with which they usually occur.
C / 3 / 3 / This is the standard frequency distribution for
D / 4 / 4 / English. Beware though, this can vary and
E / 5 / 13 / can even be completely wrong in unusual cases.
F / 6 / 2 / Use this as a guide, not a guarantee.
G / 7 / 1.5
H / 8 / 6
I / 9 / 6.5
J / 10 / 0.5
K / 11 / 0.5
L / 12 / 3.5
M / 13 / 3
N / 14 / 7
O / 15 / 8
P / 16 / 2
Q / 17 / 0.2
R / 18 / 6.5
S / 19 / 6
T / 20 / 9
U / 21 / 3
V / 22 / 1
W / 23 / 1.5
X / 24 / 0.5
Y / 25 / 2
Z / 26 / 0.2
Cryptography Handout No. 1
Name ______
Let A=6 and B=7. Then since ‘M’ is the 13th letter of the alphabet, we encode ‘M’ by using , or . We find this by the following operations: , where 7 is the remainder and we use 7 to find that the encoded letter for ‘M’ is the 7th letter of the standard alphabet, or ‘G’. Now let’s find the rest.
A: codes to __
B: codes to __
C: codes to __
D: codes to __
E: codes to __
F: codes to __
G: codes to __
H: codes to __
I: codes to __
J: codes to __
K: codes to __
L: codes to __
M: codes to __
N: codes to __
O: codes to __
P: codes to __
Q: codes to __
R: codes to __
S: codes to __
T: codes to __
U: codes to __
V: codes to __
W: codes to __
X: codes to __
Y: codes to __
Z: codes to __
14)Significance: Technology is effective in the learning of this lesson by providing a method of creating the necessary tools to communicate information in a useful manner and to create helpful practice examples for students.
15)Self-evaluation: This lesson is an effective introduction to the topic of cryptography, an application of modern mathematics being utilized by the real world, and for use as an introduction to modular arithmetic.
16)References:
“The Code Book” by Simon Singh, published 2000
“Mathematics: A Human Endeavor” by Harold R. Jacobs, published 1970
“Codes, Ciphers and Other Cryptic and Clandestine Communication” by Fred B. Wrixon, published 1998
“The Original Illustrated Sherlock Holmes” by Arthur Conan Doyle, published 2001
Dr. Sally Shao’s class on Applied Mathematics at ClevelandStateUniversity
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