> q` }(bjbjqPqP JH::~~~8L,}h:Lbbb|||||||$y~h|JJJ|bb4|Jbb|J|rzb.pZ~pvFD|L|0}vǁfǁzzǁz`td||HX}JJJJ Objectives
Understand how the mathematical concepts apply to real world network engineering.
Provide a fun introduction to the concepts of network security and cryptography.
Practice greatest common factor (GCF).
Lesson Summary:
Students will learn about the technology of network communication and how network security is a necessary aspect of network Engineering. Students will be introduced to the concept of Cryptography: converting ordinary messages to secret codes using keys. Students will be required to create a simple cryptography wheel and use the wheel to decrypt coded answers to fun riddles by using a key. The key for each coded messages must be obtained by solving a math problem, in this case greatest common factor (GCF). This lesson provides a fun secret messaging activity and motivation for the students to work on GCF problems.Subject:
Math: Application of Mathematics to Engineering, Network Security and Cryptography.
Math: Greatest Common Factor.
Grade Level:
Target Grade: 6
Upper Bound: 7
Lower Bound: 6
Time Required: 1 class period (45 minutes)Authors: Graduate Fellow: Unoma Ndili Okorafor
Teacher Mentor: Ms Sondra Junek
Other Teachers: Ms Dusty Jarvis, Ms Victoria FritzieLesson Introduction / Motivation: Students are often interested in using secret codes sometimes to pass notes in class. Ask them how they would pass written information to someone at the other end of the class through their other class mates without the couriers deciphering what the message is. Introduce the concept of a network as devices connected to allow communication, and the concept of security as the protection of persons, properties or organizations from attacks by bad guys. Ask the students to list various types of networks (including phone and computer) and to list various sensitive information they would not want to get into the hands of bad guys and why. The students should come up with answers such as social security numbers, phone numbers, home address, or credit card numbers. Then, introduce the need for network security and cryptography by asking students to consider how they would send sensitive personal information over the internet, for example in an email to the school nurse, if they knew that there were several bad guys sitting on the internet and listening in on their communication. What types of technology are they aware of right now that can accomplish communication security? What was used for communication security prior to the internet? What types of attacks can a bad guy carry out if he gets hold of their confidential information? Consider various attacks on persons, properties and organizations? Lesson Plan:
Introduce network security and software engineering to the students by presenting the HYPERLINK "Cryptography%20&%20Network%20Security.ppt" power point slides. The students follow along by filling in their worksheets on HYPERLINK "Math%20Cryptography%20Worksheet.doc" network security (page 1).
Introduce the use of the HYPERLINK "Math%20Cryptography%20Wheel.doc" Cryptography wheel and a key (in the slides) by working through an example in which the students are having lunch at a restaurant with a good friend. The name of the restaurant is a secret, and has been coded as UHG OREVWHU. The students practice using the cryptography by decrypting this secret message into Red Lobster using a shift key of 3. It is important that the students understand the difference between encrypting (going from the original message to a secret code using a key) and decrypting (going from the secret code back to the original message using the same key) on the Cryptography wheel. Be sure to tell the students that the Cryptography wheel turns anticlockwise by a number of steps equal to the shift key obtained. The message is decoded as the corresponding letters to the letters of the secret code.
Once the students have understood how to use the Cryptography wheel to decrypt messages, introduce the riddles with the answers coded. Slides 14 and 15 of the HYPERLINK "Cryptography%20&%20Network%20Security.ppt" power point give two examples. The students must solve a GCF problem in order to find the key to use in decrypting the answers to the riddles.
The students can now work in groups of twos or threes, to obtain the decryption keys by solving the GCF problem, and then decoding the answers to the riddles on their follow up HYPERLINK "Math%20Cryptography%20Worksheet.doc" solve-the riddles-worksheets (pages 2 4 for various classes, groups or levels).
Assessment:
Have the students complete the worksheet and check that they obtained the correct GCFs, and therefore the keys correctly, and decrypted the answers to the riddles. A wrong GCF solution yields a wrong key which would in turn produce gibberish or a meaningless response to the decrypted riddle answer.
Prerequisites for this Lesson:
Knowledge of Greatest Common Factor.
Lesson Extensions: Students can work on solving longer term case problems such as the Mona Lisa Art Museum problem given in the last slides of the HYPERLINK "Cryptography%20&%20Network%20Security.ppt" power point. You may also wish to change the problems the students have to work on to obtain the keys. Instead of finding GCFs the students can work on any other Math problem you want them to practice.Multimedia Support and Attachments:
HYPERLINK "Cryptography%20&%20Network%20Security.ppt" Network Security and Cryptography Power Point
HYPERLINK "Math%20Cryptography%20Worksheet.doc"Network Security and Cryptography Worksheet
HYPERLINK "Math%20Cryptography%20Wheel.doc" Cryptography Wheel
Lesson Scaling:
You can increase the number of riddles on each work sheet or make the GCF problems slightly more complex if students need more of a challenge. You could also have the groups compete to know who finishes solving their worksheet riddles the fastest.
Keywords/Vocabulary:
Network Security
Cryptography
Encryption and Decryption
Cryptography wheel
Greatest Common Factor
Materials: Give each student page 1 of the HYPERLINK "Math%20Cryptography%20Worksheet.doc" Network Security and Cryptography Worksheet and give each group only one of the other three pages (pages 2-4) of the HYPERLINK "Math%20Cryptography%20Worksheet.doc" Network Security and Cryptography Worksheet, as well as the HYPERLINK "Math%20Cryptography%20Wheel.doc" Cryptography Wheel. Each group will need a scissors in order to make a cryptography wheel from the HYPERLINK "Math%20Cryptography%20Wheel.doc" Cryptography Wheel hand out. They will cut out the two wheels (a smaller inner secret code wheel and a bigger outer plain message wheel) and place the smaller wheel on the larger wheel so that their centers and alphabets align. You can give each group a toothpick to pass through the center of the wheels in order to hold them together and enable the inner wheel turn with respect to the outer wheel.
TEKS Covered:
6.1 - Number, operation, and quantitative reasoning.
(E) Identify factors of a positive integer, common factors and the greatest common factor of a set of positive integers.
6.11 - The student applies mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.
(A) Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;
(B) Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;
References: HYPERLINK "http://cryptoclub.math.uic.edu/php/joke.php" http://cryptoclub.math.uic.edu/php/joke.php
HYPERLINK "http://www.school-for-champions.com/security/whatis.htm" http://www.school-for-champions.com/security/whatis.htm
Lesson Plan: Cryptography and Greatest Common Factor
A product of the Partnership for Environmental Education and Rural Health at Texas A&M University
Network Security & CryptographyLesson PlanCryptography Riddles?
A product of the Partnership for Environmental Education and Rural Health at Texas A&M University HYPERLINK "http://peer.tamu.edu/" http://peer.tamu.edu
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