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Prism Heddle Loom

This simple loom encodes patterns into a prism-shaped piece of cardstock.

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In “How Does a Transistor Work?” Veritasium explains how the technology behind transistor radios, televisions, mobile phones, satellites, and much of modern technology actually works.

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How to use math to send a secret message

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Learn what one-time pad encryption is, how it has been used throughout history, and how to use math to send your own encrypted messages.

Would you believe it's possible to send someone a secret message secured with absolutely unbreakable encryption using only a bit of simple arithmetic? Well, it is-the solution is surprisingly simple and was used by British, German, and American spy agencies throughout World War II. Curious to know how it works? You're in luck because today we're taking our first steps into the world of secret-agent math.

Secret Agent Math, Part 1

Here's the somewhat ridiculous but hopefully amusing scenario: Imagine you're a secret agent working for your government's top-secret espionage agency. You're sitting alone in a restaurant when the waiter approaches your table and slides a small piece of folded paper in front of you. He indicates that the note was sent by a person seated across the room-you take a look and quickly recognize him to be a trusted colleague. The waiter leaves and you unfold the paper. Given your wealth of experience in these situations, you're not at all surprised to find a senseless looking series of letters scrawled across the paper: "P-B-A". Having taken stock of the situation, you realize that this sequence of letters is an encrypted message.

How to Decrypt a Secret Message

You pull out a small notepad that was issued to you before leaving on your trip. Its pages contain sequences of completely random numbers between zero and twenty-five. Armed with your notepad and the scrambled secret message, you begin the decryption process. Here's how it works. Start by looking up the first random number in your notepad-in this case it's two-and then cross it out so you don't accidentally use it again. This first number is used to decrypt the first letter of your message. Beginning with the first letter in your message, "P," count forward through the alphabet two characters-"Q" is one and "R" is two. So "R" is the first letter of your decoded message.

Okay, now that you've got that one figured out, all you have to do is repeat the process for each of the final two letters of your message. You look-up the next random number in your notepad-nineteen. So start at the letter "B"-the second letter in the scrambled message-and count forward nineteen letters until, eventually, you reach the letter "U". This is the second letter in your decoded message. Finally, for the last letter "A," you see the next random number in your notepad is thirteen. You count forward thirteen letters from "A" and arrive at "N." So, you've now got your entire message decrypted-and it says: "R-U-N." Run?!

The One-Time Pad Method of Encryption

Alright, time out. I know this scenario is probably pretty alarming, and you're no doubt eager to learn the fate of your dramatized alter-ego. But before we get to that, let's take a minute to talk about this encryption method called the "one-time pad" that played a major role in sending secret messages throughout much of the 20th century. The name "one-time pad" comes from the fact that the series of random numbers in the notepad must be used only one time. If a pad is reused, patterns can emerge that give away the random numbers in the pad, and the encryption can then be broken quite easily by an intercepting party. Additionally, these numbers must be absolutely random (not just sort of random) or, once again, patterns can develop that make it easy to figure out the contents of the pad-and, if someone knows the numbers in your pad, your encryption is useless.

Secret Agent Math, Part 2

Now, let's get back to the story. Recall that you've just deciphered a secret message telling you to "Run!" You ponder for a moment whether or not the message is a joke-if your running was that urgent, why wouldn't your colleague just yell? But then you remember that this colleague is known for strictly over-following standard industry encryption protocols, so you realize it is a real message and make a mad dash for the door. But having taken so long to comprehend the urgency of the message, you're grabbed and hustled into the trunk of a car and driven away-leaving your colleague to ponder the folly of his ways. Apparently, he now realizes, encryption isn't always necessary-sometimes simple solutions are better. But, your alter-ego's misfortune in our drama is your own good-fortune in real life since, if for some bizarre reason you ever need to secretly share information with someone, you now can do it using a one-time pad!

The Math Behind One-Time Pad Encryption

Before wrapping-up, let's take a minute to talk a little more about the math behind one-time pad encryption. Start by assigning each letter of the alphabet a corresponding integer value between 1 and 26. A=1, since "A" is the first letter of the alphabet, B=2, since "B" is the second letter, and so on until you get to Z=26, the last letter of the alphabet. If you take the integer value that corresponds to a particular scrambled letter in your encrypted message (say the letter is "P" with an integer value of 16) and add it to the associated random number from a one-time pad (say the number is two), then you get a new integer -in this case 16 + 2 = 18-which can then be converted back into the letter "R," which you'll recognize to be the first decrypted letter in the message from our story.

How to Solve Math Problems Smartly

That's all well and good, but here's an interesting case: What would happen if the scrambled letter you were trying to decrypt was "Y," and the corresponding random number was 25? If we count forward through the alphabet from "Y," we'll obviously get to "Z," but then what? Well, in this case, the answer is to loop back around and start again at "A." That's the way the one-time pad system is defined to work. So you could start at "Y," count forward to "Z," jump back to "A," and then proceed 23 more letters forward and eventually arrive at "X." But how about this: Instead of counting forward 25 letters from "Y," couldn't you also just count backward one letter? And isn't counting backward one letter a lot easier? And a lot less error prone too? It is.

So what's my point here? Well, in math, as in life, there's usually more than one way to solve a problem-and some ways are easier than others. So here's the quick and dirty tip: work smart. Simply yelling "Run!" instead of going to the trouble of sending an encrypted message would be smart. Counting one letter backward through the alphabet instead of twenty-five forward would be smart too. Think before acting and you'll solve more problems while working less-that's a pretty tough combination to beat!

Wrap Up

And speaking of beat...up: Whatever happened to our favorite secret agent? Will math save the day? Be sure to check out the next " Secret-Agent Math " episode to find out.

Thanks again to our sponsor this week, Go To Meeting. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their online conferencing service.

Please email your math questions and comments to

mathdude@quickanddirtytips.com. You can get updates about the Math Dude podcast, the "Video Extra!" episodes on YouTube, and all my other musings about math, science, and life in general by following me on Twitter. And don't forget to join our great community of social networking math fans by becoming a fan of the Math Dude on Facebook.

Until next time, this is Jason Marshall with The Math Dude's Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Secret Agent image from Shutterstock

Would you believe it's possible to send someone a secret message secured with absolutely unbreakable encryption using only a bit of simple arithmetic? Well, it is-the solution is surprisingly simple and was used by British, German, and American spy agencies throughout World War II. Curious to know how it works? You're in luck because today we're taking our first steps into the world of secret-agent math.

Secret Agent Math, Part 1

Here's the somewhat ridiculous but hopefully amusing scenario: Imagine you're a secret agent working for your government's top-secret espionage agency. You're sitting alone in a restaurant when the waiter approaches your table and slides a small piece of folded paper in front of you. He indicates that the note was sent by a person seated across the room-you take a look and quickly recognize him to be a trusted colleague. The waiter leaves and you unfold the paper. Given your wealth of experience in these situations, you're not at all surprised to find a senseless looking series of letters scrawled across the paper: "P-B-A". Having taken stock of the situation, you realize that this sequence of letters is an encrypted message.

How to Decrypt a Secret Message

You pull out a small notepad that was issued to you before leaving on your trip. Its pages contain sequences of completely random numbers between zero and twenty-five. Armed with your notepad and the scrambled secret message, you begin the decryption process. Here's how it works. Start by looking up the first random number in your notepad-in this case it's two-and then cross it out so you don't accidentally use it again. This first number is used to decrypt the first letter of your message. Beginning with the first letter in your message, "P," count forward through the alphabet two characters-"Q" is one and "R" is two. So "R" is the first letter of your decoded message.

Okay, now that you've got that one figured out, all you have to do is repeat the process for each of the final two letters of your message. You look-up the next random number in your notepad-nineteen. So start at the letter "B"-the second letter in the scrambled message-and count forward nineteen letters until, eventually, you reach the letter "U". This is the second letter in your decoded message. Finally, for the last letter "A," you see the next random number in your notepad is thirteen. You count forward thirteen letters from "A" and arrive at "N." So, you've now got your entire message decrypted-and it says: "R-U-N." Run?!

The One-Time Pad Method of Encryption

Alright, time out. I know this scenario is probably pretty alarming, and you're no doubt eager to learn the fate of your dramatized alter-ego. But before we get to that, let's take a minute to talk about this encryption method called the "one-time pad" that played a major role in sending secret messages throughout much of the 20th century. The name "one-time pad" comes from the fact that the series of random numbers in the notepad must be used only one time. If a pad is reused, patterns can emerge that give away the random numbers in the pad, and the encryption can then be broken quite easily by an intercepting party. Additionally, these numbers must be absolutely random (not just sort of random) or, once again, patterns can develop that make it easy to figure out the contents of the pad-and, if someone knows the numbers in your pad, your encryption is useless.

Secret Agent Math, Part 2

Now, let's get back to the story. Recall that you've just deciphered a secret message telling you to "Run!" You ponder for a moment whether or not the message is a joke-if your running was that urgent, why wouldn't your colleague just yell? But then you remember that this colleague is known for strictly over-following standard industry encryption protocols, so you realize it is a real message and make a mad dash for the door. But having taken so long to comprehend the urgency of the message, you're grabbed and hustled into the trunk of a car and driven away-leaving your colleague to ponder the folly of his ways. Apparently, he now realizes, encryption isn't always necessary-sometimes simple solutions are better. But, your alter-ego's misfortune in our drama is your own good-fortune in real life since, if for some bizarre reason you ever need to secretly share information with someone, you now can do it using a one-time pad!

The Math Behind One-Time Pad Encryption

Before wrapping-up, let's take a minute to talk a little more about the math behind one-time pad encryption. Start by assigning each letter of the alphabet a corresponding integer value between 1 and 26. A=1, since "A" is the first letter of the alphabet, B=2, since "B" is the second letter, and so on until you get to Z=26, the last letter of the alphabet. If you take the integer value that corresponds to a particular scrambled letter in your encrypted message (say the letter is "P" with an integer value of 16) and add it to the associated random number from a one-time pad (say the number is two), then you get a new integer -in this case 16 + 2 = 18-which can then be converted back into the letter "R," which you'll recognize to be the first decrypted letter in the message from our story.

How to Solve Math Problems Smartly

That's all well and good, but here's an interesting case: What would happen if the scrambled letter you were trying to decrypt was "Y," and the corresponding random number was 25? If we count forward through the alphabet from "Y," we'll obviously get to "Z," but then what? Well, in this case, the answer is to loop back around and start again at "A." That's the way the one-time pad system is defined to work. So you could start at "Y," count forward to "Z," jump back to "A," and then proceed 23 more letters forward and eventually arrive at "X." But how about this: Instead of counting forward 25 letters from "Y," couldn't you also just count backward one letter? And isn't counting backward one letter a lot easier? And a lot less error prone too? It is.

So what's my point here? Well, in math, as in life, there's usually more than one way to solve a problem-and some ways are easier than others. So here's the quick and dirty tip: work smart. Simply yelling "Run!" instead of going to the trouble of sending an encrypted message would be smart. Counting one letter backward through the alphabet instead of twenty-five forward would be smart too. Think before acting and you'll solve more problems while working less-that's a pretty tough combination to beat!

Wrap Up

And speaking of beat...up: Whatever happened to our favorite secret agent? Will math save the day? Be sure to check out the next " Secret-Agent Math " episode to find out.

Thanks again to our sponsor this week, Go To Meeting. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their online conferencing service.

Please email your math questions and comments to

mathdude@quickanddirtytips.com. You can get updates about the Math Dude podcast, the "Video Extra!" episodes on YouTube, and all my other musings about math, science, and life in general by following me on Twitter. And don't forget to join our great community of social networking math fans by becoming a fan of the Math Dude on Facebook.

Until next time, this is Jason Marshall with The Math Dude's Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Secret Agent image from Shutterstock

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How to Use Math to Send Encrypted Messages

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Would you believe it’s possible to send someone a secret message secured with absolutely unbreakable encryption using only a bit of simple arithmetic? Well, it is-the solution is surprisingly simple and was used by British, German, and American spy agencies throughout World War II. Cu

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Floppy Spirit Drum

Create these wonderful spirit drums to celebrate Chinese New Year and then use all year long.

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Binary Weaving

Computers use binary numbers (Base 2), a series on "ons" and "offs" that encode information. In this activity, students use the Ascii alphabet to encode a message into woven band, and then other students can decode the information.

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Binary Dots

Counting in binary is quite straightforward and makes for an interesting and compelling activity for any student who can do simple addition. This uncomplicated game creates an opportunity to practice counting in binary. It reinforces understanding of place value and can be extended into a discussion of other bases and number systems.

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Break the Code

In this logic game, a player uses clues to help them break a hidden code in as few guesses as possible.

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Decipher the Postal Bar Code

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Resources

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Learn computer science. Change the world.

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Every student in every school deserves the opportunity to study computer science.

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Kodable is an amazing app that teaches programming to students K-2nd. It allows students to have an interactive learning experience using a gamification approach. That app will soon also have curriculum to help educators including lesson plans, vocabulary and activities. Jon and Grechen are also working on a web and android version which will be great for BYOT schools.

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"I can't live without my smartphone, but I really geek on coding. It's not so much technology that I like, but puzzle solving." Sylvia Day Last week I was lucky to meet the creators of Kodable - Grechen and Jon. Kodable is an amazing app that teaches programming to students K-2nd.

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Dot patterns for number recognition

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Sign language as another code

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real life applications

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braille as a secret code...

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American Foundation for the Blind (AFB) Braille Bug is a kids' site that teaches sighted children grades 3 through 6 about braille, and encourages literacy among sighted and visually impaired children in a fun environment packed with facts, information, games, graphics, and activities.

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review of books about secret codes

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One of my favorite childhood purchases was a book about secret codes. It included a clear red-tinted sheet that could be used to reveal a message. I wasn't the only child to find codes and ciphers fascinating. Nor was I the last. Young people continue to be interested in ways of hiding messages. Several well-regarded youth books involving codes have been published recently. The code-breaking titles in today's column are all available at Lincoln City Libraries.

Most of Paul Janeczko's books can be found in the library's poetry section. He ventures away from poetry in "Top Secret: A Handbook of Codes, Ciphers, and Secret Writing" (Candlewick 2004). This is a basic nonfiction title that introduces a variety of codes. Janeczko recommends that the reader choose a partner with whom to share and decode secret messages, and to make up a field kit. His explanations of a variety of concealment techniques are thorough and well illustrated, clearly intended as examples to practice. Throughout the book, stories of actual uses of secret codes add to the information. Jenna LaReau's copious black-and-white illustrations make this a highly browsable book for middle to upper elementary grades.

"The Code Book: How to Make It, Break It, Hack It, Crack It" by Simon Singh (Delacorte, 2001) is written for an older audience. The intended readership would be middle-schoolers and high-schoolers, though adults often seek out this kind of quality nonfiction to gain general background on a topic. Singh incorporates many historical examples into his descriptions of devices and methods, beginning with "the birth of cryptography" during the reign of Mary Queen of Scots. He successfully strikes a balance between explaining fairly complicated systems and telling compelling stories. Some of those stories may ignite hope in the hearts of youth who feel persecuted because of their intelligence and mathematical interest; many codebreaking and codemaking heroes were such outsiders. Singh explores the issues of privacy, safety and politics that new encryption techniques challenge. The book ends with some codebreaking challenges, examples and ideas for further reading.

"Chasing Vermeer" by Blue Balliett (Scholastic, 2004) is a thick stew of a novel that features two unlikely yet likable partners, Petra Andalee and Calder Pillay. They become enmeshed in a code-ridden mystery involving the paintings of Jan Vermeer. The young detectives attend the University School in Chicago where their sixth grade teacher draws them into the drama. Despite initial reluctance on both sides to become friends, both see the advantages of pooling their intelligence and skill. As Petra and Calder become more and more convinced that they're about to solve a major art mystery, they find themselves in danger. Balliett has constructed a tight weave of interconnected codes, characters and clues. Brett Helquist's black-and-white illustrations incorporate a secret message based on the pentimento tiles that Calder carries in his pockets. Those pictures heighten the mysterious atmosphere, even for readers who don't care to decipher the message. The sense of evil, the actual danger in which Calder and Petra find themselves and the complex structure of the story make this appropriate for upper elementary and middle school readers.

Thomas B. Allen reveals an interesting aspect of American history in "George Washington, Spymaster: How the Americans Outspied the British and Won the Revolutionary War"(National Geographic, 2004). Allen provides a look at Washington's less-known leadership in the Revolutionary War; among his other duties, he ran a system of spies. They employed a variety of codes and techniques. In telling this story, Allen emphasizes the risks taken by many individuals to establish our country. The reader is reminded that the outcome of the war was much in doubt at the time. The new country depended on the creativity, stealth and risk that these spies and messengers exhibited. The book's design, with its small size, historical font and illustrations resembling woodcuts, reflects the era it describes. Codes have been included in margins and captions for the reader to decode. Extensive appendices provide a map, timeline, sources and Washington's numerical code. Although it's intended for upper elementary students, this book also would be of interest to many adult readers.
Pat Leach is supervisor of youth services at Lincoln City Libraries.

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Pat Leach: Spy books help kids crack the code

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One of my favorite childhood purchases was a book about secret codes. It included a clear red-tinted sheet that could be used to reveal a message. I wasn't the only child to find codes and ciphers fascinating. Nor was I the last. Young people continue to be interested in ways of hiding messages.

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how bar codes work

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Have students search for QR, bar codes, etc. in and out of the classroom. List where they found them, what information the code contains, etc. Prize for most unusual use of code

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Blog about using QR codes in class

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Have students attempt to convey messages to one another.

Use various tools (code, morse code, QR, etc.) and evaluate how well each one worked.

Contest (like catapults) with judgements in various categories.

Expand to go to visual messages.

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Tools to intro programming to kids

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Developed by the MIT Media Lab, Scratch is a visual programming language for children age 6 and up. Since its release in 2007, over 800,000 users have joined the Scratch website and have shared over 1.7 million projects -- from games to animations. That sharing aspect is an important part of the Scratch community, so the projects that are uploaded to the site are licensed under the Creative Commons attribute and share alike license so that others can download and remix them. Scratch is available free of charge and runs on Mac, Windows, and Linux computers.
ALICE
Alice is a free and open source 3D programming environment designed to teach students object-oriented and event-driven programming. With Alice, students drag and drop graphic tiles in order to animate an object and create a program. A variant of Alice, Storytelling Alice was developed by Caitlin Kelleher as part of her doctoral work in Computer Science at Carnegie Mellon University. By emphasizing animations and social interactions, this approach was found to greatly increase the level of student interest in programming.
HACKETY HACK
Hackety Hack is an open source application that teaches the basics of programming in the popular Ruby language. Hackety Hack offers an interactive tutorial that runs on Windows, Mac, and Linux operating systems. While both Scratch and Alice use a graphical programming language with "blocks," Hackety Hack teaches the basics of Ruby syntax. The tutorial and the text editor are well-integrated, so there isn't any flipping back-and-forth to move between the How-To guide and the actual coding. Hackety Hack gives students a solid foundation in the language so they can quickly and easily start building their own apps in Ruby.
ARDUINO
Arduino is an open-source electronics prototyping platform with both hardware and software components. Arduino's hardware is programmed with a language similar to C++, and although it may not be the easiest of entry points for learning programming, there's something about building things that actually move that can be pretty compelling. Projects that use Arduino to introduce children to programming include a modification of Scratch to support simple programming on the Arduino hardware. As Google recently announced that it would allow Android mobile devices to communicate with Arduino hardware, look for more opportunities to work with this platform in the future, perhaps even via the Android App Inventor, a tool that provides a visual interface for building Android apps.
LEGO MINDSTORMS
One of the most popular toys in history, Lego may be best known for its brick-building. But Lego Mindstorm s also enables robotics-building. Lego Mindstorms' kits -- which can be purchased in educational and consumer versions -- include sensors and motors, and the programming is command-box rather than code programming. The kits come with languages supplied by Lego, but can be modified to work with third party languages. Like several of the tools on this list, Lego Mindstorms has its roots at the MIT Media Lab.

These are just a few of the options for introducing someone to programming. What other languages or tools have you used -- in the classroom or at home?

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5 Tools to Introduce Programming to Kids

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Developed by the MIT Media Lab, Scratch is a visual programming language for children age 6 and up. Since its release in 2007, over 800,000 users have joined the Scratch website and have shared over 1.7 million projects -- from games to animations.

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Computer Science Unplugged

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CS Unplugged is a collection of free teaching material that teaches Computer Science through engaging games and puzzles that use cards, string, crayons and lots of running around.

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Video Game teaches students Java

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Ayah is the founder and CEO of littleBits, an open source library of electronic modules that snap together with tiny magnets for prototyping, learning, and fun. Using step-by-step instructions, littleBits offers easy to follow DIY electronics kits consisting of tiny circuit boards engineered to be combined in order to perform custom functions. Named as one of CNN's Top 10 Emerging Startups to Watch, littleBits won Ayah a spot on Fast Company's 100 Most Creative People and Popular Mechanic's 25 Makers Who Are Reinventing the American Dream. She is also an alumna of MIT Media Lab and a TED Senior Fellow.

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Video Game Teaches Elementary Students How To Code - PSFK

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Ayah is the founder and CEO of littleBits, an open source library of electronic modules that snap together with tiny magnets for prototyping, learning, and fun. Using step-by-step instructions, littleBits offers easy to follow DIY electronics kits consisting of tiny circuit boards engineered to be combined in order to perform custom functions.

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Morse Code and Lewis and Clark

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Lewis and Clark . Classroom Resources . Lesson Plans . The Art of Communication | PBS

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Review photographs and information on various communication devices that have been developed.

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free

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Use this resource with your students to help them understand there is a secret abbreviated language they can use to communicate and its not emojis. Morse Code is a language commonly used when telephones when other means of communication are unavailable. Students will answer comprehension questions to convey their understanding and create their own secret messages.

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Morse code powerpoint

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Morse code game for music class

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Morse Code Game for Primary or Elementary Music Classes

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An easy to use game for upper primary or upper elementary music classes, that will build listening skills and musical understanding. For associated resources please visit http://www.funmusicco.com/morsecodegame

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Crypto Kids is a website created by the National Security Agency all about creating and breaking codes.

This is a fantastic critical thinking website that also taps into math, linguistics, engineering, and analyzing skills.

Blog post about using it:

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What it is: Crypto Kids is a website created by the National Security Agency all about creating and breaking codes. This is a fantastic critical thinking website that also taps into math, linguistics, engineering, and analyzing skills. I found Crypto Kids while I was hunting for an activity for students to learn more about codes as part of our Treasures reading series. Crypto Kids turns out to be an excellent site for all elementary classrooms. Students learn all about cryptology, the National Security Agency, and ciphers. Students get the chance to meet the characters of Crypto Kids which include: Crypto Cat, Decipher Dog, Rosetta Stone, Slate, Joules, T. Top, and the leader CSS Sam. Students can play logic games to test out their code breaking skills. There are three levels of game play beginner, intermediate, and advanced. As students play games, they will learn Morse Code, complete brainteasers that involve math and logic, create their own cipher machines, crack Yardleygrams and cryptograms, and learn some words in different languages. Students can then learn more about careers that use cryptograms and code breaking at the National Security Agency.

How to integrate Crypto Kids into the classroom: Crypto Kids is packed full of thinking and logic games and activities, many of which involve mathematical problem solving. Crypto Kids games and activities are a great way to get your students thinking critically before math class. Put one of the brain teasers up on the projector connected computer or interactive whiteboard for students to solve as a warm up activity. Crypto Kids games are short enough that they could be used as a math center activity on classroom computers. Students can visit the center in pairs or small groups and work on solving cryptograms together. The Yardleygrams are stories that must be solved, these are fun to solve as a whole class.

Since I was using this site to build background knowledge about codes with my students, we focused on what secret codes were, how they were used, and cracked some codes for practice. As an extension activity, I had students read the descriptions of the characters on Crypto Kids and write a short story about the character. These turned out great! Students have to use the character qualities that are written and craft a story about the character, paying attention to how they think the character would act and what special skills they could use to solve a problem.

Tips: Check out the Teacher/Parent section of the site for some additional resources.

Please leave a comment and share how you are using Crypto Kids in your classroom.

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What it is: Crypto Kids is a website created by the National Security Agency all about creating and breaking codes. This is a fantastic critical thinking website that also taps into math, linguistics, engineering, and analyzing skills. I found Crypto Kids while I was hunting for an activity for students to learn more about codes as part of our Treasures reading series.

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6th-8th

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Talking Drum resources! Info!