You’ll discover how to twist arithmetic, outsmart logic puzzles, write unbreakable codes, dig into freaky fractals, build a geometric pantograph, step through a sheet of paper, multiply by drawing lines, perform math tricks that really look like magic, decode cryptograms, and memorize absolutely anything using a hundred–year-old secret code. You’ll never be bored with math again.
Step 1. Click Here to download your copy of the Ultimate Science Curriculum Mathemagic Student Guidebook.
Step 2. Watch the videos that go with it below.
Introduction: What is Math and Why Bother with it?
Greetings, and welcome to the study of math. This unit was created by a mechanical engineer, university instructor, airplane pilot, astronomer, robot-builder and real rocket scientist … me! When I was in high school, I was so excited about math that I not only starting my own profitable math tutoring business, which was marketed mostly to my friends, but I also attended extra math classes in the evening at a local college where I was the only one with a curfew of 9 p.m. I have the happy opportunity to teach you everything I know about math over the next set of hands-on lessons – something that’s not usually a part of math unless it’s a game, and those get tiring after awhile, usually because they aren’t related the real world.
I promise to give you my best stuff so you can take it and run with it … or fly!
When I first started out writing this study unit, I was amazed at how the math camps out there for the brainiacs who had way above-average math skills operated. There was even one camp where the kids were solving math problems that even adults didn’t know how to solve. I also found a handful of remedial math camps for kids failing math during the academic year who needed to spend their summers making up for lost time. And those camps were overstuffed with busywork-style worksheets and endless rounds of drills, none of which were stimulating or designed to make kids think.
I found no place for kids in the middle of the spectrum, who want to continue honing their math skills in a fun and challenging way. That’s really sad, because that’s where most of the population is. There was absolutely nothing for the kids in the middle of the road, because the current math camp content out there was either designed for the super-smart kids or the ones falling way behind. That’s when I decided to do something about it.
While we’re not going to solve the world’s current unsolvable math mysteries, or spend time with remedial work, what we are going to focus on is content that is fun, innovative, creative, and designed to make you think. And there’s no silly cartoon-animations, fake problems designed to look real (how many pink elephants fit in the bathtub?), or endless rounds of busywork. You get enough of that elsewhere, so you won’t find it here. What you will find is real math, just like real scientists use every day, so you know what to expect when you get out there in the real world. (Like I said: no pink elephants.)
So, that leads us to the first real question: What is math?
Math can be compared to a very useful tool, like a hammer, or a collection of tools like a set of screwdrivers. A lot of kids get frustrated and bored with math because many textbooks concentrate a lot on teaching the small, meticulous details of each and every type of tool. That’s one of the fastest ways to kill your passion for something that could have otherwise been really useful!
Don’t get me wrong – you do need to know how to tell a hammer from a screwdriver. But can you tell me when to use the hammer instead of the screwdriver? It’s really important to focus on how and when to use the different tools. This is my practical approach to teaching the subject.
Most kids think math just means numbers, when the truth is that math is much more than just numbers and being good at multiplying! There are three main areas in math (at least when you first start out). Some kids enjoy adding and dividing, and for them, math is all about numbers. However, if you’re really good with shapes and how they relate, then you might enjoy geometry. And if you are good at solving puzzles and people think you’re unbeatable at certain games, chances are that logic will be a great match for your skills.
We’re going to discover what math really is, and how we can use it in our everyday lives in a way that’s really useful.
Mathemagic Camp is chock-full of demonstrations and hands-on activities for two big reasons. First, they’re fun. But more importantly, the reason we do activities is to hone your math skills, which usually don’t show up in the science arena until way later, like in high school or college. One of the biggest mistakes teachers make when teaching math is that they don’t connect it back to the real world. They treat it like a bunch of problems on paper that need to be solved, as if the story ended there.
But you already know where math is around you: it’s counting back change at the grocery store; it’s figuring out how much fuel you need to make it to the next gas station; it’s fitting all the boxes into the back of your truck; it’s how to beat the kid down the street at chess. It’s everywhere, if you only know where and how to look.
The skills in math take time and practice to master. But it’s important not to get so lost in practice sessions that you lose sight of the goal. Imagine learning a new sport, and you were always practicing, practicing, practicing… and never got around to playing a game, never kept score, never heard the crowd cheer or felt the sense of pride that comes from scoring a goal. You actually need both: practice and performance, and most teachers only settle for practice and forgo the real reason you need to learn this stuff in the first place: to be able to handle the science side of things later on down the road.
One thing I didn’t realize about math (but you probably already know) was that it’s not always right. What I mean is that sometimes math gives deceptive answers that have to be interpreted for them to make any sense. For example, I remember one time I was doing a calculation and my answer to the problem actually resulted in two answers. One answer was 53 feet, and the other was 6 inches. Both answers solved the set of equations I was trying to solve. Now, how did I know which one was really right? I mean 6 inches is different from 53 feet. I had to look back at the original problem, and as soon as I did, I realized that the answer was 6 inches, since there was no way I was going to find a 53-foot badger.
Ideally, you’d learn both science and math skills together in tandem, so you could see how one affected the other; how one was used in a way that made the other possible; where math leaves off and where science takes over, and how they intertwine. For example, you could really see how to model a car on paper as a mass-spring-damper system and write an equation to describe the motion the driver feels while driving down the road, solve that differential equation, plot out the solution on a graph, find the points where your solution exists, and run back and put a big X on the car where you want the wheels in order for the ride to be as smooth as possible for the rider (turns out that those points are at the center of percussion, kind of like the “sweet spot” on a bat when a baseball batter hits the ball in exactly the right spot so there’s almost no force felt at the grip). But it’s not always possible to teach math this way because not every teacher will have these skills.
To sum it up: math is a tool that helps scientists model the real world down on paper so we can make the problems easier to solve. Once we solve them, we have to bring them back to the real world by making sense of what we did on paper. That’s usually where we find out how good of a job we did in the first place. That’s why I always do my math problems in pencil, and I write everything down so I can easily find my mistakes.
Math by itself is an art, but math combined with science is pure joy and fulfillment, the kind I want to share with you. I’m going to give you a lot of different activities to help you develop your math techniques in learning how to think. Good luck with Mathemagic Camp!
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Lesson #1: The Magic of 11’s
Overview: Here’s our first lesson. It is so easy that one night, I wound up showing it to everyone in the pizza restaurant. Well, everyone who would listen, anyway. We were scribbling down the answers right on the pizza boxes with such excitement that I couldn’t help it – I started laughing right out loud about how excited everyone was about math … especially on a Saturday night.
When you do this calculation in front of friends or family, it’s more impressive if you hand a calculator out first to an unsuspecting friend, letting them know that you are “testing to see if the calculator is working right,” Ask for a two-digit number and have them check the calculator’s answer against yours.
Materials
- Pencil
- Paper
Lesson #2: Multiplying a 3-Digit Number by 11
Overview: If you liked multiplying two-digit numbers by 11, chances are you’re curious about what to do with a three-digit number, like 213. It’s only one more step to figuring out the answer, making this trick equally as impressive as the two-digit version.
Materials
- Pencil
- Paper
Lesson #3: Multiply by 12’s
Overview: Do you think you’ll need to know how to multiply by 12 or 11 more? Think of it this way: How often do you need to figure out how many dozen you need of something? It comes up a lot more than needing to know how many batches of 11, doesn’t it? That’s because of the way we’ve decided to group things mathematically as a society.
Here’s why: We picked 12 based on how we used to count on our fingers using the “finger segment” system. If you look at your hands, you’ll notice that your index finger has three segments to it. So do your middle finger, ring finger, and pinkie. Since you have four fingers, you actually have 12 sections for counting with (we’re not including your thumb, which is the pointer… your thumb rests on the section you’re currently on). When your thumb touches the tip of your index finger, that means “1.” When your thumb touches the middle segment, that’s “2,” and the base segment is “3.” The tip of your middle finger is “4,” and so on. That’s how we came to use the 12-in-a-batch system.
If you’re wondering why we didn’t use the 24-in-a-batch system (because you have two hands), that’s because one hand was for 1-12 and the second hand indicated the number of batches of 12. So if your left hand has your thumb on the ring finger’s base segment (9) and your right hand has the thumb touching the index finger’s middle segment (2 complete batches of 12, or 2 x 12), the number you counted to is: 24 + 9 = 33.
Fortunately we now have calculators and a base-10 system, so this whole thing worked out well. But still the number 12 persists! So this is a very useful skill to have at your fingertips. It’s very similar to the shortcut used when multiplying by 11, but it also involves some doubling. You’ll find this is a really cool (and FAST) way to multiply by 12. And it’s a lot faster than using the Babylonian finger-segment system. Try some problems on your own and check your work with a calculator.
Materials
- Pencil
- Paper
Lesson #4: Divisibility
Overview: Do you know that 8 can be divided by 2 completely? The answer may be yes because it is a small number; therefore division can be carried out easily. However, can you figure out if 9,054,137,828 can be divided by 7 completely without a remainder?
Conducting long division for large numbers can be tedious (and boring). This lesson gives us an opportunity to answer such questions within seconds.
Divisibility is a concept which implies that a number should be divided by another completely. Since 8 can be divided completely by 2, we say it is divisible by 2. In this lesson, we will discuss quick tests that can make us say whether a number is divisible by 2, 3, 4, 5 and 7.
Materials
- Pencil
- Paper
Lesson #5: On What Day Were You Born?
Overview: People celebrate their birth dates every year, but are these days similar to the days they were born? Not usually! This is not only a neat trick but a very practical skill – you can figure out the day of the week of anyone’s birthday.
If you were born in the 20th Century, (1900-1999), we can use math to find out on which day of the week you were born. If you’re a little too young for this, try it with a parent or grandparent’s birthday when you first start out. (I’ll show you how to adjust it for different centuries a little later.)
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Table of Months Jan. 1 (0 for leap year) Feb. 4 (3 for leap year) Mar. 4 Aug. 3 Apr. 0 Sept. 6 May 2 Oct. 1 June 5 Nov. 4 July 0 Dec. 6 |
Materials
- Pencil
- Paper
Lesson #6: $1 Word Search
Overview: Have you ever heard of a dollar word search? It’s a special kind of puzzle where the letters in a word add up to a coin value. For example, an A is worth a penny, the letter B is worth two cents, C is worth three cents, and so on. A word like “excellent” is worth $1.
Materials
- Pencil
- Paper
Lesson #7: Isn’t That SUM-Thing?
Overview: This is a neat trick that you can use to really puzzle your friends and family. You’re going to sum five different numbers; three of them are random picks from the audience. The trick is that by only knowing the first number, you can predict the final number every time.
Materials
- Pencil
- Paper
Lesson #8: How to Add and Multiply Fast
Overview: Want a peek under the ”hood” of my brain when I do a mental math calculation? This lesson includes steps that take a slow-motion, step-by-step snapshot of what goes on when I add numbers in my head. The first thing you need to learn is how to look at the whole problem when adding, and also learning how to multiply from LEFT to RIGHT, both of which are opposite from most math techniques out there. I’ll show you how to do this. It’s easy, and essential to working bigger numbers in your head.
Materials
- Pencil
- Paper
Lesson #9: Squaring a Two-Digit Number
Overview: This neat little trick shortcuts the multiplication process by breaking it into easy chunks that your brain can handle. The first thing you need to do is multiply the digits together, then double that result and add a zero, and then square each digit separately, and finally add up the results.
Materials
- Pencil
- Paper
Lesson #10: How to Square Bigger Numbers
Overview: Squaring three-digit numbers is one of the most impressive mental math calculations, and it doesn’t take a whole lot of effort after you’ve mastered two-digit numbers. It’s like the difference between juggling three balls and five balls. Most folks (with a bit of practice) can juggle three balls. Five objects, however, is a whole other story (and WOW factor).
Once you get the hang of squaring two-digit numbers, three-digit numbers aren’t so hard, but you have to keep track as you go along. Don’t get discouraged if you feel a little lost. It’s just like anything you try for the first time. When you’re new at something, in the beginning you aren’t very good at it. But with practice, these steps will become second nature and you’ll be able to impress your friends, relatives, and math teachers.
Materials
- Pencil
- Paper
Lesson #11: Folding a Cube
Overview: There’s more than one way to fold a cube from a flat sheet of paper! In the video that goes with this lesson, I’ve used Post-It notes since they are square, but you can cut out your own pieces of paper and stick them together with tape. Materials
- Pencil
- Paper
Lesson #12: Mobius Strip
Overview: Although the Möbius strip is named for German mathematician August Möbius, it was co-discovered independently by Johann Benedict Listing, a completely different German mathematician, but at around the same time in 1858. Weird, right? But that’s not the only strange thing about the Möbius strip. It’s a non-orientable surface. This means it has a path that will take a traveler back to their point of origin. Are you completely confused now?
Materials
- Pen
- A pair of scissors
- Paper
- Tape
Lesson #13: Stepping Through Paper
Overview: Did you know that you can step through a sheet of paper using only a pair of scissors to help? Does this sound impossible? Great – let’s get started.
Materials
- A sheet of paper
- A pair of scissors
Lesson #14: Sizes of Geometry
Overview: Remembering and visualizing most shapes is pretty easy, right? An octagon can be a challenge for some (it has eight sides, while the commonly-confused hexagon has six sides). In this activity, we are going to use our memory to try to recall and draw some everyday objects such as a quarter, a playing card, and more, at their actual size. What objects around your house can you think of to use and test yourself?
Materials
- Pencil
- Paper
- A dollar bill, a button, a playing card, an eraser, or any other random item
Lesson #15: Fractals
Overview: Fractals are new on the mathematics scene, however they are in your life every day. Cell phones use fractal antennas, doctors study fractal-based blood flow diagrams to search for cancerous cells, biologists use fractal theory to determine how much carbon dioxide an entire rain forest can absorb.
Fractals are in the mountains, clouds, coastlines, central nervous system, flower petals, sea shells, spider webs… they’re everywhere! And the really nifty thing about fractals is that they are not only cool, they’re super-useful in our world today.
Many mathematicians today are building on the work pioneered by Karl Weierstrass (1872), Helge von Koch (1904), and Waclaw Sierpinski (1915) to figure ways of using the ideas behind fractals. One of the most interesting parts about fractals is that many ideas about fractals were first thought up of in our lifetime. Many different fields, including medicine, business, geology, clothing fashion, art, and music use ideas about fractals.
Fractals are beautiful (there is something hauntingly stunning about the computer-generated images of objects such as the Mandelbrot set, Julia sets, the Koch snowflake). But that’s not all – they are useful in our technology world. However, you’ll find that many research mathematicians still roll their eyes at the mention of the word “fractal,” mostly because the discussions you’ll find out there concerning fractals are missing the most important element – the mathematical content! This is why you’ll often find both students and teachers thinking that fractals are reserved only for art and video games, when that’s only one side of a multi-faceted concept.
There is solid mathematics behind the pretty pictures – in fact, with a good program, most kids can create their own fractal images after starting with the mathematics (which is often more beautiful than the images themselves!)
I’m going to help you unravel some of the mystery of fractals while having a lot of fun doing it. There are lots of easy-to-teach topics involving ideas from fractal geometry.
Materials
- Pencil
- Paper
- Grid made of triangles
Lesson #16: Chaos Fractal Game
Overview: This is a game that is based on fractals. You’ll need the triangle grid paper and a die. This is a great demonstration on how probability can be used can be used with a game to come up with beautiful patterns.
Materials
- Three pens with different colors, possible blue, green and red
- Dice (well, really just one die that you are okay with drawing on to color-code it)
- A paper with triangular grids (refer to last pages of this lesson)
Lesson #17: Real Geometry: The Pantograph
Overview: A pantograph, first invented in the early 1600s, was used to make exact copies before there were any Xerox machines around. It’s a simple mechanical device made up of four bars linked together in a parallelogram shape.
Here’s how it works: By simply tracing an object with the pointer, the pantograph makes a copy larger or smaller depending on which point you attach your pen and pointer. Some pantographs were adjustable – meaning that they could change their pivot points to adjust the size of the copies. We’re going to make one of these to see how geometry can really be used in the real world.
Materials
- Paper
- 2 mechanical pencils
- Masking tape
- 4 brass fasteners
- 2 yardsticks
- Strong scissors or saw to cut the yardsticks into three 16″ lengths and one 8″ length
- Drill with drill bits
- Scrap piece of cardboard, wood, or other old table space to practice on (your table may get scratched)
Lesson #18: Graphical Multiplication
Overview: The trick looks impressive, so be prepared for jaw-drops when you show this to kids and adults. But can you figure out how it works? I’ll give you a hint: Think about how to represent placeholders of powers of 10…
Materials
- Pencil
- Paper
Lesson #19: Paperclip Trick
Overview: Math isn’t just about numbers or shapes… it’s also about games and thinking about things in a new way. This problem is a great example of this. It’s a neat logic question that also involves some spatial thinking, like geometry, to work yourself out of what seems like a paradox. Before you look at the solution on the next page, see if you can figure it out for yourself.
Materials
- 11 paper clips
- Three cups
Lesson #20: New Year’s Puzzle
Overview: This is a really fun calendar riddle I learned back when I was a student that really had me going for days before I figured it out. This one really seems like a paradox at first. It’s a math logic puzzle that will really blow your mind. Are you ready?
Materials
- Pencil
- Paper
Lesson #21: Logic Numbers
Overview: This is a neat logic trick which allows you to flip over a stack of cards numbered 1-10. When you flip them back upright, they are in numerical order. There is a special way to make it work, so pay close attention! Materials
- Pencil
- Paper or 10 index cards
Lesson #22: Checkerboard Paradox
Overview: Once in a while, mathematicians come up against something that really seems impossible on the surface. These seeming “impossibilities” not only cause them to sit up and take notice, but often to create new rules about the way math works, or at the very least understand math a little better.
Be warned, however, that some paradoxes are really false paradoxes, because they do not present actual contradictions, and are merely “slick logic” tricks. Other paradoxes are real, and these are the ones that shake the entire world of mathematics. There are several paradoxes that remain unsolved today.
Materials
- Pencil
- Template from this page
Lesson #23: Hex
Overview: Hex is a super fun game! It starts with a grid of hexagons (six-sided shapes) and two players. You can color in any cell on your turn. The ultimate goal is to be the first one to complete a chain across to the other side of the board.
Using the pie rule can help with the advantage that the first player gets. This means the second player can choose to switch positions with the first player after they’ve made their first move. Can you use your logic skills to find strategies that make getting across the board easier?
Materials
- Two different colors of markers or crayons
- Hex board (refer to next page)
Lesson #24: Magic Squares
Overview: Magic squares have been traced through history as known to Chinese mathematicians, Arab mathematicians, Indian and Egyptian cultures. Magic squares have fascinated people for centuries, and historians have found them engraved in stone or metal and worn as necklaces. Early cultures believed that wearing magic squares would ensure they had long life and kept them from getting sick.
Benjamin Franklin was well-known for creating and enjoying magic squares, and it was all the rage during his time. Here’s the deal: We’re going to arrange numbers in a way so that all the rows, columns, and even the diagonals add up to a single number (called a Magic Sum). The first Magic Square was published in Europe way back in 1514.
Materials
- Pencil
- Paper
Lesson #25: Bagels
Overview: This is one of my family’s favorites! It’s a guessing game, but you can use logic and strategy in order to guess the numbers very quickly. I’ll show you how to use the game to guess numbers even larger than three digits. Once you’ve mastered the strategies in this game, you’ll never lose another game of Mastermind again.
Materials
- Two people with brains
Lesson #26: Tic-Tac-Toe
Overview: The first folks to play this game lived in the Roman Empire, but it was called Terni Lapilli and instead of having any number of pieces (X or O), each player only had three, so they had to move them around to keep playing. Historians have found the hatch grid marks all over Rome. They have also found them in Egypt!
In 1864, the British called it “noughts and crosses,” and it was considered a “children’s game,” since they would play it on their slates. In recent times (1952), OXO was one of the first known video games, as the computer played games against a person.
Tic-tac-toe can be fun, but when you get a “cat’s game” (no winner), it can get a little boring pretty quickly, right? I’ll show you some cool ways to change the game to make it more interesting by changing one or two of the basic rules. It’s much more engaging and strategic that way! Currently there are more than 100 variations of tic-tac-toe, and I’m going to show you my favorite ones. In fact, last time I taught a live science workshop, all 120 kids played this at the same time with squeals of delight!
Materials
- Pencil
- Paper
Lesson #27: Don’t Make a Triangle
Overview: This is a cool two-player geometry game with lots of strategy involved. You’ll need paper and two different-colored markers or crayons. The object is not to draw a triangle (or to force your opponent to draw one).
Materials
- Two different colors of crayons, markers, or pens
- Paper
Lesson #28: Math Dice Game
Overview: Did you know I carry a set of dice in my pocket just for this game? It’s as old as the hills and just as fun to play now as it was when I was a little math whiz back in second grade. (No kidding – when we had ”math races,” I was always team captain. Not quite the same thing as captain on the soccer field, though…)
This is one of those quick-yet-satisfying dice games you can play to hone your thinking skills and keep your kids busy until the waiter arrives with your food. All you need are five or six standard 6-sided dice and two 12-sided dice. (Note – if you can’t find the 12-sided dice, just skip it for now. You can easily substitute your brain for the 12-sided dice. I’ll show you how.)
You need to do two things to play this game. You can use a calculator with this game, but usually the kids without the calculator win the round, as it usually takes longer to punch in the numbers than figure out the different possibilities in your head (and that’s what you’re working on, anyway!) If you’re a highly visual learner, then use paper and a pencil so you can scribble down stuff as you go.
Materials
- Six 6-sided dice
- Two 12-sided dice
- Pencil (optional)
- Paper (optional)
Lesson #29: Big Numbers
Overview Numbers really can be huge – some are too big to even imagine! Have you ever seen a million pieces of candy? Or have you ever even tried to count to one million? We’ll try to figure out about how long it would take just to count to one million. I’ll also show you how to write some really big numbers!
Materials
- Pencil
- Paper
Lesson #30: Exponents
Overview: Scientists use exponents all the time to write very large or very small numbers in a very short space. It’s like shorthand for long numbers. It’s also easier to work with large numbers in exponential form.
Materials
- Pencil
- Paper
Lesson #31: Math at a Rock Concert
Overview: Here’s an interesting math puzzle. If you’re at a concert that’s also being broadcast live on the radio, who will hear the music first? Will it be you, or people listening on the radio? I’ll show you how to use the speed of sound versus the speed of light to find the answer. Materials
- Pencil
- Paper
Lesson #32: Rail Fence Cipher
Overview: Cryptography is the writing and decoding of secret messages, called ciphers. Now for governments, these secret ciphers are a matter of national security. They hire special cryptanalysts who work on these ciphers using cryptanalysis. The secret is that solving substitution ciphers can be pretty entertaining! Ciphers are published daily in newspapers everywhere. If you practice encoding and decoding ciphers, you too can become a really great cryptanalyst.
Materials
- Pencil
- Paper
Lesson #33: Twisted Path Cipher
Overview: This cipher method uses a matrix and a path in order to encode your message. The shape of the path you create within the matrix of a Twisted Path Cipher determines how difficult it will be to break the code.
Materials
| I | N | S | I | D |
| E | T | H | E | O |
| L | D | P | I | A |
| N | O | X | Q | Z |
- Pencil
- Paper
Lesson #34: Shift Cipher
Overview: Shift ciphers were used by Julius Caesar in Roman times. The key is a number which tells you how many letters you’ll shift the alphabet. These are fairly simple to encode and decode. However, you have to be extra careful when encoding because mistakes can throw off the decoding process.
Materials
- Pencil
- Paper
Lesson #35: Date Shift Cipher
Overview: The Date Shift cipher is a much harder code to break than the simpler Shift Cipher. This is because the Date Shift number key varies from letter to letter, and also because it’s polyalphabetic (this means that a number or letter can represent multiple letters).
Materials
- Pencil
- Paper
Lesson #36: Pig Pen Cipher
Overview: The Pig Pen cipher is of the most historically popular ciphers. It was used by Freemasons a century ago and also by Confederate soldiers during the Civil War. Since it’s so popular, it’s not a very good choice for top-secret messages. Lots of people know how to use this one! It starts with shapes: tic-tac-toe grids and X shapes. I really like it because coded messages look like they’re written in an entirely different language!
Materials
- Pencil
- Paper
Lesson #37: Polybius Checkerboard Cipher
Overview: Polybius was an ancient Greek who first figured out a way to substitute different two-digit numbers for each letter. In the Polybius Cipher we’ll use a 5×5 square grid with the columns and rows numbered.
Materials
- Pencil
| A | B | C | D | E |
| F | G | H | I | J |
| K | L | M | N | O |
| P | Q | R | S | T |
| U | V | W | X | Y/Z |
- Paper
Lesson #38: Cracking Ciphers
Overview: Cryptograms are solved by making good guesses and testing them to see if the results make sense. Through a process of trial and error, you can usually figure out the answer. Knowing some facts about the English language can help you to solve a simple substitution cipher. For example, did you know that an E is the most commonly-used letter in the English alphabet? It’s also the most commonly-used letter to end a word.
Materials
- Pencil
- Paper
Lesson #39: Playfair Cipher
Overview: This is a type of cipher that is very difficult to break because no specific letter or number represents any specific letter. The Playfair Cipher uses a matrix of numbers and letters to develop the key.
Materials
- Pencil
- Paper
Lesson #40: Telephone Cipher
Overview: This is a cipher that is written using the telephone keypad. It’s pretty simple to use once you understand the basics of how to make it work for the entire alphabet. (Have you ever noticed that the Q and Z are missing from the keypad?)
Materials
- Pencil
- Paper
- Access to a telephone keypad, or use ours below
Lesson #41: Scytale
Overview: In this lesson, I’ll show you how to use a actual cipher machine called a scytale. This was first used in ancient Greek and Roman times, most notably by the Spartans. To make a scytale, use a cylinder with a piece of paper wrapped around it. Then simply print your message in rows that run along the length of the cylinder. When the paper is unwrapped, the message is scrambled!
Materials
- Marker pen
- Paper strip (Make your own by cutting your paper into 1” strips and taping them together end-to-end.)
- Cylindrical object, like a toilet paper tube or paper towel tube
Lesson #42: Secret Phonetic Codes
Overview: If only you could keep better track of big numbers, adding and multiplying your head wouldn’t be such a problem! But fear not… I have a trick that might be just the ticket for your brain!
Use this secret phonetic math code to code and decode sentences into numbers. Developed over a hundred years ago, this is the code that the expert mathematicians use when doing large calculations in their head. This is exactly how Dr. Arthur Benjamin from Harvey Mudd University squares 5-digit numbers in his head, without a calculator!
Materials
- Pencil
- Paper
Lesson #43: Factorials!
Overview: If I said “3!” would you think the 3 is really excited, or that you have to shout the number? In fact, it’s a mathematical operation called factorials, and boy, are they fun! They may seem complicated at first, but they’re really a very basic concept. The exclamation point behind a number means that you multiply that number by each successively lower number, in order, until you get to 1. So “3!” would be equal to 3 x 2 x 1 = 6. Materials
- Pencil
- Paper
Lesson #44: Probability
Overview: In math, probability is how likely it is that something will occur (or not). Probability is expressed in a range from 0 to 1. A probability of zero means that a thing will definitely not happen – it’s impossible. But a probability of one means that it definitely will happen – it’s certain. Any number larger than 0, but smaller than 1, means that a thing might happen. The number 1/2, or one half, is right in the middle and it means there is a 50/50 chance. Do you think there’s a greater chance for a person to get struck by lightning, or to be hit by a meteorite?
Materials
- Pencil
- Paper
Lesson #45: Three Doors
Overview: Ever dream about winning big on a game show? Would it surprise you to learn that there’s math behind it all? Probably not, since you’ve made it this far through this book. Here’s the deal: This lesson in probability teaches how to increase our chances of winning in a game.
Materials
- Pencil
- Paper
Want More Science Activities?
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Thank You!
Thanks for the privilege as serving as your coach and guide in your science journey. May these videos bring you much excitement and curiosity in your learning adventure!
~Aurora
Supercharged Science
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