This is a neat logic trick which allows you to flip over a stack of cards numbered 1-10. When you flip the back upright, they are in numerical order. There is a special way to make it work, so pay close attention to the video. I’ll show you exactly how it works.
Imagine you’re in the car with the kids, excited to see your extended family (or at least, specific members of your extended family), and you’re not quite there yet.
And the kids been glued to their video games, cell phones, and electronic devices the whole time. You know it’s not good for them, but at least you have some peace during the car ride. You shrug it off, not too worried about it, thinking about all the running around with cousins they’ll do once they get there.
And then you hear…
“Are we there yet?”
“I’m bored.”
“I’m hungry.”
…and whining.
Now what do you do?
It seems impossible for kids to entertain themselves these days without the use of batteries.
That’s what spurred me to create this “Pen & Paper Games” packet that I want to share with you. It’s full of my very best on-the-go, play-anywhere games that you don’t need any equipment (other than a brain) to play! These games I’ve played with my kids over the years, even standing in lines at Disnleyland.
By the way, Bagels is still our favorite line-waiting game, because it’s so fun to play and easy to teach the on-lookers who are wondering why we keep shouting “PICO!” and “FERMI!” followed by uproarious laughter. Bagels is good for the car too, only maybe without the shouting. It’s basically a mental version of the old Mastermind game, but don’t tell them that! Just enjoy the game and have fun learning and exploring our wonderful world.
Everyone old enough to remember the Rubik’s Cube craze of the 1980s in the USA also remembers how it was near impossible to solve the thing! Originally created by a professor of architecture Erno Rubik, it was sold to a toy company in 1980 as the “Magic Cube”.
To date, over 350 million cubes have been sold worldwide, making it the world’s top selling puzzle game, and most people think of it as the best-selling toy of all time as well.
The original goal of creating this object was to help teach his students how to create something that rotated independently in layers without falling apart. Rubik didn’t realize he had created a puzzle until he scrambled it, and it took him over a month to solve it the first time!
There are eight corners and twelve edges, and when you do the math to figure out the number of possible combinations the puzzle has, it’s about 43 quintillion, or:
43,252,003,274,489,856,000
So what do you do with this thing? How DO you solve it?
It has to do with identifying the different layers, and solving one layer at a time. Here’s how you can do it:
Please login or register to read the rest of this content.
Download the official solver’s guide here. Or you can build a LEGO machine like JP Brown did to solve it for you!
There’s also a World Cube Association where folks keep track of cube competitions and records. The fastest cube solve was set by Mats Valk in 2013 – he can solve it in under 6 seconds. Some of the more creative competitions include solving the cube while blindfolded (record is 23.8 seconds), with only one hand (record is 12.6 seconds), only using the feet (record is 27.93 seconds), and underwater using a single breath.
Kaleidocycles are a three-dimensional paper sculpture you can turn around and round! Flexagons were first created by Arthur Stone at Princeton University in 1939, which were later published in 1959 to the general public in Scientific American.
These are simple to make and fun to play with. When I first showed them to my own kids, they immediately made one for each kid in their class, and also stumped the teacher that day when they asked how it worked. Please login or register to read the rest of this content.
The video below is made by Vi Hart, a smart and spunky mathemusician who has made amazing videos about the history of hexaflexagons that are fast-paced and fun.
[/am4show]
This is a really neat game invented in 1967 by two mathematicians that was soon after published in Scientific American, where it caught fire with people all over the world. It’s a very simple game with a lot of interesting mathematics in it, and all you need are two people, a pencil, and paper.
Having trouble with your 6, 7, 8, and 9 multiplication tables? Sneak a peek at this nifty trick for multiplying single digits together. All you need is a set of hands and about ten minutes, and you’ll be a whiz and multiplying with your hands.
Please login or register to read the rest of this content.
One day, my kid asked me how a calculator comes up with its answers. That’s a great question, I thought. How does a calculator do math?
After thinking about it, I realized this was a great way to teach him about binary numbers. I am going to show you how to not only count in binary, but also help you understand the basis of all electronic devices by knowing this key element.
If you hate long division like I do, then this lesson will be very useful in showing you how to make the most out of your division tasks without losing sleep over it. It’s easy, quick, and a whole lot of fun! If you haven’t already mastered your multiplication tables, make sure you have one handy to refer to as you go along.
If you don’t have the patience to do multiplication on paper for every single math problem that comes your way, then you’ll really enjoy this math lesson! You’ll be able to multiply one and two digit numbers in your head, which you’ll be able to use when checking your answers on a math test, or just whenever you need to multiply something quickly when paper’s not around.
Please login or register to read the rest of this content.
In school, you are trained to solve math problems on paper, at a desk. The problem with that is, for most people, math problems don’t usually come with a desk or a pencil. They pop up in the checkout line when paying for groceries, figuring out your gas mileage at the pump, or when counting calories at a restaurant. Learning how to solve math problems in your head is an essential everyday life skill, especially if you don’t want to be ripped off in money transactions.
This math lesson 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.
Numbers that are not fractions or decimals, are called integers. Numbers like: 2 and 144 and 299,792,458 (that’s the speed of light in meters per second) are all integers!
Integers can be positive or negative. If the number is greater than zero, like 4, 16, 25… then it’s a positive integer. Negative integers are -15, -42, -1 million.
It’s important to know how to handle both positive and negative integers because they come up all the time in algebra. You probably already have experience in working with positive and negative decimals and fractions, so now let’s do a quick review so you can make sure you’ve mastered the basics.
Please login or register to read the rest of this content.
What is math? It can be compared to a very useful tool, or maybe a collection of tools. Sometimes textbooks concentrate a lot on teaching about the small details of each and every type of tool. But it’s also really important to focus on how and when to use the different tools. This is my practical approach to teaching the subject. And it’s also important to note that math is much more than just numbers! If you’re really good with shapes and how they relate, you might enjoy geometry. And if you are good at solving puzzles, chances are that logic will be a great match for your skills.
NOTE: Be sure to pause the video when the timer reaches 6:30 to work on the Earn, Break Even, or Lose problem.
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 does 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-ten system, so this whole thing worked out well. But still the number 12 persists! So I thought you’d like this video, which expands on the idea of quickly multiplying two-digit numbers and three-digit numbers by eleven. This is very similar to the shortcut used when multiplying by eleven, but it also involves some doubling. Are you ready?
Can you look at a number and tell right away if it’s divisible by another number? Well, it’s pretty easy for 2 – if it’s an even number, it’s definitely divisible by two. Testing whether a number is divisible by five is easy as well. How can you tell?
In this video, I’ll show you some tricks to determine if a number is divisible by 3, 4, 6 and 7 before you start to divide. Some are simple and fast and some are a bit more complex. These can be very useful tricks for working with larger numbers (or just really fun to play with for a bit).
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 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. Watch the video and I’ll teach you exactly how it works.
This is a really fun riddle! It’s a math logic puzzle involving the calendar that will really blow your mind. Pay close attention to the clues I give in the video and see if you can work out how it works. Pause the video at about the 1:30 mark if you would like to try and work out the answer before I show you how it works!
This is a neat logic trick which allows you to flip over a stack of cards numbered 1-10. When you flip the back upright, they are in numerical order. There is a special way to make it work, so pay close attention to the video. I’ll show you exactly how it works.
Magic squares have been traced through history as known to Chinese mathematicians, Arab mathematicians, India and Egypt cultures. The first magic squares 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 by wearing magic squares, it 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). In this video, I show you the first Magic Square published in Europe way back in 1514. Plus, I show you how to make your very own Magic Square. You can use it to test your friends.
If you’ve watched my “What Is Math?” video, you’ve seen a sample of the Bagels math logic game. 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. In this video, I’ll show you in more detail how it works. I’ll also 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.
If a friend had chose a three-letter word and asked you to guess it, how would you start? It seems like it might take a while to narrow it down, right? This is a neat word guessing game that uses some strategy to make the guessing both a little easier and more fun. When you try to guess your partner’s three-letter word, they can simply give you one of two clues that will make it a bit easier to narrow down the answer. Watch the video for an explanation.
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? In this video, 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 over 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!
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, 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.
In this video, I’ll show you how to use the Rail Fence Cipher. Before you start, say this three times fast: cryptanalysts use cryptanalysis to crack ciphers!
In this video, I demonstrate a Twisted Path Cipher. It 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. Watch the video to learn exactly how it works.
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. Watch the video to see why it’s important to double check your work!
The Date Shift cipher is a much harder code to break than, for example, the more simple Shift cipher. This is because the shift number varies from letter to letter, and also because it’s polyalphabetic (this means that a single number can represent multiple letters). I’ll explain it all in the video.
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 an entirely different language! Watch the video to learn how it works.
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. Take a look at the video and I’ll show you how it works.
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. Watch the video below to learn some more tips and tricks to get you on the right track to being an expert cryptogram solver!
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. Are you completely confused? That’s okay! Just watch the video and I’ll show you how it all works.
This is a neat trick that you can use to really puzzle your friends and family. If someone gives you a three-digit number, you can actually figure out what the end result will be after you’ve received two additional numbers, but before you actually know what those numbers are. Does this sound confusing? Watch the video and I’ll show you how it works.
This is a super hard cipher to break. It’s encoded by taking pairs of letters and numbers from a matrix. There are three rules to follow.
Play Fair sounds really complicated, but that also makes it a tough code to crack! Watch the video and I’ll explain it all for you.
This is an alternate method of secret writing that’s completely different from encoding and decoding message ciphers. It involves using special inks that are invisible until something is done to make them appear on the paper. There are hundreds of formulas to make these special inks and some formulas even have multiple ways to develop the ink. Some recipes involve special chemicals, but many invisible inks can be made using materials that you have in your home. Watch the video and I’ll share a few recipes and teach you more about this method.
In this video 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! Watch the video and I’ll show you the trick to proper message decoding.
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? In this video, 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!
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 one.
So 3! would be 3 x 2 x 1 = 6.
Take a look at the video for an explanation of how factorials work and how they can be used.
Once in awhile, mathematicians come up against something that really seems impossible on the surface. These seemingly “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.
In math, probability is how likely it is that something will occur (or not). Probability is expressed from 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?
Imagine that you are on a game show with a chance to win a car. There are three doors and the car is behind one of them. You just have to choose the correct door! You can use probability to get an possible advantage in choosing the correct door. Watch the video, and I will explain how it works.
If you’ve ever wanted to sneak a peek into my cabinet of educational games and books for kids, now is your chance. Use this list for gift ideas, boredom busters, and just plain family fun. Some of these games you can pick up at the store, and the rest are the home-made, print-it-out, cut-and-play variety that your kids will really learn from.
I first made this list because I felt that so many games are watered-down versions of either bingo or “roll the dice and see where you land”, with the occasional card pick. I was curious to see if there were any truly great educational games still available, or if they were all just brain candy.
My games listed here are designed to develop strategy, critical thinking, and chaotic surprise in addition to having the kids learn practical knowledge along the way (not trivial fluff). And when a kid memorizes the card deck, it works in their favor because now they know the entire periodic table.
Here you’ll find games including arithmetic, fractals, equations, chemistry, physics, and more. If you have any you’d like to add to the pile, just submit it in the comments section so everyone can benefit. Are you ready?
Note: This list is growing so please check back for updates!
A lot of science supplies can be purchased online these days, especially the hard to find stuff. However, if you’re in the market for oddball items from a company that reuses industrial overruns, here it is:
Math GamesHere’s the video of the Element Song:
Here’s the video of the Nano Song:
Note: You can find more songs at the Harvard Physics Song site, but be sure to preview them before sharing them with your kids as they are more appropriate for college-level students!
What Pi Sounds Like by Michael Blake (see video below):
Most resources that public school advisers suggest for gifted or bright kids are a ‘mile wide and an inch deep’ – they don’t really go into depth on any one area. After traveling to dozens of home school conventions for several years across the country and seeing what math options are out there, I searched for more options than what’s traditionally on the exhibit floor.
After talking with math professors from Harvey Mudd, Stanford, Princeton, UCLA, and others, I thought you might like to know about their recommendations for resources that might be useful to you on how to deliver math skills in a way that really lasts.
For kids just starting out with Math: Dr. Wright’s Kitchen Table Math
For kids not quite ready for Algebra: Singapore Math Series
For kids Algebra through Calculus: Art of Problem Solving
These two work well together, and lead right into each other. If you’re looking for a DVD series, then you’ll want to get Arthur Benjamin’s 24-lecture ‘Joy of Mathematics’ DVDs.
These resources are for kids that are really into math and enjoy diving deep:
Want a peek under the ‘hood’ of my brain when I do a mental math calculation? This video is 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 add from LEFT to RIGHT, which is opposite from most math classes out there. I’ll show you how to do this – it’s easy, and essential to working bigger numbers in your head.
Here’s what you do:
Please login or register to read the rest of this content.
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 2nd 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.)
Please login or register to read the rest of this content.
Here’s our first MATH 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 and let 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.
If you really want to go crazy, you can have math races against the calculator and its operator, just as the Arthur Benjamin video shows. (Only you don’t need to do the squaring of five-digit numbers in your head!) Have fun!
Please login or register to read the rest of this content.
If you can multiply 11 by any 2-digit number, then you can easily do any three digit number. There’s just an extra step, and make sure you always start adding near the ones so you can see where to carry the extra if needed.
Please login or register to read the rest of this content.
We’re going to throw in a few math lessons here and there, so if math really isn’t your thing, free free to just watch the videos and see what you think. All of these lessons require only a brain, and once in awhile paper and pencil, so this area is ‘materials-free’ and jam-packed with great mathematical content. If you’re the parent, stick a calculator in your pocket and test out your kids as they go along.
Some of what we cover here is based on the book “Secrets of Mental Math” by Arthur Benjamin, an incredible professor at Harvey Mudd College. He’s also known as the “Lightning Human Calculator”. Here’s a video about him you may enjoy:
Please login or register to read the rest of this content.
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.
Slightly confused? Great – we made a video that outlines each step. There’s a definite pattern and flow to it. With practice, you will be able to do this one in your head within a very short time. Have fun!
Please login or register to read the rest of this content.
If you really want to baffle Aunt Edna next time she visits, then these tips are for you. As a kid, I was never very good at Scrabble, mostly because I played with adults and my word range simply wasn’t as large… so it was highly unfair.
Here’s a way to tip the scales if you feel like you’re in the same boat as I was. The words below can score you big points, both on the board (if you use the triple boxes) and also in the eyes of your family!
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-digits. 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.
The video below has two parts:
One day, my kid asked me how a calculator comes up with its answers. That’s a great question, I thought. How does a calculator do math?
After thinking about it, I realized this was a great way to teach him about binary numbers. I am going to show you how to not only count in binary, but also help you understand the basis of all electronic devices by knowing this key element.
Cryptarithms are a puzzle where the digits are replaced by letters or symbols. When the numbers are replaced by letters of the alphabet and it spells something readable, it’s called Alphametics.