If you haven’t memorized your multiplication table yet, I am going to show you how to you need to memorize only three of the 400 numbers on a 20 times table in order to know your table.

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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.
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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.


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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.


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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.
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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.


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If you haven’t memorized your multiplication table yet, I am going to show you how to you need to memorize only three of the 400 numbers on a 20 times table in order to know your table.


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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.


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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.
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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?


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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).


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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.


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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.


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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.


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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.


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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!


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Have you ever heard someone refer to a “million billion” of something? Is that more or less than a “billion million?” In this video, I’ll show you how to write down these numbers and figure out which one is larger.


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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:
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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.)
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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!
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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:
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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!
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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:


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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.


Please login or register to read the rest of this content.