Using advanced thinking methods to "trick out" ways to learn math.
Arthur C. Clarke once wrote, "Any sufficiently advanced technology is indistinguishable from magic." And that is how I view the Idea of magic. It is a sufficiently advanced method of doing something which is not comprehended by the masses. Or, as I like to say, "That which can't, and does."
Math Mojo's goal is to help people who have not mastered the boring, drudgery way of school math, by introducing them to the "magical" ways of advanced thinking. It happens to be easier than the drudgework, and it is certainly more fun.
So we won't be learning how to make other people look foolish, we'll be learning how to make ourselves actually smarter. Now that's magic!
What about those boring tricks?
Well, we can use them to teach some concepts. Just don't try to entertain anyone with them.
"Think of a number between 1 and 100, and don't tell me what it is.
"Now take your age, multiply by it by 2, add 5, multiply by 50, and subtract 365.
"Next, take that number add your secret number, (the one you thought of from 1 to 100) then add 115 to the total."
"The first half of the final number is your age, and the other part of the number is your secret number!"
Wow, isn't math boring! But it is easy to figure out.
Breaking it into steps:
Let's call your age "x".
x*2 = 2x
That's simple enough; it means double your age
(2x + 5) * 50
This is the first part of what makes it a puzzle.
(2x + 5) * 50 could be simplified to 100 x+250.
What you have actually done here is multiply your age by 100 and add 250.
To that, you are doing the rest of the equation. Which looks like this:
-365 + secret number + 115
When you subtract 365, add your secret number, then add 115, you are really simply subtracting 250 and adding your secret number, (because of the commutative law of addition)
As an example, let's say your secret number is be 47, so -365 + 47 + 115, which can be commuted to -365 + 115 + 47, which simply means -250 + 47.
So if you do the two parts of the equation together, you have
100 x + 250 - 250 + secret number.
I'm sure you can see how this simplifies to 100 x + secret number.
From there, you can understand that you are basically taking your age, putting two zeros at the end (which is the same as multiplying it by 100), and adding the secret number to that. Since the secret number is between 1 and 100, it will never have more than two digits. Adding a one or two-digit number to a number that ends with two zeros is the same as just taking the first number and sticking the second number behind it.
Simply put, the "magician" is saying, "Take your age and stick some number behind it. Now tell me what it is, and I'll tell you what you told me." Spooooky!
The reason that it seems puzzling is because the method artificially complicates the equation. This is a very primitive use of what magicians call "misdirection."
Read on ...
Numbers Juggling (Times without the Tables)
Think outside the "Tables"
I wrote this e-book because I was disgusted with the way we are normally taught how to multiply. This booklet will open your eyes to a new world. You will learn a method to teach any child basic multiplication of single-digit numbers (what we normally call "the times tables" or "multiplication facts") in about two minutes.
The booklet then goes on to show how to "lock this knowledge in."
It also comes with seven e-mail lessons that will show you the math behind the method, so you can actually understand and show your child why it works!
And here's the big news: I've just added over a dozen videos to help you super-charge your learning and practicing. They are easy to follow and fun. I "hold your hand" as you practice, until you can do over thirty multiplications in a minute.
I truly believe that every parent and teacher should know what is taught in this booklet, so every child can have a meaningful, helpful method for dealing with this important subject.
You can order "Numbers Juggling - (Times without the Tables)" here.
Math Magic Links
Please don't add a bunch of cheesy "tricks." Feel free to add quality math sites that try to raise our standards. Remember - "GIGO!"
Math Mojo Homepage
Learn easy and fun ways do math without stress. Ma more...1 point
Math worksheets
Children can learn common maths problems just by s more...1 point
http://mathmojo.com/chronicles
The official weblog of MathMojo.com. Critical thin more...0 points
http://squidoo.com/multiplication
One of my other squidoo pages0 points
http://learn2multiply.com
An amazing method to learn the "tables", more...0 points
Educational Games
What do kids do best? Play of course. Why not enco more...0 points
Boring "Tricks" Part II
The last words on boredom. After this, we do some real magic!
Dai Vernon (affectionately known among magicians as "The Professor") was arguably the greatest sleight-of-hand magician of the twentieth century. He was also possibly the greatest magic theorist of that century. One of his favorite sayings was, "Confusion is not magic."
Puzzles like this simply confuse people, which frustrates them. They are not amused, they are generally bored and annoyed. You may be amused, but you won't entertain anyone with this stuff. You won't fool too many people with it, either. Everyone suspects the trick works on the above principles, but they just don't know the exact equation. Not because they couldn't figure it out if they wanted to, but because they don't think it's really worth figuring it out.
Trying to entertain someone with a "trick" like this is like trying to be the "life of the party" by playing "Blowin' in the Wind" on your guitar.
I was going to say, "Leave the math tricks to the professional magicians," but it is a rare magician indeed who can make them interesting. And the ones who can are doing much more advanced things than the silly puzzle above.
Magic performance requires skills way beyond "knowing the secrets."
Real magic, on the other hand (not the show kind) is what you use to improve yourself and the world. It is a method ("sufficiently advanced") that you can use to teach, learn and accomplish meaningful things.
Is there ANY value to those boring tricks?
Yes! (But not as "tricks.")
Figuring them out as puzzles is a fine recreational and pedagogical passtime. It's fun to figure out how things work. That's what separates them from good performance magic. With a good performance, the audience is enchanted. That is different from simply being fooled.
But if you waded through the above "trick" and explanation, you may have actually been interested in the ways the math worked. That is wonderful thing in itself. There are plenty of sites with simple number tricks on them, and I'm sure you can find them if you need to impress yourself or small children. (OK, I know I'm being snide, there. I'm kidding though, I know these things are fun to investigate.)
Now that we are finished with "number tricks," let's learn some real math with magical methods. That's better than hokey magic with mathematical methods.
Speed Multiplication by 11 (and 12)
The first "trick"
- Speed Multiplication by 11 (and 12)
- Even if you don't know the "tables," you'll be able to multiply HUGE whole numbers, like 459,287, 563 x 11 in your head, without pencil and paper, and before the "wiseguys" can even get their calculators out of their bags.
Any second-grader and most first-graders will be able to learn this method in a couple of minutes. Although it's not a "kiddie" trick.
If you're not familiar with this trick, you are going to be massively surprised at how cool it is.
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Great Math Books for Every Home
Personal Recommendations from Professor Homunculus
The Number Devil: A Mathematical Adventure
From the amazon.com review: "...introduce basic concepts of numeracy, from interesting number sequences to exponents to matrices. Author Hans Magnus Enzensberger's dry humor and sense of wonder will keep you and your kids entranced while you learn (shhh!) mathematical principles."
Professor Homunculus sez: "If you are helping a child learn math, this book is a MUST!"
Amazon Price: $12.92 (as of 11/11/2009) 
Playing with Infinity: Mathematical Explorations and Excursions
From the a reader's review on amazon.com: "This book explains the why's behind math from principles as basic as counting to as complicated as series, geometry, and even some calculus principles. It is written in a conversational tone with lots of pictures (yes, and numbers). Each chapter builds upon the last, and it is easy to follow (though sometimes dense). It was my first "fun" math book and is still by far my favorite."
Professor Homunculus sez: "I couldn't agree more!"
Amazon Price: (as of 11/11/2009)
Mathematics for the Million: How to Master the Magic of Numbers
This book is a classic. It was the book that launched the intellectual self-improvement movement in America. It is perhaps the best book on general math ever written. Hogben takes you from the birth of mathematics to calculus in a lucid, human way. Even if you use only this one book, you will not only understand everything you will need for all of high-school math, and most of college math, but you also have a good basis for understanding the spirit of mathematics. H.G. Wells called it, "A great book, a book of first-class importance."
Amazon Price: $12.89 (as of 11/11/2009)
What interests you?
Reader Feedback
bilbo959 wrote...
I checked out some of your other math lenses for my daughter, and I can't wait to show her this one.
Posted May 13, 2009
ag wrote
I am a GED teacher and am always looking for creative ways to teach. This website is very interesting and I will be ordering your booklet.
Posted May 13, 2009
chetbyles88 wrote...
I bought your "Times without the Tables" booklet for my students. So far it has had a great "hit rate" of helping kids who otherwise never "got" the tables. Thank you for your work.
Posted May 04, 2009
jorge wrote
hey, great stuff, it will help a lot to me to finish my thesis. thanks.....
Posted January 15, 2009
MrMarmalade wrote...
I like this lens it has shown me a lot that has always puzzled me. Thank you Top Five stars and Fav u
Posted December 22, 2008
Hi,
This a very good lens,Iam a great fan of math-magic.These ways can be used to teach kids the math-magic.Thanks for your info.
Your feed back to my thelocalmagician blog would be appreciated.
Posted September 05, 2008
Cyndy wrote
this site is neat! it makes math fun and approachable! and as a newly hatched math fan (hated it at school, but now i am learning for fun - who knew?!) i found it fun and interesting!
Posted June 28, 2008
MarkZagnut wrote...
Excellent. I am a magician, so I like how you differentiate "magic" from "tricks." If people would realize this difference, and appreciate it, they'd understand a lot more about the nature of reality. I know that sounds absurd, but it's true.
Posted May 31, 2008
sidvicious2008 wrote...
Valuable info. You don't see stuff like this anywhere else. I like your style.
Posted May 29, 2008
Max_Nix wrote...
Thoughtful stuff. I hope people understand the deeper meaning behind it. I like recreational math, as well. Big Martin Gardner fan.
Nice work!
Posted April 16, 2008
Evelyn_Saenz wrote...
What a great lens! I have added it to my favorites and joined your fan club.
Playing games is a great way to practice and learn math. Using a Hands-On Approach to learning is the best way for children to truly grasp mathematical concepts. I look forward to reading more of your lenses.
Posted March 24, 2008
SteveRogers wrote...
I like your ideas very much. They make more sense than normal math teachers. I wish math teachers would learn something from this.
Best of luck!
Steve
Posted February 04, 2008
Sue in MA wrote
Thanks! I'm a 5th grade teacher who wants to interest students in math. Magic is a great way to do it! I'm booking your site on favorites!!!
Posted January 30, 2008
Vaughn wrote
Good idea!!! Moe kids should log on!!!
Posted January 30, 2008
by Homunculus
My name is Brian Foley (a.k.a. "Professor Homunculus" at the mathmojo.com site).
I am not a "math guy" and never was. I don't care about the sch... (more)
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