We’re going to use what I call “numbers crunching” to check. That is the same as using the nines-remainders. You do know how to get the nines-remainder of a number, don’t you? It’s very simple, but it takes a bit of explaining. [...]]]> To check multiplication of single digits by longer numbers with playing cards:

We’re going to use what I call “numbers crunching” to check. That is the same as using the nines-remainders. You do know how to get the nines-remainder of a number, don’t you? It’s very simple, but it takes a bit of explaining.

It also pays to know why checking with nines-remainders works. Both of those things are beyond the scope of this article, but I’m working on a booklet and a video about how to check your answers for all of the basic operations of math using “number crunching”. There are lots of tips and shortcuts that make this method absolutely simple and effective. Let me know if you’re interested by using the “Contact” box near the upper right hand corner of this page.

(This video will be re-edited and uploaded by the end of Wednesday, April 30)

If you know about crunching, you’ll be interested to know that practicing with cards like this is perfect for checking with crunching. It turns out that if you crunch all the digits from zero to nine, you get a crunch number of 0.

Since we’ll always use sets of cards to represent the digits from zero to ten, we’ll always get a crunch number of 0.

So take whatever digit you were multiplying by, you’d have to multiply it by 0 to get your final check number. As you know, anything times zero is zero, so whenever you practice with cards like this, your check number will always be zero!

So if the crunch number of your answer is anything but zero, you have made a mistake somewhere.

Starting with ten cards is pretty easy. It turns out that as long as you use complete sets of all ten digits from 0 to 10, you will always have a check number of 0, no matter how many sets you use. So you can use ace to ten of as many suits as you like (as long as you remember that the tens count as zeros, and aces as ones).

That makes sense, doesn’t it? Because if a single set of zero to nine crunches to 0, then two sets must also crunch to 0, because 0 + 0 still equals 0.

In a very few days you should be able to work yourself up to multiplying any single digit number by a full set of forty cards (four sets of ace to ten, with all suits) within a few minutes. And then another minute or so to check them.

One of the benefits of doing it like this is that you are going to have to do all the additions and subtractions to get the nines-remainder of a forty or forty-one digit number in order to check it. That’s great practice in those two operations.

This is a fantastic morning exercise for children or adults. When you do something like this before breakfast, your mind becomes much more awake than it would have been.

Watch the video, then try it.

By the way, you may have noticed that at some point in video, I say, “The number has to crunch to nine,” where you may have thought I meant to say, “zero.” But remember, in Mod 9 (nines-remaindering, or “crunching”) zero is nine.

Did you know that technically, you can use any digit-remainder to crunch with, not just the nines-remainder? Most of the shortcuts (ask me about them) don’t work with nines-remainders other than nines, though, so that’s why we use nines, mostly.

Elevens-remainders are good to use as well. They have some shortcuts, just not as many as the nines, though. If you need to be absolutely sure of your answer, it’s best to check with the nines, and the elevens. I’ll have more posts up soon about each of them, and they’ll be thoroughly covered in the booklet that will be out soon.

Remember, a little bit of knowledge can be dangerous; so when you use numbers-crunching, be aware that it is “just a trick” until you understand it more deeply.

The first set of videos will be about how to practice multiplication using playing cards. So grab a deck [...]]]> Math Mojo has got some surprises for you. New lessons on how to improve your basic math skills, and videos! Professor Homunculus is getting his Video Mojo workin’ to bring you some great new stuff.

The first set of videos will be about how to practice multiplication using playing cards. So grab a deck of cards and let’s get going!

First, take out all the Spade cards from the deck – we’ll only be using those. Then, remove the court cards (the Jacks, Queens and Kings) from those cards. Consider the Ten to be a zero and the Ace to be a one.

Now you’ve got 10 cards, which represent the digits zero through nine.

Shuffle the cards. Now decide, in your mind, which digit you’d like to multiply by.

Deal the cards, face up, on the table so that you can see the faces of all the cards.

Get out a piece of paper and a pencil.

Depending on how advanced you are at multiplication, start at either the right (if you multiply the “school” way) or the left (if you know Math Mojo) of the spread deck, and start multiplying, writing only the answer (not the carries – never write the carries!)

In the video, we’ll be multiplying all the digits from 0 to 9, by 3. It’s simple to start with 3.

After you learn how to do it, try multiplying the cards by the other digits.

We’ll multiply by some higher digits in future videos.

You may have noticed that I don’t know my left from my right in this video. My bad!

Tomorrow we’ll practice checking, using this same example.

“I need help learning multiplication. Can you help me learn to multiply?”

Professor Homunculus replied:

I have lots of questions to ask you, but first, here is something you can do right away to help you learn multiplication by 2, 3 and 4:

Get out a deck of cards. Make sure [...]]]> A girl recently asked:

“I need help learning multiplication. Can you help me learn to multiply?”

Professor Homunculus replied:

I have lots of questions to ask you, but first, here is something you can do right away to help you learn multiplication by 2, 3 and 4:

Get out a deck of cards. Make sure they are all (52) there. Now count them by twos. If you end up saying “fifty-two,” and have no cards left, you got it right.

Now try by threes. If you end up saying “Fifty-one”, and have one left over at the end, you got it right again.

Now try by fours. If you end up at “fifty-two” and have none left over, you’re right again.

Now do that over and over. Always count by twos, threes, and fours, no matter what you are counting from now on.

If you get a group of coins, like pennies, as change, count them by threes.

If you have to count the amount of kids in a class, count by threes or twos.

And so on.

Actually counting things in groups is a lot better than looking at tables, and parroting them back.

If you really want a great way to learn to multiply very fast and easily, consider getting a copy of “Numbers Juggling – Times without the Tables.”

You can find a link to it on the right-hand side of each page of these Math Mojo Chronicles.

Also, have you checked out MathMojo.com? Go there and click on the link for “speed multiplication by 11 and 12″. (It’s down the page a bit).

Then, check out:
http://www.squidoo.com/multiplication/
It will teach a cool multiplication trick, but you’ll only be able to do it if you first learn (and practice) what you learn at the “speed multiplication by 11 and 12″ link, above.

You are actually in luck. Recently a new book came out, and I have to say, it is a great book for girls to learn math from.
It’s called “Math Doesn’t Suck,” and it was written by an actress who is also (of all things) a mathematician. It’s a pretty awesome book.

Now for my questions:

How are you at addition? How are you at your other subjects in school? How are you with sports? Do you practice anything regularly (a sport, musical instrument, game?)

When you wrote the comment, were you aware of your misspellings and grammar mistakes? I’m not asking to judge you, just for info for how to help you.

Any answers to those questions will help me figure out how to help you better.

a) help you (or your child) with life in general and the education that counts, or b) just help you (or your child) pass the next math test?

If your answer was b, you just saved yourself some time and effort for [...]]]> Do you want to understand and be able to multiply in order to:

a) help you (or your child) with life in general and the education that counts, or
b) just help you (or your child) pass the next math test?

If your answer was b, you just saved yourself some time and effort for the next few minutes. You don’t have to read any further. But you’d be costing yourself (or your child) years of frustration. Passing a little (or big, standardized) test is just jumping through an artificial, meaningless, hoop. You don’t have to be a slave to the school system.

If you really need to beat the system, you need to game it. You need to learn math much, much better than they teach it to you in public schools. Then their tests will be a joke, and you will blow them away without being intimidated. But if you just want to learn enough to get through the next test, brother, you are digging your own educational grave.

It doesn’t make sense to accept their dogma, and then blame them for feeding it to you. Do something about it, now. Pick a subject you feel you’re lacking in, and then find alternative ways to supercharge yourself at it. “Ah speet on yo’ steenkin’ test from a high altitude!”

This is going to sound like heresy, but here it is – If you have a test that you don’t really have a good chance of passing because you don’t understand the material, don’t just cram and hope you’ll pass – Forget about the test, totally! Plan to fail it, but use that time to find a better way to learn. Go to the library, scour the internet, ask a friend, or check a bookstore for in formation related to the subject, and don’t stop looking and learning about it until you understand it better than anyone else in your class. Being “good enough” will never make you good enough. Make sure you can “speet on the steenkin’ test.”

Then, instead of just failing the test that you would have failed anyway, you fail the test, but actually learn the material so you will not fail any more tests on the subject, and you’ll be on your way to real knowledge.

Imagine this scenario:

Little Smike is faced with a test of basic multiplication, which his schoolmaster, Mr. Wackford Squeers, is going to give on Friday. Now, Mr. Squeers knows nothing about multiplication except for “the multiplication tables” (a posters of which he has hanging in various places on the walls of his classroom). And all he knows about how to teach or learn them is to “just shut up and memorize them!,” although he’s never even taught his class anything about methods of memorization.

Smike has tried and tried. He has shut up, he has stared at “worksheets,” he’s spent time with flash cards, and has even suffered through silly songs and rhymes, but he just doesn’t get it. Is Smike stupid, or does Smike just need a way to understand multiplication, instead of just learning how to parrot back meaningless information? Isn’t it often the smartest people who have the hardest time learning, because the methods of teaching are so insipid?

Mr. Squeers laments the fact that, though he is working so hard, his students just don’t seem to learn. What could be wrong with the little urchins? Why don’t they learn, despite his best pedagogical intentions?

Being from a family of administrators, Mr. Squeers subscribes to the time-honored platitude of, “You can lead a horse to water, but you can’t make him drink,” in order to excuse his ineffectiveness. He has certainly taught the little tykes well. Why don’t they just learn? (Perhaps he’ll have to thrash them.)

Poor Mr. Squeers. What he doesn’t realize, is that if they haven’t learned, he hasn’t taught. He can inculcate, threaten, or test them to the high heavens, but that’s not teaching. Perhaps if he made the water taste better. Perhaps if he offered the horse some milk, some lemonade?

You can make a horse drink, you just don’t always have to use water. You can teach multiplication. You just don’t need to use the times-tables.

Luckily for Smike, there is a new assistant in the class, a Mr. Nickleby. Mr. Nickelby knows an interesting

method of multiplication, which he learned from a magician while touring with a traveling stage company.

The method requires the use of basic addition and subtraction, rather than “multiplication tables.” It is counter-intuitive, but much more effective than the tables.

Unfortunately, Smike hasn’t been taught addition or subtraction adequately, because the class had to rush to “cover material” in because of the “No Child Left Unstressed” Act. But Mr. Nickleby has a plan – What if Smike spent the time between now and Friday actually learning simple addition and subtraction? That he could manage, it’s much easier than memorizing meaningless “multiplication facts” from a chart.

To make it even easier, Mr. Nickleby shows Smike a simpler way to add than is taught in most of the better schools. He uses a tool called an abax. And he teaches Smike how to subtract from left to right, instead of the old, less effective method. This builds Smike’s confidence, even though Smike hasn’t learn anything that will help him on Friday’s “multiplication facts” test.

On Friday, Mr. Squeers snickers as Smike fails the test miserably.
“Nickelby, old boy, it seems like your ‘star pupil’ is a miserable failure,” he chortles in his schadenfreude*.

“Yes, Sir. Failure there is for sure, Mr. Squeers.”

By the following Monday, though, Smike is the only child in the class that has a through understanding of basic addition and subtraction. He can perform these operations from left to right, without paper, quicker than than even Mr. Squeers can do it with pen and paper.

With that, Nickleby helps Smike parlay that knowledge into learning the basic multiplications up to ten-times-ten, in about five minutes. Smike will never forget what eight times seven is again. He will never struggle or be insecure about “multiplication facts,” whereas most of the other students had forgotten them by the weekend.

The moral of the story? Schools may suck, but education doesn’t have to.

The next few posts at the Chronicles will be about a Roadmap to Multiplication. I’ll be outlining the skills anyone would need to get a deep understanding of multiplication, and how to get those skills.

*Schadenfreude – “taking joy in the suffering and misfortunes of others.”