Saturday, November 11, 2006



Loni a homeschooling mom of nine kids is going down a treacherous path.

We bought some cheap multiplication math books, and I taped a sheet of paper at the front of each, with tricks, poems, and cartoons of ways to get them to remember these!

I found most of these at Multiplication.Com. One of my favorites is learning the 9's table:

The NINE multiplication fastest is the one less = nine method
Subtract one from the number you are multiplying by. 9 x 5 (One less than 5 is 4)
The first number in the answer is 4. The two numbers that make up the answer will equal 9. So 4 + __ = 9 (5)
The last number in the answer is 5

9 x 5 = 45
One less than 5 is 4 (45)
The answer adds up to nine. 4 + 5 =9
Tricks like this frustrate me to no end. The intentions are well meaning, but the results can be horrible.

My 6th grader was able to get through 3rd grade by using multiplication table tricks like this, but the problem is that she relied to much on them. Multiplication tables should be learned to mastery, and here is why:

Multi-digit multiplication: When performing problems such as 456 x 35, knowing your multiplication facts to mastery reduces your reliance on working memory, which in turn allows you to use your working memory to perform the carrying and adding functions in the standard algorithms. The more things you have to juggle in your working memory, the more likely you are to forget a step and end up with a mistake in a several step problem.

Division: Not only should you know that 6 x 7 = 42, but if given the number 42, you should be able to recall that its the same as "6 x 7". Unfortunately the 9's trick that is used above doesn't work backwards. If given the problem 54 divided by 9, you can not easily reverse the procedure. The problem becomes even worse if you have a problem like 56 divided by 9.

Factoring: Factoring is a key component to algebra. Factoring relies on being able to quickly recognizing multiplication facts and breaking the number down into smaller products. Once again the tricks do no work backwards.

If Loni really wants to help her kids then she will skip the shortcuts and drill her kids over and over till they can spit the facts out like they can their names.

At our house, we use flash cards. Every child in our house is tested on their multiplication tables at least once a day. We also practice doing reverse multiplication tables. The kids are shown the answer, and have to spit out all the multiplication facts that make up that number.

Last year our 6th grader had to get tutoring for her math. Since then I have re-taught her tables, and on her last interim report in math, she was getting a 91.

Don't be fooled people, some knowledge needs to be committed to memory, and hard work is required.

Update: Rightwingprof has corrected me and pointed out that the trick does work backwards... but a child would have to know all the multiples of 9's to know when to use it, and if they did... then they probably wouldn't need to.


rightwingprof said...

I learned my nines that way. I don't think tricks get in the way of mastery, at least not multiplication tables, because you use it so much. You may learn your nines that way, but you don't continue to rely on it.

rightwingprof said...


"If given the problem 54 divided by 9, you can not easily reverse the procedure."

Sure you can. 5+1=6.

rory said...

You may learn your nines that way, but you don't continue to rely on it.

Not true. Until recently our 6th grader used these tricks. She also uses skip counting by 2's for the 4's. Mentally counting for most of the rest.

p.s. good to see you out and about after the elections, I was worried about you.

rightwingprof said...

What's going on with all the underlining on your blog?

And as for the elections, I figure I could rant and get ulcers, or be entertained. I'm hoping Kucinich runs again so we can laugh at more Goddess of Peace speeches and crying, sincere hippie wannabe college student fans.

The glass is half full, ya know?

Anonymous said...

My son's learning multiplication as I write and he's learning tricks like this to help with the meorization process.

First he learned how to skip count by 2s, 5s, 10s.

Then they teach skip counting by 4s just requires skipping every second number when counting by 2s.

Then he leaned the nines trick.

What these tricks do is help tie in new knowledge to existing knowledge. This makes learning easier. But, the multiplication tables ultimately have to become automatic.

CrypticLife said...

I don't find anything particularly harmful in these tricks. If one can use the tricks reliably and rapidly, it becomes easier to move to other concepts while practicing. A lot of them remain as tricks, though, and it would be great to teach some of the reasoning behind why they work.
Here's an excellent page on that. I'd consider it to provide the advantages of both considerable practice with the multiplication table and a significant focus on understanding.

rory said...

Sorry about the underline thing... I made an html mistake, and as you will see in my next post, I was too busy to fix it.

I am going to stick to my guns and maintain that the tricks are on the whole bad.

Though they might help some kids learn the facts, these are probably the same kids who would learn them by osmosis.

There are kids... many kids who never progress from the tricks to mastery.