wordpress.com has a “stats” feature that allows you, among other things, to see what search terms people have used to find your blog. It turns out that most hits that I get from search engines are by people wanting to know how to memorize their multiplication tables (they find the post Multiplication Tables, which doesn’t actually give any advice on memorizing them). I’ve started to feel so guilty about this that I decided I should write a post giving tips on memorizing multiplication tables (or times tables) hoping that it would be helpful to some of those folks searching for help. Then maybe they will read some of the other posts and get hooked on math ;)
So here goes:
We start with something that sounds totally unrelated (but stick with me): James A. Michener’s Novel Texas. In that book there is a character named Miss Barlow, who is a school teacher. Michener has her: “Standing before a massive map of Texas that showed all the counties in outline only, she said softly ‘Your Texas has two-hundred and fifty four counties.'” Miss Barlow goes on to challenge the students to be able to name, from memory, every county when pointed out on the map. One big obstacle to achieving this feat (besides the shear immensity of the number of counties) is that many of the counties in West Texas and the Panhandle are nearly-identical little rectangles. But never fear! This teacher has a method to cut this memorization down to size. First you select any five counties that you wish. The only criterion for the selection of your counties that must be met is that each must be in a different region of Texas. In other words, you can’t group them all together. You have to pick counties scattered around Texas. Once you have those five counties nailed down and committed to memory you “could build upon them the relationships required in Texas history,” and continue to learn the names of the surrounding counties, until you have all 254 memorized.
Now let’s look at the multiplication table and see what it is like. Here it is, the 0 – 12 multiplication table in all its glory:
The only thing that I’ve left off are the numbers! But don’t worry about those! We’ll get to them soon enough. (By the way, why do we ever ask kids to memorize the 0 – 12 multiplication table? We use a base ten system. Memorizing 0 – 9 should be perfectly sufficient). And here is Texas:
Almost eerie how similar they are isn’t it? Look at all of those identical little squares in the multiplication table and those counties stacked one on top of another in Texas. Let’s try to approach the multiplication table from Miss Barlow’s view point. Actually the multiplication table is much easier than the map of Texas. Texas has 254 counties, but our multiplication table has entries to remember.
Here’s how I remember them.
Also, let’s face the fact that there are some really easy ones: The zero-times-blank-row and the blank-times-zero-column are a piece of cake, so is the one-times-blank-row and blank-times-one-column, and let’s face the fact that the ten-times-blank-row and blank-times-ten-column are just as easy. So already we have knocked out a big chunk of the table:
Of course everyone knows that 3 times 7 is the same thing as 7 times 3. We can get rid of almost half of our squares:
Looking more like Texas all the time. Now 5’s are easy, at least if you are multiplying by an even number, just chop it in half and throw on a zero. There’s also a handy trick for 9’s. For instance 9 times 7 is 63. The 6 is one less than 7 and the 3 is 9-6. It works with all of the single digit numbers, for instance 9 times 3 is 27.
Multiplying a single digit number by 11 is also easy, just write it twice, for instance 8 times 11 is 88. Now maybe it’s not exactly easy, but I think that everybody should be able to memorize the double of every number from 2 to 12:
Once you know those, it is pretty easy to multiply 12 by any number less than 5. Just write the number and then its double:
We don’t have much left to memorize! Finally, I think that it is worth while to memorize all of the squares. Here are the ones that we haven’t dealt with so far:
But maybe you don’t want to do that much work. So how about you just memorize and . Then if you memorize one more fact: , and look at the table, you might notice something:
Every square left blank is directly adjacent to (above, below, to the right or the left) a filled in square. Now build upon these the relationships required in arithmetic: For instance, let’s say that you want to know , well you know , so . You want to know ? Well, you know , so . Voila! Multiplication is a snap. Of course it’s going to take a lot of practice, but good luck! I hope it helps.