How to Remember Multiplication Tables

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 13\times13=169 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:

2\times2=4, 2\times3=6, 2\times4=8, 2\times5=10, 2\times6=12,

2\times7=14, 2\times8=16, 2\times9=18, 2\times10=20, 2\times11=22,

2\times12=24.

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:

3\times12=36 and 4\times12=48

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:

3\times3=9, 4\times4=16, 5\times5=25, 6\times6=36, 7\times7=49,

8\times8=64, 11\times11=121, 12\times12=144

But maybe you don’t want to do that much work. So how about you just memorize 7\times7=49 and 12\times12=144. Then if you memorize one more fact: 4\times 7=28, 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 8\times7, well you know 7\times7=49, so 8\times7=7\times7+7=49+7=56. You want to know 4\times4? Well, you know 4\times5=20, so 4\times 4=4\times5-4=16. Voila! Multiplication is a snap. Of course it’s going to take a lot of practice, but good luck! I hope it helps.

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21 Responses to How to Remember Multiplication Tables

  1. john says:

    Do you know how complicated you made that sound?.I read it over 9 times & i still did not understand.I’m going to another site.

  2. William Stewart says:

    Hi,

    13*13 = 169 not 139!

  3. Collette says:

    it made sense to me, but i need something thats going to make sense to my 9 year old. but thanks any how. sure makes it a bit easier for myself

  4. Dalena says:

    I’m 12 and i understand what your saying but i dont get the 12 timetables and maybe you could help out with my 4, 7and 8 timetables.

    Either way, the 9 time tables was really clever! :D

  5. me says:

    so, im 12, and this is very understanding to me, i have a little bit more than a day to remember my 4, 6, 7 and 8 tables. (i already know the rest.) it would be nice if you said something that would get me learning a little quicker?

  6. NO NAME says:

    Thanks for this info. Really good to finally find a good website!

  7. Math-Aids.Com is a free resource for teachers and parents. You can make an unlimited number of printable math worksheets for children, the classroom or homework practice. The answer key is included with each math worksheet as it is created. The worksheets are randomly generated so when you request one it will be different every time. Each math topic has several different types of math problems so you may choose which area to focus on in that subject.

    I have built a special section just for Multiplication Math Topics.
    These topics include Times Tables, Single and Multiple Digit Multiplication, Missing Factor, Decimal and Negative Number Multiplication Worksheets.

    I will be glad to add any topic that you may need.

    Here is the link:

    Multiplication Worksheets

    Please consider adding a link on your site for you and your readers.

    Thank you very much.

  8. UYUURURY says:

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  9. ahmad salame says:

    it was so bad that it made me throw up

  10. Inga says:

    Wow, people are so brutal. I am a tutor, and I appreciate yours and others’ efforts to make the multiplication facts more accessible to learners. I think people have too high of expectations, wanting to put no effort at all and just by osmosis get these facts in their heads. I made a finger method for multiplying by 3′s, but just like you, I received so much criticism that I decided to not publish more videos explaining other times tables. You can’t learn these facts overnight, but by using yours and other methods and working on a few concepts at a time, I know these facts can stick. Thanks for your effort and help!

    • toomai says:

      Thanks for your positive comment! This is (still!) the post that gets the most traffic on my blog, so it’s nice to hear something positive about it!

  11. Pip carey says:

    Wow! now that’s a new way to look at it, not sure how many times tables we’ve learnt but sure did get us interested in them!

  12. Dave says:

    In any case children have to memorize the times table. I and my friends who are adult just know the facts, nobody remember so sophisticated rules. May be it is better to memorize the multiplication tables instead of rules? And what about division – with those rules kids can’t divide fast.

    For my students I use this resource. It helps just memorize.

    http://mathskillbuilder.org/memorize_multiplication_table.html

    It works great. I like it.

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