Question

Dear Mitch,

When I heard you were finally going to make public a few of the answers you give to the questions people send you, I could not believe it, I really couldn't, but now I've seen it for myself. QUESTION: I know you believe that it is almost always better to understand something than have it memorized without understanding, and I agree. But my granddaughter just started a new school, and for some reason she says she's about the only one in the class who doesn't know her times tables. Any tricks just to get a few stuck in her head so she's not self-conscious until she does really learn multiplication?

-- Rosemary M.

Answer

Rose! Oh Rose! Don't be such a worrier; your little girl will be fine. BUT YES, I do have a few ideas:

Going through the whole giant multiplication chart that everyone seems to have up on their wall after third or fourth grade, the first thing you notice is that certain parts are easier than other parts. So, if you made a chart like that, and you wanted her to do some easy ones, why not start with the line of zeros up and down. Then the ones. Then the twos, I bet she can count by twos... Skip the threes for now. Skip the fours, just for now. Fives. If you hum to her just a little bit of the tune that little girls with jump ropes and pigtails chant as they do their jump-roping, that famous 5, 10,15,20,25, 30... You'd be surprised to see that most children have heard the tune so many times and for so long and that they don't even know that they know that they sort-of-kind-of know it, and which I'm sure you'll know completely again by the time you go to sleep tonight. Sing: 5,10,15,20,25,30,35,40,45,50,55,60.....

That brings us to the sixes, skip 'em, we'll come back to them.

Do the tens, I bet she can almost do the tens....

And the elevens are very easy, and kids forget that sometimes, but talk about a pattern!

Now go back to the nines. They're probably the most famous for only being easy AFTER someone teaches you the 9's trick that works like magic... On the child's fingers....

nd here's how you do it:

The 9's

Place both of your hands out in front of you with the palms facing you and all ten fingers fully extended vertically (as though you were checking your hands to make sure you've gotten them clean after washing off paint). To make sure you are holding your hands correctly, you should check to make sure that the first finger in the row of ten and the last finger in the row of ten are both thumbs, with the thumb of YOUR left hand on YOUR left and the thumb of YOUR right hand on YOUR right.

Now, starting on your left, count out on your fingers the number that you are trying to multiply by nine. For example, if you were asked what **nine times four** equals, you count aloud from your *left *to your *right* (the same way you go from left to right when you're reading a book: one, two, three, *four*). And STOP counting on your fourth finger.

Then, bend that fourth finger down as much as you can while keeping all your *other* fingers stretched out as much as you can. (With some fingers it sometimes takes a little practice, but *any*one can get the hang of it enough to get the right answer!)

Okay, so now you take a careful look at your hands, and you will notice that some of your stretched out fingers are on one side of the gap made by the curled down finger, and some of your stretched fingers are on the other side of the curled down finger. In this case, when you did nine times four and curled down your fourth finger, you should have three fingers extended on the LEFT side of that curled gap and six extended fingers on the RIGHT side of that curled gap.

Which looks like this:

Try another: 9 x 8

You start with all your fingers standing straight up, and count out eight, going from left to right like you read, and using one finger for each count until you get to the eighth finger. Furl that one down until you have a gap or space there. Then notice on the left side of that gap you have **seven** fingers standing up, and on the right side you have **two** fingers standing out and up and tall. (Always remember that for this to work you have to think of your thumbs as just two of your ten fingers and nothing different from that).

Which is 7 2

And that's the answer: 72

This trick will always work all the way from 9 times 1 (which would be 0 fingers followed by 9 fingers, or 09 (like on a digital alarm clock), up to 9 times 10 (which would be 9 fingers outstretched on the left side of your last thumb, which is the one that ends your left-to-right count and gets curled up), and would leave zero fingers outstretched on the right side of that curled-up thumb, or 90.

Click here for a drawing of how your hands should look for entire 9 times table!

(This will open a new window. Close the window when you're finished to return here.)

(Oh, and by the way, if you want to check your work to make sure you counted everything correctly, just add the two digits of your answer together and – even though you did multiplication -- they should always ADD up to nine.) Look:

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

9 x 6 = 54

9 x 7 = 63

9 x 8 = 72

9 x 9 = 81

9 x10 = 90

See what I mean about the two digits of the answer adding up to 9, even though this is multiplication and not addition! (But be careful, because this way to check your answer only works for the nine-times table!)

Practice until you don't even have to bother with your fingers for the nines (even if that takes a long, long, time).

The 4's, 5's, and 6's

Okay, there are lots of ways to do the 4's. For example, many students find a method called "visualization" to be very helpful. That's just a fancy way of saying that the person tries to think of something that is real and familiar enough to picture in your head, and, of course, it has to be something that will help the thinker "see" his way toward the answer. So with 4's, if you think of the wheels of a car, and you imagine seeing one car, then you can easily count the four wheels. 1 car x 4 wheels = 4 wheels. If you imagine 2 cars, and count their wheels you will have 8 wheels. 2 cars x 4 wheels = 8 wheels. (2x4 = 8) For three cars, you would add four more wheels, and you would count twelve altogether. For four cars, you could hold out four fingers or draw four marks on a piece of paper, and count up (add) 4 wheels and 4 wheels and 4 wheels and 4 wheels, probably counting two at a time, as though there really were cars lined up in front of you and you do your counting in pairs of wheels: first, the wheels on the front of the first car, then the wheels on the back of the first car, then the wheels on the front of the second car, then the wheels on the back of the second car, then the wheels on the front of the third car, then the wheels on the back of third car, and so on...

If you are in a classroom, though, and not your bedroom doing homework or just practicing, then it can be even better to glance at a few chairs, because almost all classroom chairs are made with four legs. So one chair has four, two chars have eight, three chairs have twelve, and so on. Or try thinking of something else that interests you that you that you find easy to picture in your head, like dogs or horses. Most dogs and horses have four legs, and thinking of the legs in groups of four (or visualizing them) can make it a lot easier to figure out until you do each one enough times to just know it by heart – even if you then still want to check your work with dogs, horses, brand new kittens, or giant lions....

And if that way works out really well for you, try it with other numbers and other things from the real world. For example, for fives, if you're one of those people who find that using their fingers gets them mixed up, try to think of an elephant with a big trunk hanging down to pick up a peanut from the ground. When you count the trunk as though it were just another leg, like a spare, then you can count five legs for each elephant. Speaking of spares, if you imagine one of those fancy antique cars with the spare tire stuck flat to the back of the trunk, you can count tires in groups of five...

Going back to three's, you can think of triangles, or tricycles, or tripods (the things that hold up cameras...

For sixes, you can try to imagine a person riding a horse, and count how many feet there are in each image of person-on-a-horse. (6, I hope!).

Now, this method can be a little tricky for sevens, because there aren't so many things that always come in groups of sevens, so... IT'S TIME FOR A WHOLE NEW TRICK:

The 7's

WHEN YOU COME TO A MULTIPLICATION FACT THAT YOU CAN'T REMEMBER, OR DON'T HAVE AN EASY WAY TO FIGURE OUT, TRY SWITCHING AROUND THE ORDER OF THE NUMBERS. For example, if you see 7 x 9 = , and you can't remember the answer, try writing down 9 x 7 = .

Just by doing that simple step, you can almost always use one of your other methods to get to the answer. And for this one, 9 x 7, you can use the finger trick that always works for the nines!

Make 7 x 4 into 4 x 7, and you can think of seven dogs, and count up all their feet! (just count up by fours on your fingers until you've used seven fingers – one for each dog.)

Or think of the wheels of 7 cars parked in a row!

Make 7 x 5 into 5 x 7, and you should be able to hum (SILENTLY!) the jump-rope tune in your head for fives.

Make 7 x 10 into 10 x 7,

Make 7 x 11 into 11 x 7,

7x 2 into 2 x 7

7 x 3 into 3 x 7,

And by now you probably get the idea!

BUT there's one you just cannot switch around. (or you can, but it won't help) That's 7 x 7 , of course!!

--Mitch