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2x2 to 2x7 2x8 to 3x6 3x7 to 4x6
4x7 to 5x7 5x8 to 6x9 7x7 to 9x9

#1 | #2 | #3 |#4 | #5 | #6

I give these away for free. All I ask is that you print them in color.

There are six JPEG files; each fits on a standard piece of 8.5"x11" paper. Print them out on a color printer, laminate them if possible, then cut them up and use them. They will make the acquisition of multiplication facts faster and more fun. Color is an essential part of the design. If you don't have access to a color printer, download them onto a floppy disk and take it to a friend or local copy shop who can print them in color. If you only have black and white, there is no point in using these. You might as well make your own flash cards with a black marker.

Each page has six flash cards, for a total of 36 flash cards, from 2x2 to 9x9. The six JPEG files were compressed at "maximum quality" and range from 150 to 200K.

I have not included files for the other side of the flash cards. It's easier to just write the "2x2" etc. by hand.

Teachers and parents, please read this:


Math must be learned a step at a time. Many students don't memorize the multiplication tables; discouraged, frustrated, they are left behind. They cannot progress to long division and fractions. They hate math.

These flash cards are intended to help teenagers and adults catch up. I have designed the graphics with them in mind.

Once they learn the "times tables," then long division and fractions are easy.

Multiplication facts are absolutely essential. Occasionally, someone will claim that the calculator makes memorizing times tables unnecessary. Wrong. Does television make literacy unnecessary? No.

Why flash cards? Why pictures?

I actually started this project as an interactive multimedia computer program, but changed my mind for two reasons: most people don't have access to a computer, and flash cards are simply better. They are cheap, handy and effective. However humble and plain, flash cards are a time-proven way to memorize facts. Adding a picture to a flash card can stimulate more brain cells, and create a stronger impression, making it easier to remember.

How to start:

How you use flash cards is more important than how they look. The following suggestions are based on personal experience as a teacher, expert advice (thanks to Sharon Johnson, O.C.D.E.), and recent experiments by neuroscientists using fMRI brain scanners (Los Angeles Times 10-1-1998).

First, test the entire set of 36 cards once, including even the real easy ones (2x2, 2x3). Don't take any for granted, but check them all, because people usually are rusty on the easy ones too. Put aside any cards which are done instantly, without any pause or mental calculation. Only the "hard" ones remain.

From these, choose seven to be learned first. The neuroscientists say that more than seven is too many, causing the short-term memory to overflow. Actually, about twenty flash cards is a reasonable number for something like foreign words, but seven seems to be just right for these times tables cards.

Starting with just these seven, take one at a time and study each card's picture and other clues (rhymes, printed phrases). Involve the senses by talking about it out loud, describing the picture, making up a goofy story about it. The weirder the better. Use sound effects. Imagine being in the picture. Trace your finger over shapes in the picture. Draw a rough sketch of the picture on a piece of paper. Instead of merely repeating the fact "3x6=18" out loud, add a little music, like some jingle on a TV commercial. The neuroscientists say that it's necessary to spend at least eight seconds "paying attention" to form a lasting memory, but who's in a hurry? This is important, so slow down, take time. This isn't the "flash" part yet.

Time is what makes flash cards work. Only practice for a short period of five to fifteen minutes, maximum. Concentrate on the flash cards. First look at the side that asks the question "3x6=?" and try to remember the answer. Then turn it over and study the picture and repeat the entire phrase "3x6=18" out loud. Go over these seven cards three times in each practice session. Then stop, and don't practice again for two to twenty-four hours. Less than two hours is too little. Like an athlete, the brain must rest between exercises. It's part of the process. More than twenty-four hours is too much, though; the brain will forget too much.

Once a particular card is learned, set it aside and replace it with a new one to be learned. Success leads to confidence, and as more cards are mastered, there is a sense of relief and even fun. It becomes more of a game.

What next?

I have added color directions for decimals and fractions. Download and print out in color. They are designed to fit on 8 1/2 x 11 paper. Check them out at decimals and fractions.

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