Ask Dr. Math: FAQ

Some people seem to have real difficulty learning their multiplication facts. Parents, teachers, and students have written to Dr. Math asking for help with learning their multiplication tables (see some of the best answers from our archives). For an enjoyable twist, see also Russian Peasant Multiplication. There are many ways to help us remember such things, but what works best will be different for different people. For example, you can try to remember something by saying it repeatedly, writing it, acting it out, representing or drawing it, making up a game or story or song about it, and so on. Usually, the more ways you use to connect it to your brain, the easier it is to remember it. Here's how this might work with multiplication facts. You can make a multiplication table. Since 1 times any number is just that number, we can leave the 1's off. Multiplying a number on the left by a number on the top gives you the number ("product") where the row (across) meets the column (down). Here's 4 x 7 = 28 (shown in red): x | 2 3 4 5 6 7 8 9 10 11 12 --+------------------------------------------ 2 | 4 6 8 10 12 14 16 18 20 22 24 | 3 | 6 9 12 15 18 21 24 27 30 33 36 | 4 | 8 12 16 20 24 28 32 36 40 44 48 | 5 |10 15 20 25 30 35 40 45 50 55 60 | 6 |12 18 24 30 36 42 48 54 60 66 72 | 7 |14 21 28 35 42 49 56 63 70 77 84 | 8 |16 24 32 40 48 56 64 72 80 88 96 | 9 |18 27 36 45 54 63 72 81 90 99 108 | 10 |20 30 40 50 60 70 80 90 100 110 120 | 11 |22 33 44 55 66 77 88 99 110 121 132 | 12 |24 36 48 60 72 84 96 108 120 132 144 Some people describe a row (or column) as "skip counting," so the row beginning at 5 is the row of "5 times" facts, or "skip counting by 5s." x | 2 3 4 5 6 7 8 9 10 11 12 --+------------------------------------------ | 5 |10 15 20 25 30 35 40 45 50 55 60 These "times tables" can be memorized as a smaller chunk by themselves. Sometimes making a song or story helps you learn them. SchoolHouse Rock (select Multiplication, or see Schoolhouse Rock Lyrics) provides a good example. Finding patterns A good way to learn multiplication facts is to look for other patterns in the table. For example, notice that (4 x 7) is the same as (7 x 4). You can represent this by showing that 4 rows with 7 pennies in each row add up to 28 pennies, and those same 28 pennies can be rearranged as 7 rows with 4 pennies in each. In fact, the answer is the same when you reverse the order in which you multiply any pair of numbers, which means that you really only have to know half of the products in the table. 4 o o o o o o o o o o o o o o o o o o o o o o 4 o o o o o o o o o o o o o o o o o o o o o o 7 o o o o 7 o o o o o o o o When you begin using the table to learn multiplication facts, move one finger across and one finger down to meet at the product, and say the facts aloud as you do this. For example:  "4 x 7 = 28"  AND  "7 x 4 = 28." You can then write the fact out in numbers and in words. You might use colors or add illustrations to make it more attractive and fun. Another pattern you may notice is that the products in the 9 times table have a special property: for each product, the sum of the digits is 9. This leads to a neat finger math trick you can use for this special case: see Finger Multiplication for the 9s from the Ask Dr. Math archives. Flashcards If you are writing the numbers down, you can make flashcards. For example, write "4 x 7" and "7 x 4" on one side of an index card, and "28" on the other side. You can show either side of a flashcard and try to say what's on the other side. This will remind you that you can get a product, like 36, by multiplying different pairs of numbers. Playing cards You can also use regular playing cards to help practice with multiplication facts. Remove the Kings and Queens from a deck of "Jumbo Index" cards. Use a broad-tip marker to write an "11" on each Jack and a "12" on each Ace. Shuffle and then have someone else flip over two cards. Your goal is to say the two multiplication facts that go with the pair of cards. Keep the pair aside if you can't say the product in a short time. Focus on the facts that give you trouble. For example, if you want to concentrate on practicing the 12's table, turn over single cards, with each card representing "12 x (card value)". The Game of Factor: Having fun always makes learning easier, so use games to help you practice multiplication. For example, you can use your special playing card deck to play a game like "Factor." You need to know that a factor is a number that divides evenly into a product, so that 1, 2, 3, 4, 6, and 12 are all factors of 12. Each player gets 6 cards. The first player declares a "Target Product," which has to be a product of two cards in his or her hand. Each player shows the cards of numbers that are factors of the target product. Everyone must agree that each of the numbers is really a factor. Each player gets the sum of their correct factors as points for that hand. Scores are recorded. The cards are shuffled and dealt again. The next person to the right declares the target product for the new hand. The game ends when the first person reaches more than 100 points. You can adjust the game by changing the winning total, or playing with partners, or by using a target number that is the product of three card values, etc. For more, see some of the best answers from the Dr. Math Archives, or explore Learning to Multiply, from the Teacher2Teacher FAQ.

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