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View Diary: You don't need to know "times tables" to learn Algebra (60 comments)

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  •  right, how else would they be learned? (10+ / 0-)

    In effect, we learned arithmetic the same way--through rote practice--but we had a smaller set of digit pairs to memorize (starting with 0 through 9).

    I think multiplication tables provide a fundamental building block towards other math skills like being able to do division more quickly, and enables quicker understanding of factoring.

    •  Factoring - Bingo! (0+ / 0-)

      It's much tougher to see the relationships quickly when you don't know the times tables. I'm currently tutoring a young man in algebra who is weak in his general arithmetic. He can eventually get to the answers, but it is painfully slow.

      Free: The Authoritarians - all about those who follow strong leaders.

      by kbman on Tue Dec 10, 2013 at 12:47:18 PM PST

      [ Parent ]

    •  The non-rote way to learn the times table (1+ / 0-)
      Recommended by:

      is to learn the patterns.

      Anybody can multiply by 0 (You get 0) or by 1 (the number you are multiplying) without really having to think about it. That's two rows and two columns down.

      Multiplying by 5 is easy. Odd numbers times 5 end in 5, and even numbers times 5 end in 0. The first digit is half of the other number, rounded up. So 5x7 is 2.5 rounded up, or 3, followed by 5: 35.

      Counting by 2s is easy.  (0) 2, 4, 6, 8, who do we appreciate? Half done right there. And then the same numbers over again with a 1 in front.

      Counting by 4s is easy. Count by 2s, and leave out every other one.

      Multiplying by 9 has a simple rule. Take one less than the number to multiply as the first digit, and pick the second so they add up to 9. So 9x7 starts with 6, and you put a 3 with it to get 63. Check it out. Adding the decimal digits of a multiple of 9 always gives a smaller multiple of 9.

      What's left? 3, 6, 7, 8. We're getting there.

      Counting by 3s isn't as trivial as counting by 2s, but it isn't hard. It helps to remember that 3 times an odd number is odd, and 3 times an even number is even. Also, if you add the digits of a multiple of 3 you get 3, 6, or 9. So 3x7 is 21, which yields 3.

      For multiples of 8, the first digit mostly goes up by 1, and the second digit always goes down by 2.
      48 <--The exception, but 40+8 isn't a problem

      Two rows and columns to go, for 6 and 7, except actually you only need to learn how to multiply them by themselves and each other, because we have already done every other multiple of the last two. So

      36 42
      42 49

      Done. Of course, in the classroom, you should take some time to practice each rule and make sure you understand it before moving on the the next, and throw in a few other useful rules, such as doubling: 1 2 4 8 16 32 64 128 256, which is essential for computers, and squares: 0 1 4 9 16 25 36 49 64 81 100, or adding up odd numbers

      0 1
      1 3
      4 5
      9 7
      16…Wait a minute, what's going on here? Ah, for that you need a teeny bit of algebra. And then I would like to introduce you to my friend Galileo, who used that simple pattern to work out gravity. You could look it up.

      All of mathematics should be taught by bringing out the inherent patterns, because real math actually is the study of patterns. Geometric patterns, numeric patterns, logic patterns…And then it's a lot more fun than doing it without knowing why or what for.

      Ceterem censeo, gerrymandra delenda est

      by Mokurai on Tue Dec 10, 2013 at 01:06:48 PM PST

      [ Parent ]

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