Another approach to multiplication November 14, 2011Posted by mareserinitatis in math, teaching, Uncategorized, younger son.
Tags: arithmetic, math, multiplication, teaching
My younger boy has been working through multiplication, and the problems he’s doing are getting more difficult, so I decided it was time to start working with the dreaded memorization.
I’ve talked before about simply giving kids multiplication tables to work from. My younger son, however, seems like he’s a little better with memorization, so we took the following approach.
Most kids have a fairly easy time with learning to count by twos, threes, and fives. So that’s where you start. The other thing the child needs to know is how to add with carrying. If the child can do that, the rest of the tables are easy. Since counting by 2s and 3s is known, we’ll start with fours.
If you have a problem involving a 4, say 8 x 4, then you have them compute 8 x 2. Once they have the answer to that, have them double it. So basically, once they know all their 2s, they can easily obtain their fours. The same principle goes for 6s and 8s. For a multiplication problem involving a 6, they can either add the corresponding problem with twos three times or take the threes problem twice. Finally, for 8s, they can work from twos to fours, and then from fours to eights.
With the younger boy, this means that if he has a problem like 8×7, he first figures out 2×7. He doubles that answer to get 4×7, and then doubles it again to get 8×7. For him, adding things up goes a bit faster.
For nines, he uses the finger method: he holds down the finger that corresponds to the multiplier, moving from left to right. That is, if he has 3×9, he holds down the third finger from the left. To the left of that finger, he has the number of tens (in this case, 2), and to the right he has the number of ones (7). So the answer is 27.
So what do you do about 7s? Actually, given you have methods for everything else, the only one to memorize is 7×7. On the other hand, if you have a kid that sort of stuck when it comes to commutivity of multiplication, then another way to deal with it is that it’s the sum of the threes problem and the fours problem. (7×7 = 3×7 + 4×7 = 21 + 28 = 49)
Tens are usually pretty easy, so I’ll skip that one.
Eleven and twelve were learned by breaking them into two parts. First, take the number times ten and then take it times one (for eleven) or two (for twelve) and add the results. So 12×9 would be 10×9 plus 2×9.
I’m fairly certain this method would have never worked with my older boy. He has very poor working memory and ADHD, so I don’t think he was able to do a lot of this in his head (and was always resistant to writing it down). For him, I think using a multiplication table was a better approach. For the younger boy, though, who seems to enjoy working through problems and has a very good working memory, this has been a far more, and I might even say quicker, method.