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Topic:  strategy for division 
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Subject:  RE: strategy for division 
Author:  markovchaney 
Date:  Oct 2 2006 
understanding the division process.
We explore division with education students for elementary school by looking at
what's actually going on. Division can be thought of as repeated subtraction. So
we start with examples like "Find what 533 divided by 41 equals by repeatedly
subtracting 41 from 533 and keeping track of how many times you can do this.
They see that it can be done exactly 13 times.
Then we ask why multiplying by 10 or 100 or 1000 is so easy, and they generally
know it is because one merely needs to append the requisite numbers of zeroes to
the right of the last digit in the number.
Next, we ask, "How can you use this fact to shorten the "repeated subtraction"
process you used above?"
It takes some thought to see that you can repeatedly subtract 410 from 533 until
you have less than 410 remaining (in this case, that's once). But since we are
dividing by 41, not 410, that "once" represents not one but 10. Now, we proceed
as before, subtracting 41 from the remaining 123. This can be done exactly 3
times. So our quotient is still 13, as before, but this was determined in 4
subtractions rather than in 13, saving a lot of time. THis method extends, of
course, to larger dividends and/or divisors.
We also have students model this with base ten blocks, which is very helpful to
many of their future students.
Now, the point, of course, is that when one teaches the long division algorithm
mechanically, as a process to be memorized without the slightest understanding
of what's really going on, you need mnemonics like yours to help recall the
steps, hopefully without missing any and doing them in the right order. I
believe NONE of that is necessary if students are helped to actually understand
the process in the first place.
Your mileage may vary and likely does already.
On Oct 1 2006, Connie H wrote:
> I ahve always used the steps of:D,M,S,C,B,R
Divide: Daddy
> Multiply: Mother
Subtract: Sister
Compare (the difference in the
> subtraction to see that it is not as large as the divisor): Cat or
> Cousin
Bring Down: Brother
Remainder or Repeat: Rover
Hope this
> helps in remembering the steps of a long divison problem.
 
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