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Q&A #113


7-8th grade Multiplication and Division

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From: Cindy Wilkins (for Teacher2Teacher Service)
Date: May 25, 1998 at 19:07:26
Subject: 7-8th grade multiplication and division

I agree with Suzanne - music is an excellent way to learn multiplication
facts.

With my remedial 8th grade students, I used the repeated addition and
subtraction method. (I'm not sure about the authenticity of this next story,
but it really grabs my kids attention: repeated addition and subtraction is
how
it was taught up until WWI - students who had figured out the 'short cut',
i.e.
multiplication tables, were pegged as officers while the rest became infantry.
It wasn't long before the multiplication tables became an integral part of
education.)

Here's how it works:

Division: just keep subtracting - when your remainder is too small for another
subtraction, count how many times you performed the subtraction operation and
record: bring down the next number and repeat.

     _____
  23/425
     23
     --
     19     I can't subtract again, so I put a 1 in the 10's place
       5    bring down the 5 (not a separate line, please)
     ---
     195
      23
     ---
     172
      23
     ---
     149
      23
     ---
     126
      23
     ---
     103
      23
     ---
      80
      23
     ---
      57
      23
     ---
      34
      23
     ---
      11   I can't go any farther.  I subtracted 8 more times and only have 11
           of the 23 I need to subtract again, so my answer is 18 11/23.

My students practiced multiplying and dividing throughout the year, and by the
end of the year, only one student still required this technique - the others
had learned enough of their tables to make the process much quicker and much
less paper-intensive.

Example: Multiply

   23
 x 42
  ---
   23
   23   first, write 23 down twice, then mark off the units column
  23x
  23x
  23x
  23x   now, write 23 four times with the units column marked off
 ----
  966   add your columns

- Cindy

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