From: dpicard@uva386.schools.virginia.edu (David Picard)
Subject: Memorizing Multiplication Tables
Organization: Virginia's Public Education Network (Charlottesville)
Date: Sun, 27 Sep 92 03:34:27 GMT

Just one teachers opinion about the multiplication tables. By
the way, I teach 4th grade, the seeming make-or-break year for
memorizing the "x" tables.
As I see it, there are really 55 multiplication facts. Teaching
kids early on that 6x7 is the same as 7x6 eliminates the need
to memorize the fact twice. Many kids never even think of
reversing the two integers if they are stuck. They think it is
against the rules.
Once the associative property is understood, kids can be
taught some easy tricks to reduce the list of facts rather
quickly.
First, anything x0 = 0. You just reduced your list from 55 to
45.


Second, anything x1 = itself. Your list is now at 36.
               
Third, the 5's tables has so many patterns and repetitions,
most students don't struggle very long with these. Once these
are committed to memory, we're down to 28.
            
Fourth, Multiplying by 2 should not be difficult because it is
the same as adding the number to itself. 7x2 = 7+7. Students should have
their addition facts from 1 to 20 mastered before they work on
the multiplication tables, so the 2's tables should not present
many big problems. The list is now 21.

Fifth, The "nines tables" are easily unlocked once students are
made aware of the predictable pattern. If any number (less than
10) is multiplyed by nine, the first digit in the product will
be the number which comes before it. (ie, multiply 7 times
nine, and the digit in the tens column of your answer is 6,
which is one less than 7) The number in the ones column will be
a digit which, when added to the first digit, would give you
the sum 9. This sounds a little bit complicated, but it is not
once students try it a few time. There is even a method which
involves using our human calculators (fingers) to multiply by
9 which is based on the same pattern of digits. Once these are
learned, we have knocked off 6 more facts. We are left with 15
facts.     

In my opinion, these 15 are the real challenge. They are:

3x3 4x3 6x3 7x3 8x3 4x4 6x4 7x4 8x4 6x6 7x6 8x6 7x7 8x7 and 8x8.

These can be taught by teaching kids the "one-up or one-down"
strategy. If they can't recall a multiplication fact, they
should see if they can recall a fact which uses one of the
multiplicands (is that right?, oh well, one of the numbers
being multiplied) and another number which is one higher or
one lower than the other. (ie. I don't remember the answer to
the problem 7x6. I do, however, remember that 7x5=35. If 5
groups of 7 = 35, 6 groups of 7 must be 35 = 7 more or 42.)
This strategy also sounds difficult, but becomes automatic with
a little practice. (I still use this strategy to remember 7x6
and 6x8) 

Of the 15 facts remaining, all but 7x7 can be solved using this
strategy. 

Even if students cannot master this strategy, there is still
hope. I don't like kids to do a lot of drillwork, but if it's
neccessary to unlock these 15 facts which will open up a world
of possibilities for them, I send home flash cards and they do
just that.

I would agree that the teacher and his/her attitude toward the
subject have a lot to do with how students do with their math
facts. Teachers who continue to grow professionally and expose
themselves to materials like Mathematics, A Way of Thinking by
Robert Lorton develop confidence teaching math. Children pick
up on this confidence (or lack therof) and emulate it.

Just my opinion,

David				Have you ever heard a parent say,
                                 "I don't worry about who my child
				  hangs out with, he's a slow
				  learner?"
				Children emulate those who
                                  make them feel like they belong.