Re: [MATHEDCC] multiplication facts

Martha Haehl (haehl@KCMETRO.CC.MO.US)
Sat, 6 Mar 1999 13:10:09 -0500

On the same line as RWW's, laying out objects in a grid, or using graph
paper to represent multiplication also helps understand the distributive law
properties and break down multiplication into whatever combinations are
manageable for the student. For example, 7 x 8 is a 7 x 8 grid. This could
be considered as 5 rows of 8 each plus 2 rows of 8 each as suggested by the
last email, or 2x8 + 2x8 + 2x8 + 8, or countless number of other ways.
Laying out 2-digit multiplication similarly and letting students develop
their own algorithm for determing the number of squares can also be a good
way to teach multiplication to students who seem to be missed by the
commonly-taught algorithm.

For some people, flash cards and repition works, for others, something more
concrete is needed to hang on to the numbers.

Martha

-----Original Message-----
From: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>
To: mathed:; <mathed:;>
Cc: RWTNTS@RITVAX.ISC.RIT.EDU <RWTNTS@RITVAX.ISC.RIT.EDU>
Date: Thursday, March 04, 1999 5:38 PM
Subject: Re: [MATHEDCC] multiplication facts

Some suggestions from John Flanigan, including

> 2. Carry flash cards on your person and go over them while waiting at the
> bus stop, dentist's office, ticket line. Throw each away, with ceremony,
> once it is mastered.

I'm not sure what it means to "master" a piece of knowledge -- new layers
of knowledge always seem to carry a risk of driving out the old. I'm not
much of an advocate of blind memorization of anything, and would rather
tie it to some "key" or illuminate it by understanding in order to jog one's
memory (if needed).

This works for bigger problems -- 8 x 13 for example is really easy if you
think of a double deck of cards (2x52=?). If someone were having trouble
with
the recall of 56 as the product of 8 and 7 but could remember that 28 was
4 times 7 I would suggest thinking of 28 as 30-2 and doubling it to 60-4.
you could also conceive of 7x8 as (5+2)x8 or 40+16.

Developing an array of such strategies for a given situation ought to allow
the
person needing to do the memorization to choose one or two approaches that
make
sense to them. If one were working in an environment where such results
needed
to be constantly produced (are there any such environments outside the
classroom?) then the cues and indirections would gradually fade in
importance
-- though they could be switched back to if one ever got "rusty".

A good time to practice mental arithmetic, I find, is when falling asleep
(or
trying to). Start running through the natural numbers, factoring each one as
you go. Or work backwards from 1000 or something...

Well, we each have our tricks, I guess.

RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623

>>>> The plural of mongoose begins with p. <<<<

****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************

****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************