Discussion:  All Topics 
Topic:  Identifying Tools for Your Specific Needs 
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Subject:  RE: Identifying Tools for Your Specific Needs 
Author:  Mathman 
Date:  Jun 16 2005 
> we still
> get confused! Does anyone have a simple tool or explanation for the
> rule for multiplication and division?
If noone got confused, we'd all be famous physicists instead of teachers?
So, all we can do is to play the odds, and do our best. A rule I found useful
to them was "Same = positive" when applied to multiplication. It also helped to
show that (2) was the same as (1)(2), and the same rule applied.
Also, ...VERY important!... make first time problems consistent in appearance
and method of solution, and develop into more difficult [variety] slowly, if
allotted time allows. They are already difficult enough for them.
So, 3  (2) + (5) + 1 = 3 + 2  5 + 1
Now ALWAYS collect positives first then negatives:
= 3 + 2 + 1  5 = 6  5 = 1
Again: 3  (2) + (12) + 5 = 3 + 2  12 + 5
= 3 + 2 + 5  12 = 10  12
and now apply that stage which will aready have been studied, subtraction of two
numbers to get a negative result if the second is greater.
Multiplication: Don't just DO several examples, but STUDY several to see
patterns that are useful. Practice several problems getting signs ...before
continuing further.
E.g.
(4)/(3) = +
(5)/+25) = 
(4)(3) = +
(4)(3)(5)(7)(8) = + [even # of negatives. First study that
pattern.]
(4)(3)(5)(7)/(8) = + [same]
...etc.
Do single term to completion, then move to two terms then more.
It *will* become more difficult for them as they progress. So it is, as with
sorting out formulas for one variable. Like the "inkblot" image of Christ; some
see it, some can't in a lifetime. A pattern to one is chaos to another.
Practice problems are easily devised on a spreadsheet, and all said and done,
practice and so familiarity is the key. I got 90% in French in high school. I
can't [to my regret] speak French. You have to live it.
David.
 
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