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 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
On Jun 16 2005, WandaB wrote:
> we still
> get confused! Does anyone have a simple tool or explanation for the
> rule for multiplication and division?

If no-one 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.