| 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 |
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> 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.
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