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 Discussion: All Topics for Patterns and sequences Topic: PEMDAS

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 Subject: RE: PEMDAS Author: hcctreeman Date: Dec 3 2007
I like the way you teach the concepts of PEMDAS.  The talk on this discussion
board is a little disturbing.  Rather than getting rid of the acronym, once the
students master the procedures of the basic types of problems, I like to just
explain like, KT8 does according to her post, that the acronym encompasses more
than the basics like fractional exponents and complex fractions.  I work with
developmental students at a community college and as such don't have the
pleasure of working with gifted students, but even these "under-acheivers" can
understand that PEMDAS is a building block and are able to escalate those
processes into more complex problems.  Kudos KT8.

One thing that I like to do to clear up the issue of -2^2 not being the same
as (-2)^2 is to add or subtract the former from an integer.  Most don't even
think of 5-2^2 as 5+4 even though they think, incorrectly, that -2^2 is 4.
By showing the exponent in the context of an expression involving another
operation, they usually start to see the error of their way.  :)  I hope this
helps.

As far as the calculator goes, have you tried teaching them to enter the
numerator and getting a simplified form and then entering the denominator and
getting the simplified form?  Then they can take the quotient.  Then have them
enter the entire expression to see if they can match the result.  This may help
them see why they need the groupig symbols.

On Dec  1 2007, KT8 wrote

> I really like that idea of + and - as separators - I'm gong to use
> that!

More thoughts on O of O:

I teach 7th and 8th grade
> gifted students and they are pretty familiar with "PEMDAS," but I
> teach them that it is now time to get more sophisticated than the
> simple operations represented by that acronym. They learn that P
> stands for "grouping symbols," including the fraction bar, absolute
> value bars and radicals, in addition to parentheses and brackets.
> And that "exponents" includes fractional exponents - ie, square
> roots and cube roots. Because they should understand by now that
> multiplication and division are inverse operations and any division
> problem can be written as a multiplication problem, they "get"
> working from left to right with MD and AS.

Where students have
> the most trouble is remembering that -2^2 equals -4, and that's
> because of order of operations. You do the exponent first (2^2=4),
> then take it's opposite, ie, multiply by -1.

When they're
> entering long expressions into a graphing calculator, they don't
> always realize that they need to put parentheses around an
> expressions that were above and below a fraction bar in a
> handwritten problem. Ex: (4+2)/(3+7) is not equal to 4+2/3+7 or
> (4+2)/3+7. The original problem would have looked like this:

4+2
> ____
3+7

(That's the best I can do in "text only" format).

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