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 Discussion: All Topics Topic: Order of Operations (BOMDAS)

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 Subject: RE: Simplify the OOO using terms Author: hcctreeman Date: Nov 30 2007
On May  9 2006, lukus wrote:
> On Mar 24 2003, Mathprof wrote:
> My students never have problems
> with Order Of Operations because
> they are told to split all
> expressions into terms.

A term starts
> with a + or - that is
> NOT in parentheses.

Thus, to evaluate 5*4
> +3(6-8)+3^2-8+5
> the student writes 5*4   +3(6-8)   +3^2   -8   +5
> Each term is
> evaluated    +20  -6  +9  -8  +5

The reults are now
> combined
> according to the rules of Algebra.   +34 -14 = +10
> !!!WRONG***WRONG!!!
> Students discover that the individual terms
> can be evaluated in ANY
> order.

Creating terms is particularly
> important with expressions
> such as  10-3(2) where students tend
> to write 7(2)=14

Of course,
> all this assumes that students
> know how to oparte with signed
> numbers.
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+34 -14 = +20

EASIER
> TO THINK OF BOMDAS THIS WAY:

BO MD AS
BO MD SA
BO DM AS
BO DM
> SA

AS LONG AS YOU KNOW THAT "M" & "D" ARE INTERCHANGEABLE AND "A"
> & "S" LIKEWISE, BUT "M" OR "D" MUST BE PERFORMED BEFORE "A" OR "S".
> IN "MD" IT DOES NOT MATTER WHICH (M OR D) IS DONE FIRST
EX 5x4÷2=?
> .....20÷2 = 5x2 !

????So you believe that multiplication and division are interchangeable???
After reading all of these posts with some trepidation about eliminating PEMDAS
or whatever, It appears to me that there are some problems with your
arguments.

1)Try 8/2x4 interchanging multiplication and division.  Done properly, the
result will be 4x4=16.  If you interchange the multiplication and division
order, you end up with 8/8=1.  It matters tremendously whether you use M or D
first if D comes first there is a different answer.

2)The problem comes from not teaching the concept fully and from teachers who
really don't understand the order of operations for integers (see my point
1).

3)Pemdas is a stepping stone which applies to integers.  Once the students get
to algebra, the algebra teacher needs to make that point absolutely clear to the
students.

So you see, it is not the fault of some clever acronym that causes the problems
that you all are facing, it is improper teaching of the use of them.  I face the
same problems in Developmental College courses, (the lowest students come to me)
but the problem is usually quite obviously that the students were taught the
concepts incorrectly.

LIKEWISE FOR "AS"
EX 5+4-2=? .....9-2 = 5+2