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Subject:   RE: Expressions vs Equations
Author: LFS
Date: Jan 24 2011
Oh my gosh - someone else that thinks this a crucial point. I even wrote to
SmartTech (smartboard) when they wrote (something like) "Solve 3x+2-2(x+1)."
to say: 'Use the word SIMPLIFY not SOLVE.'.
I like to say that "simplify problems" look like snakes  ...=...=... winding
down the page. "Solve problems" are paragraphs. Solve 3x+1=7 (hit Enter) 3x=6
(hit Enter) x=6/3 (hit Enter) x=2.
One difficulty is that on the next to last line, we tend to write:
x=6/3=2 (We don't hit Enter and write x=2.) Although it is easier for us, this
very much confuses our students.
Also, I was a rather disappointed in the example problem given for draft CCSS
(Core Curriculum State Standards) which asked: Are the following equations:
(a)y=x^2+3x+2, (b) x^2+3x+2=0, (c) x^2+3x+2=(x+1)(x+2), (d)(x+3/4)^2-1/4, (e)
Aside from the fact that the question was grammatically incorrect, I consider
this just semantic gibberish and completely not agreed upon by most
mathematicians. It is much more important that we agree on the words in front of
each of these when posed as a problem and the structure of the answer.  
(BTW, once we start using x and y, I think we should ALWAYS write y(x)=3x+2,
y(x)=x^2+3x+2,... If I use y=3x+2, then I have a horrible time trying to
differentiate between a function and its value at x=a. If I ALWAYS write
y(x)=3x+2, they see that this is an entire function and that y(2)=3*2+2=8 is the
value of that function at x=2 and they can look to see if (2,8) is a point on
the function.)

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