[Numeracy 236] Re: what is the difference between
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Mon Mar 29 18:24:57 EDT 2010
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George,
Here is my version of the why. In -22 and (-2)2 You have the right
idea. With the first of these the square is only clearly happening to
the 2, but you would then apply the negative 1 for an answer of -4 So it
really reads -1 X 2X2. In the second version the writer has clearly
indicated that the problem is -2X-2. Does it make a difference? No,
except to get students thinking about what is included and how to show
it clearly and this understanding can allow you to do some things like
separate out a negative in more complicated problems later.
The second problem is also -1x the absolute value of -6. I was always
taught to take the absolute value first, because that is the number,
after which you apply the negative.
It seems to me that the text you are using is very particular about the
language and is really trying to get students to see the hidden "1". I
frequently tell my students that "the math people" are just like us.
They like to write in shorthand, but you need to think of it as if they
wrote all the parts out.
Carol King
Fernley Adult Education Center
cking at lyon.k12.nv.us
________________________________
From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On
Behalf Of George Demetrion
Sent: Monday, March 29, 2010 1:19 PM
To: Numeracy List
Subject: [Numeracy 235] what is the difference between....
Good afternoon colleagues.
In my newly articulated and highly pleasant role as a Transition to
College math teacher, I've come ac ross the following
-22
(-2)2
According to my book the answer to the first problem is -4 while the
answer to the second is 4. The examples are easy enough to follow, but
a little light on the explanation. In the first problem the notation in
the book states that 2 is the base; thus (2.2)=4 and, I assume, we keep
the negative sign, so that the answer becomes -4. The second problem is
easy enough. I get (-2.-2)=4.
What's missing as far as I'm concerned is a clear and simple explanation
of the reasoning behind the first problem - 22 d
I deduced that the second problem is based on an order of operations
problem solving menthodology and I'm thinking the same thing for the
first problem in which the negative sign indicated a -1. Thus, on this
hypothesis, I am carrying out an order of operation (exponent first,
including the implied paranthesis (2.2) multiplied by -1 in which this
later stage is last on the order of operations process.
Questions:
1. Is my hypothesis for problem #1 correct?
2. If not, what would be the correct explanation?
3. Whether or not the hypothesis is correct what woould be the simplist
accurate explanation to provide my students with?
One more question -/-6/= -6, which I translate to mean is that the
opposite of the absolute number -6 has an absolute value of 6; therefore
its opposite is -6.
a) is this correct
b) If so, is there an easier way to state it?
c) If it is correct what is the best way to teach it to TCC students
with limited mathematical experience
d) If it is incorrect, what would be the correct answer?
Okay, we're just about through with integers. Onto fractions.
Best,
George Demetrion
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