[Numeracy 239] Re: what is the difference between....
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Mon Mar 29 19:36:54 EDT 2010
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I think your hypotheses are correct. For the first example, the
simplest explanation IMO, is that this follows the Order of Operations
PEMDAS.
In the first example, there are no ( )P , so next in the PEMDAS
order is exponentiation (E). 2 is raised to the second power,
resulting in 4. Next comes multiplication M, by -1. the answer is -4.
In the second example, the parentheses are executed first, (-1 * 2).
this answer is -2, which is then raised to the second power. Final
answer is 4.
It is really based on PEMDAS ( order of operations).
In your second example, I would clarify the language as such: -/
-6 / = -6
This is the opposite( - )of the absolute value of -6, ( /-6 /. )
The absolute value of -6, / - 6 / , is 6.
The opposite of 6 is -6.
I would not use the term "absolute number".
Cheers!
Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net
On Mar 29, 2010, at 1:18 PM, George Demetrion wrote:
> 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
>
>
> ----------------------------------------------------
> National Institute for Literacy
> Math & Numeracy discussion list
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