[Numeracy 239] Re: what is the difference between....

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Maureen Carro mcarro at lmi.net
Mon Mar 29 19:36:54 EDT 2010

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
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
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

>

>

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