[Numeracy 235] what is the difference between....

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George Demetrion gdemetrion at msn.com
Mon Mar 29 16:18:55 EDT 2010



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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