[Numeracy 240] Re: what is the difference between....

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Rachel Lyon rlyon at lyon.k12.nv.us
Mon Mar 29 19:50:57 EDT 2010


Another way of 'reading' the problems -22 and (-2)2



-22 can be read as 'minus' 2 squared which is - (2)(2) = - 4 In this
case the negative sign is not attached to the original number but rather
the answer: same as -23 would be - 8 or -(2x2x2) and then the - sign
with the answer.



(-2)2 is read as negative 2 squared which is (-2)(-2) = 4 because the
2 negatives make a positive. To match above example: if you had (-2)3
you would have (-2)(-2)(-2) which is equal to -8 (negative 8).





________________________________

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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