# [Numeracy 268] Re: what is the difference between....

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Carol King cking at lyon.k12.nv.us
Wed Mar 31 17:04:17 EDT 2010

Our text indicates that absolute value is a measure of your distance
from 0, but suggests it is not the same as the term positive 6. I have
taken it to mean that they are congruent, but not the same entity.

Carol King

________________________________

From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On
Behalf Of Chip Burkitt
Sent: Tuesday, March 30, 2010 2:28 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 253] Re: what is the difference between....

I disagree. Technically for all x<>0, |x|>0. A positive number is any
number greater than 0. Therefore, the absolute value of a nonzero number
is positive. Besides, distance without direction is also always
positive.

On 3/30/2010 2:12 PM, Carol King wrote:

I would point out that technically an absolute value is not a positive
number. It represents the distance from 0 either negatively or
positively on the number line. It operates mathematically like a
positive number, but it is not the same as the positive number. I don't
know if I would share that with struggling students.

Carol King

cking at lyon.k12.nv.us

________________________________

From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On
Behalf Of Michael Gyori
Sent: Monday, March 29, 2010 4:55 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 241] Re: what is the difference between....

Hi again George and all,

If /-6/ means the absolute value of negative 6, then I stand corrected.
I didn't realize the forward slashes might have been bars.

In that case, absolute values are positive. So, the negative of the
absolute value of -6, which is +6, = -6. On the other hand, -(-6) [i.e,
in parentheses] would be positive 6.

Also, I always teach part numbers (fractions, decimals, and percents)
before I teach integers. I find it interesting that you delve into
integers first. Do you have a reason for doing so?

Michael

Michael A. Gyori

Maui International Language School

www.mauilanguage.com <http://www.mauilanguage.com/>

________________________________

From: Michael Gyori <tesolmichael at yahoo.com>
<mailto:tesolmichael at yahoo.com>
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
<mailto:numeracy at nifl.gov>
Sent: Mon, March 29, 2010 1:30:03 PM
Subject: [Numeracy 237] Re: what is the difference between....

Hello George and all,

See my attempt at making sense of your message. I will embed my
thoughts in green into your post below:

Michael

Michael A. Gyori

Maui International Language School

www.mauilanguage.com <http://www.mauilanguage.com/>

________________________________

From: George Demetrion <gdemetrion at msn.com>
To: Numeracy List <numeracy at nifl.gov> <mailto:numeracy at nifl.gov>
Sent: Mon, March 29, 2010 10:18:55 AM
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

When a number is positive, we don't sign it. For example, 2+2=4 really
means +2 (+) + 2 = + 4.

In that vein, we really have negative times positive 2 squared (or
the negative of positive 2 squared) equals -4.

(-2)2

In this case, the 2 is signed as a negative, or you can see it as the
negative of positive 2 = negative two, times itself, = +4.

I teach my students rather early on that unsigned numbers are actually
signed by an invisible "+" before them, just like whole number have an
invisible point (.) to their right, which is the border separating whole
numbers from decimals (part numbers). 345 is the same as 345.

Something "of something" is always multiplication. In the case of - +,
we are saying the negative of positive, which leads me to negative times
positive. That leads me to teach (also quite early on) the golden
rules, namely, positive x positive and negative x negative = positive,
while negative times positive or positive times negative = negative.

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.

-/-6/ = -6 strikes me as being incorrect. If I'm wrong, PLEASE CORRECT
ME: In language, the equations reads to me, negative times negative 6 =
POSITIVE 6, because a negative times a negative = a positive.

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
<http://gfx2.hotmail.com/mail/w4/pr01/ltr/emoticons/smile_thinking.gif>

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