# [Numeracy 274] Re: Is an absolute value positive?

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Thu Apr 1 12:15:04 EDT 2010

Carol,

Regarding your question about a context for the absolute value of -6 and 10:

What is the distance you travel (i.e., miles on your odometer) if you travel
6 miles in the wrong direction and then turn around and go 10 in the correct
direction?

Absolute values help when you want to consider only the magnitude of a
number, not the direction.

_____

From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On Behalf
Of Carol King
Sent: Wednesday, March 31, 2010 2:37 PM
To: chip.burkitt at orderingchaos.com; The Math and Numeracy Discussion List
Subject: [Numeracy 269] Re: Is an absolute value positive?

To help with such questions and occasional inaccuracies in our material I
bought a mathematics dictionary (looks like I will be modifying the text
again.).

According to the Collins Dictionary of Mathematics: 1. Absolute value is the
positive real number equal to a given real but disregarding its sign; Where
r is positive, absolute value of r = r = absolute value of -r.

Less helpful is definition 2. it is a modulus. A Modulus is defined as a
positive real number that is a measure of the magnitude of a complex number,
and its equal to the square root of the sum of the squares of the real and
imaginary parts of the given number. Thus the absolute value of x+iy is the
absolute value of x+iy = the square root of x squared + y squared.

For me this creates the question of if I have the absolute value of -6 plus
10 is it saying I have 16 of something? If so why didn't the question just
occur as 6+10? As I understand it absolute value is used in problems that
are actually expressing range type ideas. What is the ultimate purpose of
this concept; into what context can a student put an absolute value
question?

_____

From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On Behalf
Of Chip Burkitt
Sent: Wednesday, March 31, 2010 1:31 PM
To: numeracy at nifl.gov
Subject: [Numeracy 266] Re: Is an absolute value positive?

Aaron and All,

It's a kind of philosophical question. I can count marbles, for example. If
I have 3 marbles and take away 2, I'm left with 1. If I have 3 marbles, and
I take away 4... Wait a minute; everyone knows I can't take away 4 marbles
from 3. When it comes to counting things you can touch and see, you can't
have a number less than zero. We only use negative numbers to count or
measure conceptualized quantities. For example, we have negative numbers on
the temperature scale because we have chosen by convention to start the
scale at 0 where water freezes. If we start at absolute zero, we can only
have positive numbers. (Temperature measures the average motion of molecules
in a substance. At absolute zero, all molecular motion stops. You can't have
less motion than none.) Similarly, sea level is an arbitrary spot for
measuring heights and depths. If we started instead from the center of the
earth, there would be no negative heights or depths. Negative numbers are a
mathematical abstraction that allow us to find answers to certain kinds of
problems, primarily subtraction problems where the number being subtracted
is greater than the one being subtracted from.

If I could take 4 marbles from 3, then I would have an absence to contend
with, and the mind recoils from the presence of an absence. I would have to
add a marble to this absence in order to have nothing. In this sense,
Michael is right; negative numbers have no existence. I was merely being

On 3/31/2010 12:06 PM, Kohring, Aaron M wrote:

Michael,

I'm not sure I understand your statements.

If amounts to the left of zero on a number line are 'negative' and distances
below sea level are considered 'negative' and temperatures below zero are
considered 'negative'. Then doesn't that distance to the left or below or
downward serve as a definition for 'negative'?

Aaron

Aaron Kohring

Research Associate

UT Center for Literacy Studies

600 Henley St, Ste 312

Knoxville, TN 37996-4135

Ph: 865-974-4258

Main: 865-974-4109

Fax: 865-974-3857

akohring at utk.edu

From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On Behalf
Of Michael Gyori
Sent: Wednesday, March 31, 2010 12:24 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 261] Re: Is an absolute value positive?

Greetings Chip and all,

Unfortunately, what you owe is a positive amount (the distance from zero to
the left or downward). This might serve as a good example of why absolute
values are positive.

The negative has no existence other than a notation on a balance sheet.

Michael

Michael A. Gyori

Maui International Language School

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

_____

From: Chip Burkitt <mailto:chip.burkitt at orderingchaos.com>
<chip.burkitt at orderingchaos.com>
To: numeracy at nifl.gov
Sent: Wed, March 31, 2010 3:23:50 AM
Subject: [Numeracy 259] Re: Is an absolute value positive?

Wow! I wish I could get my bank to agree that negative numbers have no
existence. I'd never be overdrawn again.

On 3/31/2010 1:38 AM, Michael Gyori wrote:

Greetings Carol and all,

I suppose the question is what is meant by "positive." If we view numbers to
represent quantities (of whatever), then they are intrinsically positive.
Negative quantities have no existence, and perhaps we can regard the notion
of absolute value to reflect just that.

As for teaching absolute values to "struggling" learners, my sense is we
shouldn't underestimate their ability to make sense of things. Quite on the
contrary, the challenge lies in our (educators') ability to facilitate
meaning.

Michael

Michael A. Gyori

Maui International Language School

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

_____

From: Carol King <mailto:cking at lyon.k12.nv.us> <cking at lyon.k12.nv.us>
To: The Math and Numeracy Discussion List <mailto:numeracy at nifl.gov>
<numeracy at nifl.gov>
Sent: Tue, March 30, 2010 9:12:47 AM
Subject: [Numeracy 250] Re: what is the difference between....

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

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

_____

From: Michael Gyori <mailto:tesolmichael at yahoo.com>
<tesolmichael at yahoo.com>
To: The Math and Numeracy Discussion List <mailto:numeracy at nifl.gov>
<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

Michael

Michael A. Gyori

Maui International Language School

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

_____

From: George Demetrion < gdemetrion at msn.com >
To: Numeracy List <mailto:numeracy at nifl.gov> <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 DemetrionImage removed by sender.

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