[Numeracy 265] Re: Is an absolute value positive?

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Chip Burkitt chip.burkitt at orderingchaos.com
Wed Mar 31 16:05:16 EDT 2010


Yes, what I *owe* is positive, but what I *have* in my account is negative.

On 3/31/2010 11:23 AM, Michael Gyori wrote:

> 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

>

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

>

>

>

> ------------------------------------------------------------------------

> *From:* Chip Burkitt <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

>>

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

>>

>>

>>

>> ------------------------------------------------------------------------

>> *From:* Carol King <cking at lyon.k12.nv.us>

>> *To:* The Math and Numeracy Discussion List <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 <mailto:cking at lyon.k12.nv.us>

>>

>> Fernley Adult Education.

>>

>> ------------------------------------------------------------------------

>>

>> *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>

>> *To:* The Math and Numeracy Discussion List <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>

>> *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

>>

>> **-2^2 **^

>>

>> ^ ^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 - 2^2 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

>>

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