[Numeracy 265] Re: Is an absolute value positive?
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Wed Mar 31 16:05:16 EDT 2010
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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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