[Numeracy 253] Re: what is the difference between....

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Chip Burkitt chip.burkitt at orderingchaos.com
Tue Mar 30 17:27:52 EDT 2010


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 <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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