[Numeracy 258] Is an absolute value positive?
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Wed Mar 31 02:38:21 EDT 2010
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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
________________________________
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
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
MauiInternational Language School
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
MauiInternational Language School
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
-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 negativeof 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
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