[Numeracy 130] Re: introductions
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Tue Feb 9 12:38:23 EST 2010
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Re: Subtracting Negative numbers
Think about a checkbook balance. I take a check from you for $8.00. Then I
find out that your friend had already given me cash for the $8 you owed me.
We decide that I'll keep the cash (it's spent!) and you change your
checkbook balance. You are *subtracting the negative* $8.00 you recorded, as
I am tearing up the check.
You add the $8.00 back in, to correct your ledger, right?
*Subtracting a negative number always means adding it's opposite. Always.*
Another number line example is a thermometer. If I adjust a temperature
forecast to "take away" negative 8 degrees, I add 8 degrees back.
As this signed integer rule is difficult to solve/review the theory by
example or number line each problem, it is worth memorizing the 2 steps once
you (they) have seen why it is true.
Note: Adding of signed numbers is done well/easily using a number line
approach - left for negative, right for postiive. If learning that *subtraction
means changing the sign to addition* - you can reassure students that they
only need to know how to add signed numbers. I have taught this successfully
to level 2 students.
Mary Jean Wiegert
ABE Math Instructor
Whatcom Community College
Bellingham, WA
On Mon, Feb 8, 2010 at 6:16 PM, George Demetrion <gdemetrion at msn.com> wrote:
> Thanks Carolyn:
>
> Greatest Common Factor = Low number for reducing fractions
> Lowest Common Denominator High number for adding or subtracting fractions
> with different denominators
>
> e.g 3 and 8 or (2.2.2) In this case there is no reduction possible so the
> GCF is 1
> 3 and 8 for LCD 3 and 2.2.2. Since there are no common factors, multiply
> all =24
>
> Question: Now what is all this Absolute Number business all about, which
> in itself I do get, but then we get such things as -(-8) which = 8 is read
> as "the opposite of negative 8." I get that in an abstract sense, but
> processing that to bring it to a level of automaticity is another thing
> altogether.
>
> More importantly,
>
> - What is the significance of this level of mastery when students are
> working on basic integers?
> - What is its actual mathematical function?
> - Intuitively, I'm sensing that it may have some value when it comes to
> algebra (yes? no?) and if so then perhaps higher levels of absolute number
> functionality can be taught at that time (yes? no?) after students mastered
> more of the basics of negative numbers, fractions, decimals, proportions and
> basic algebraic equations
>
>
> This brings up to my mind the importance of:
>
> 1. Sequencing skill development from basic to more advanced
> 2. Maximum possible simplicity as a critical scaffolding strategy in
> its own right
> 3. Incorporating mathematical meaning making and inquiry as a critical
> part of the ongoing work
> 4. Individual and collaborative scaffolding
>
>
> BTW I think these and other pivotal steps have more overall pedagogical
> significance than say whether or not or the extent to which one utilizes
> manipulatives. To be sure manipulatives and other methods can be important,
> but I would view such methods as a secondary rather than a primary issue.
> In short, they belong in the arsenal of teaching tools in the facilitation
> of the primary goal--learning.
>
> Best,
>
> George Demetrion
>
> ------------------------------
> Date: Mon, 8 Feb 2010 16:18:30 -0700
> Subject: Re: [Numeracy 109] introductions
> From: dickins2 at wncc.net
> To: gdemetrion at msn.com; numeracy at nifl.gov
>
>
> What is the difference between the Lowest (or least) Common Denominator and
> the Least Common Multiple and what different functions do they accomplish?
>
> The LCD is the smallest number that will go INTO each of the numbers, while
> the LCM is the smallest number that each of the numbers will divide into
> (the smallest number that is a multiple of both numbers).
>
> Suppose the numbers are 15 and 21. The LCD would be 3: 15 = 3 * 5; 21 = 3 *
> 7. The number they have *in common* is 3.
> Suppose the numbers are 49 and 98. The LCD would be 49: 49 = 7 * 7; 98 = 7
> * 7 * 2. The numbers they have *in common* are 7 and 7, and 7 * 7 = 49.
>
> Try 45 and 21 for the LCM. What is the smallest number that is a multiple
> of both numbers? 45 = 3 * 3 * 5, 21 = 3 * 7. The LCM = 3 * 3 * 5 * 7 or
> 105. (Each number has a 3, so the first three only counts once. There is an
> extra 3 in 45, plus the 5. 21 still has a 7. Multiply all those together.
> Or let's try 15 and 49. 15 = 3 * 5, 49 = 7 * 7. No numbers in common, so
> multiply them all together. LCM = 3 * 5 * 7 * 7 or 735.
>
> Does that help?
>
> Carolyn Dickinson
> Western Nebraska Community College
> Scottsbluff, Nebraska
>
> On Sat, Feb 6, 2010 at 12:56 PM, George Demetrion <gdemetrion at msn.com>wrote:
>
>
> Good afternoon all.
>
> While I am an experienced adult educator I am a newbie math teacher, but
> I'm plugging away in my first transitions to college basic math course.
>
> We've had two three hour sessions thus far in a 15 week course and things
> are moving along okay.
>
> To be sure I've put a lot of time practicing my math through basic algebra
> and concentrating on the assignments in our weekly sessions.
>
> I'm learning and I'm also getting a good experiential dose of math phobia,
> which in turn, in the process of transforming in the process of learning and
> then drawing on my overall teaching skills, especially incorporating basic
> explanation, a lot of practice and collaborative scaffolding instructional
> processes.
>
> One technical question:
>
> What is the difference between the Lowest (or least) Common Denominator and
> the Least Common Multiple and what different functions do they accomplish?
>
> Keep it simple and straightforward, please.
>
>
> George Demetrion
> East Hartford, CT
>
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