[Numeracy 130] Re: introductions

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Mary Jean Wiegert underwiegert at gmail.com
Tue Feb 9 12:38:23 EST 2010


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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