[Numeracy 139] Re: introductions
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Wed Feb 10 21:18:49 EST 2010
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For learners who struggle with the double negative, but do well in
Language Arts I illustrate it with the double negative in a language
arts context: If I am not not going to the store, what am I doing?
Answer: I must be going to the store. If I am taking out taking out 8,
as in 10 - (-8), then I must be adding it. As very unmath-like as it
is, students who are really verbal start to grasp the issue.
Carol King
Fernley Adult Education
Cking at lyon.k12.nv.us
________________________________
From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On
Behalf Of Mary Jean Wiegert
Sent: Tuesday, February 09, 2010 9:38 AM
To: gdemetrion at msn.com; The Math and Numeracy Discussion List
Subject: [Numeracy 130] Re: introductions
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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