[Numeracy 114] Re: introductions
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Sun Feb 7 20:08:52 EST 2010
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George,
I would say that your method of finding the LCM and thus the LCD using
prime factorization is the precursor to what will need to be done
when the student encounters algebraic fractions with variables
( denominators with xzy). I would stick with it if they understand
it and are headed to Algebra. The concept will transfer better. This
method is taught in Pre-Algebra as opposed to the other method which
is taught when addition and subtraction of fractions are initially
taught in the upper elementary grades. The way it is taught
initially, as in Barbara's example, works just fine in many problems
we solve as adults.... most things involving measuring, eg, sewing,
building, and cooking. In these situations, the fractions are simple
and use constant numerals. So... it depends on where your students
are headed I would say.
Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net
On Feb 7, 2010, at 12:53 PM, George Demetrion wrote:
> Thanks Barbara,
>
> From what I'm gathering is based on what you are laying out here is
> that the least common multiple is the least common denominator, but
> is a different way than prime factorization to get there.
>
> In terms of instructional usefulness (and I'll know more once we're
> actually on the topic), I'm assuming prime factoring for adding or
> subtracting fractions with different numbers is important in finding
> the Lowest Common Denominator. Where that becomes difficult,
> following the methodology you describe below provides an
> alternative. Fortunately, my AM students get prime factorization so
> should be able to solve for the LCD.
>
> In terms of my own mastery it took me a fair amount of time to get
> prime factorization and calculate accurately; to get LCD and and
> Greatest Common Factor (a method for reducing fractions) and then to
> truly get what their purposes were.
>
> Thus far, when explaining and practicing with prime factorization
> the students readily get it. Whether that is due to (1) the care
> I've taken in seeking both to grasp the purposes of these procedures
> as well as to master them through a great deal of practice; (2) to
> the innate learning strengths of the students themselves, or (3)
> some combination thereof would make an interesting teacher research
> project. What I do sense is that straight forward and accurate
> explanation of procedure and purpose of any given function or
> operation is useful combined with a lot of practice, and working
> with students through their strengths and at any current level of
> mastery. Longer term, building increasing math awareness as a
> metacognitive capacity (in my case as a newbie within myself as well
> as within the students) is also an important pedagogical goal that
> I'll be working on through the course.
>
> George Demetrion
>
>
> From: bamurr at metrocast.net
> To: gdemetrion at msn.com; numeracy at nifl.gov
> Subject: Re: [Numeracy 109] introductions
> Date: Sat, 6 Feb 2010 18:22:16 -0500
>
> The least common multiple is used to find the lowest common
> denominator.
>
> Example: Add 1/2 + 1/3 + 1/4 + 1/6
>
> The multiples:
> of 2 are 2 4 6 8 10 12 14 16 18 20 22 24. . .
> of 3 are 3 6 9 12 15 18 21 24 . . .
> of 4 are 4 8 12 16 20 24. . .
> of 6 are 6 12 18 24 . . .
>
> The least common multiple is 12 and this is also the lowest common
> denominator. Notice that 24 is also a common multiple, but it is
> not the least common multiplie. It is also not the lowest common
> denominator, although it would be A common denominator.
>
> 1/2 = 6/12
> 1/3 = 4/12
> 1/4 = 3/12
> 1/6 = 2/12
>
> The sum is 15/12 = 1 3/12 = 1 1/4
>
> ----- Original Message -----
> From: George Demetrion
> To: numeracy at nifl.gov
> Sent: Saturday, February 06, 2010 2:56 PM
> Subject: [Numeracy 109] introductions
>
>
> 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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