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Teachers' Lounge Discussion: Understanding abbreviations

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From: Jeanne 
To: Teacher2Teacher Public Discussion
Date: 2000062816:50:23
Subject: Re: HELP... Greatest Common Factors

This may sound silly, but one of the first things I do is make sure my
students have read the entire problem.  Some students don't realize
that math problems require reading EVERY word.  These students skim
through and thus miss some important information.

Ask your daughter to read it out loud for you slowly.  This way you
know she's read it, and she can get re-acquainted with the problem
herself.


Here's another silly statement.  I ask "What is 'ugly' about the
problem?" In other words, what is/are stopping the student from
proceeding.  Sometimes it's a not knowing what some of the words mean.
Sometimes it's not understanding the process.  Sometimes it's not
understanding the question. It could be a combination of any of these.


For this particular problem, it critical your daughter know what a
"GCF" is and what is meant by "divisible."


Let's start with the fact that 850 is a "plain ol' common factor" of
those two numbers.  (We'll address the issue of 850 being the
"greatest common factor" in just a bit.)

If 850 is a factor of a number, n then n = 850 times a counting
number, c or n = 850c, for short.  Thus, the two numbers in your
daughter's problem are from the following list of numbers:

       850(1),  850(2),   850(3),   850(4),    850(5),    850(6), ...
(I'll call this list Q for ease of reference.)


Some information:  "greatest common factor"--

Let's look at 850(4) and 850(6).  The number, 850 isn't the GREATEST
common factor because 2 is a common factor to 4 and 6.  These numbers
can be rewritten at 1700(2) and 1700(3), respectively.

This requirement means that we can eliminate some of the numbers from
this
list:  850(multiples of 2, except 2 itself)
       850(multiples of 3, except 3 itself)
       850(multiples of 5, except 5 itself)
          and so on.

What remains of list Q is 850(1),  850(2),   850(3),  850(5) ... where
everything in the parentheses, other than 1 is a prime number.

But this is some fairly advanced thinking, your daughter may not be
ready for this.  If she is, GREAT!



Back to the problem...

List Q:   850(1),  850(2),   850(3),   850(4),    850(5),    850(6),
...


The problem asks for two numbers where (1) 850 is the GCF, (2) one is
not divisible by the other, and (3)they be the smallest numbers.

Ask your daughter to choose two numbers from the list and make sure
the pair she chooses satisfies all three conditions.


Suppose we choose 850(1) and 850(2).
     Condition 1 is met.
     Condition 2 IS NOT met.  850(2) divided by 850(1) is a whole
number. Therefore, these two numbers don't work.

Choose another pair of numbers.

Hope this is helpful.

-Jeanne, for the Teacher2Teacher service


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