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Q&A #5988


Adding and subtracting fractions

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From: Gail (for Teacher2Teacher Service)
Date: Mar 19, 2001 at 07:24:31
Subject: Re: Adding and subtracting fractions

I have an unusual approach to this for my fifth grade students, and they have 
had some wonderful successes building number sense...

I have my students use a fraction chart or fraction pieces/bars to list out
several equivalent fractions for each of the fractions in the problem.
Then, they are free to select one fraction from each "set" to use to solve
the problem.  Here is how it works:

     1/2   2/4   3/6   4/8   5/10   6/12
   + 3/12  1/4                      3/12
   ______

            They can choose to add 6/12 and 3/12, or 2/4 and 1/4.  Either
one will get them the correct answer, and the benefit of using 2/4 and 1/4 is
they won't have a fraction that has such large terms...

Here is another example:

  10/12   5/6
- 5/10    3/6   4/8   2/4   1/2
________  The way "we" would have solved as this fifth graders would have
been to list out the multiples of 12 and 10, and then find the least common
multiple...   60...   so the new problem would have been

  50/60
- 30/60    which doesn't seem like such a tough problem,
_______         but 20/60 is not in lowest terms (though, it isn't hard to
                     simplify)


My students would do 5/6 - 3/6 and get 2/6, which is familiar to them, and
they would have little trouble recognizing it is 1/3.

Let me preface all this by saying that my students found equivalent
fractions in this same way, using fraction charts and pieces...  then looking 
for similarities in the sets.  They "discovered" ways to name equivalent
fractions using what they noticed about the fractions in the sets...

When they looked at all the "halves" they noticed that the numerator was
always half as large as the denominator...   the thirds had a "third as
large" relationship, and so on...   After some experimenting, they decided
they could multiply to find the equivalent fractions, just like we do.

I would encourage you to let them select their equivalent fractions the way
I have shown.  There is no reason I can think of why they should HAVE to use
the least common denominator, when they are demonstrating great fraction
sense by finding several options.

 -Gail, for the T2T service

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