Q&A #20527

Fraction Readiness

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 26, 2009 at 14:52:06
Subject: Re: Fraction Readiness

>Students in grades 4,5,6 really seem to struggle with fraction concepts
>such as comparing and ordering fractions, finding equivalent fractions,
>etc.  Is there a "recommended sequence" for developing these concepts?
>What resources/teaching ideas have you found helpful in getting students
>to understand these concepts?


Having only taught sixth grade once, my remarks may not be valid.  
However, this question is one with which high school students 
frequently struggle.  Finding equivalent fractions logically seems to
be the starting point with this development, once the idea of a 
fraction is understood.  I would then follow by comparing fractions to 
see which was greater or less than another. Ordering can be done
once size...greater than or less than...is determined.  If I were faced 
with this situation I would probably do as follows:

The "how-to" for each teacher depends upon teachers' preference 
as well as students' experience.  I like manipulatives and might start 
with squares or circles which are shaded to show the fraction.

Dividing each "part" of the fraction into the same number of parts 
can show that the fraction does not change even though the number 
of parts increase and the size of the part decreases. By taking each 
part (1/demoninator) and subsequently dividing it into N parts you 
can see the visualizaation of 1/denminator becoming n/(n*denominator).  

The entire fraction m/demominator when such changed shows that
 (m)(n/(n* denominator) is equalivant to m/denominator.

What I have written is algebra.  What I would do is try to see what 
happens when I chose integers. Eventually I would hope that students 
would recognize that they are just multiplying by 1, but 1 in its many, 
many forms of n/n.

Typically in comparing fractions students are directed to find a 
common denominator or common multiple for each denominator, 
change each of the fractions to one having the common
denominator and then look at the numerators to see which has 
the greater or lesser number of equivalent parts.  It is changing 
fractions to equivalent fractions; however, the value of 1 or n/n for
each of the fractions will be different.

Once each pair is related to greater than or less than, then the 
ordering is almost implicit.

Since you state grades 4, 5 and 6 for these concepts, I would hope 
that by grade 6, students would understand the ability of looking at 
fractions as ratios. Ffrom this point, there are  less cumbersome
ways to attack comparison and ordering using "Cross-multiplication."  
I put this in quotes because it really is multiplying each numerator by 
the product of the denominators.

High school students frequently do  not understand how to work with 
proportions so doing cumbersome techniques in elementary school 
might lessen difficulties in high school.

Ralph, your question is very appropriate for elementary teachers to 
think about.

 -Marielouise, for the T2T service

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