Q&A #20527

Fraction Readiness

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From: Gail (for Teacher2Teacher Service)
Date: Dec 21, 2009 at 23:17:14
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?

I taught elementary school for quite a while before moving "up" to middle 
school...   and I think part of the reason students have so much trouble is 
related to what Pat says.  They don't have enough experience with what the 
fraction means, prior to jumping into activities that cause them to think 
abstractly about the fractions.  I wish teachers in the elementary grades 
would take more time with models of fractions, many different models, that 
would help students build an understanding of what it means to be "one half" 
or "two thirds" or "five eights" of something.  

Once students are able to demonstrate their understanding by identifying the 
fractions shown in models, and creating models to show given fractions, then 
they are ready to compare models, and determine equivalence.  This should 
still be done concretely and semi-concretely, not abstractly by finding 
common denominators.  Students can use what they find about equivalent 
amounts to make "rules" about how to rename fractions (find common 
denominators), and how to compare fractions (using benchmarks like 0, 1/2 
and 1, and by looking at common numerators as well as denominators).

One of the exploring activities I used to do with my fourth graders involved 
using fraction strips or bars to find all of the pieces that named the same 
size amounts…   ½ was usually where students chose to begin, and I would 
write all of the equivalent fractions as equations, recording my students’ 
observations…   ½ = 2/4, ½ = 3/6, ½ = 6/12, etc.  Then we would “step back” 
and see what we noticed.   Usually the first thing they would say is that 
the numerator was always half of the denominator for these fractions…  and 
the next observation was usually that if you multiplied the denominator “2” 
by the other numerator, you got the denominator of the second fraction.  
While I was glad to see them noticing this, I didn’t really want them to 
make that a “rule”, so I chose a non-unit fraction (like 2/3) for the next 
set, to see if all of our observations worked each time…

 -Gail, for the T2T service

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