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>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 Thanks for visiting our on-line community. Visit Teacher2Teacher again at http://mathforum.org/t2t/ It is now possible to make a financial contribution to help The Math Forum. Please read more about this possibility: http://www.drexel.edu/ia/mathforum/.
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