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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? Ralph, 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 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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