Meaning for Fraction Activity Some critical considerations observations In this activity sequence did we ever know absolute amounts of given quantities NO Yet we were able to conceive a relationship between the size amount of the whole and the parts and to express the size amount of either one in terms of the other This is a conceptually powerful relationship that is independent of the absolute amounts MTE 494 08 26 09 Foundational images and mental operations that generate meaning of fraction Partitioning an amount of something into some number of equal sized parts equipartitioning Iterating duplicating conjoining parts of equal size to make a whole amount of something Comparing the size amount of each part with that of the whole Comparing the size amount of the whole with that of each part Expressing the size of either the whole or each part only in terms of the size of the other MTE 494 08 26 09 A generative conception of fractions This sequence of activities develops a meaning of fractions as reciprocal relationships of relative size Reciprocity is embedded in the fact that thinking of amount A being 1 nth as large as amount B means thinking that amount B is n times as large as A and vice versa Fractions do involve partitioning amounts into some number of parts but the partitions must be of equal size AND the focus must be on thinking of the size of the parts whole in relation to that of the whole parts Fractions are NOT absolute amounts or counts of things MTE 494 08 26 09
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