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- W3163056798 abstract "This chapter begins with the discussion of two major real-life contexts leading to the concept of fraction, as an extension of integer arithmetic, when the division of two integers does not results in an integer: the part-whole context and the dividend-divisor context. The division of integers is typically introduced through two modeling contexts: measurement and partition. One can say that the part-whole and the dividend-divisor contexts for fractions extend, respectively, the measurement and the partition contexts for integers. Consider the relation (6 div 2=3 ). It can be interpreted as measuring, say, six pies by two pies as a way of creating three two-pie gift boxes. Alternatively, this division of six by two can be interpreted as partitioning six pies between two people evenly, so that each person gets three pies. Whereas replacing two by four does not result in an integer number of pies for either the measurement or the partition contexts, fractions are typically introduced when dividing a smaller number by a larger number. Consider the case of dividing 3 by 4. As an extension of integer arithmetic, one can interpret this operation as measuring 3 pies by 4 pies resulting in the number 3/4 which, in the form of abstraction, shows how many times the number 3 includes the number 4. Alternative interpretation of dividing 3 by 4 is partitioning 3 pies among 4 people evenly. This action can demonstrate physically that each person would get 3/4 of a pie. Indeed, each of the three pies can be divided in four pieces and the resulting twelve pieces are then partitioned among four people so that each person gets three pieces of the one-fourth of a pie. The former context of division is called the part-whole context and the latter context of division is called the dividend-divisor context." @default.
- W3163056798 created "2021-05-24" @default.
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- W3163056798 date "2021-01-01" @default.
- W3163056798 modified "2023-10-14" @default.
- W3163056798 title "Modeling Mathematics with Fractions" @default.
- W3163056798 doi "https://doi.org/10.1007/978-3-030-68564-5_4" @default.
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