Division Quilts: A Measurement Model

  • Division Quilts: A Measurement Model

    Sarah S. Pratt, Tina M. Lupton, and Kerri Richardson
    Students can create an image of the measurement model of division as an alternative to the long-division algorithm.
    When division is taught as an algorithm in isolation, student understanding of it has limited flexibility. Current expectations in mathematics education include that students should be able to identify and use relationships between operations (NCTM 2000, Common Core State Standards for Mathematics [CCSSM] CCSSI 2011). As teachers seek activities to assist students in understanding division as more than just the algorithm, they find many examples of division as fair sharing. In actuality, Fischbein and his colleagues (1985) defined two types of whole-number division: partitive (fair sharing) and quotative (measurement). Students are able to engage in activities that draw on their intuitive sense of what it means to share fairly; however, teachers have few activities to engage students in a quotative (measurement) model of division. Division Quilts is one such activity that allows students to connect to their understandings of quotative division, thereby enhancing their understandings of the operation of division. Furthermore, engaging in both forms of division models gives students opportunities to connect in rich ways when presented with the division algorithm.
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