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ERIC Number: EJ1074791
Record Type: Journal
Publication Date: 2015-Sep
Pages: 8
Abstractor: ERIC
ISSN: ISSN-1073-5836
Division Quilts: A Measurement Model
Pratt, Sarah S.; Lupton, Tina M.; Richardson, Kerri
Teaching Children Mathematics, v22 n2 p102-109 Sep 2015
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. However, teachers have few activities to engage students in a quotative (measurement) model of division. Efraim Fischbein and his colleagues (1985) defined two types of whole-number division: partitive (fair sharing) and quotative (measurement). It is this second type of division that the authors present in "Division Quilts." This activity will allow students to connect to their understandings of quotative division, thereby enhancing their understandings of the operation of division. The authors present a model that teachers can use to assist students in connection with everyday experiences; that demonstrates using manipulatives; and relates to their understanding that each group must receive the same amount. The model also shows division as repeated subtraction, which connects as an inverse operation to multiplication as a recursive process. Engaging in both forms of division models gives students opportunities to connect in rich ways when presented with the division algorithm.
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Grade 5; Intermediate Grades; Middle Schools; Elementary Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A