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The focus of this unit is the development of fractions. It begins with the story of a class field trip. The class is split into four groups and each group is given submarine sandwiches to share for lunch. Upon returning from their trip, the students quarrel over whether some received more to eat than others.
Note: This unit begins with the fair sharing of submarine sandwiches on a field trip. This context was field-tested by the Freudenthal Institute and the University of Wisconsin, under the direction of Thomas Romberg and Jan de Lange, in preparation for the writing of Mathematics in Context: Some of the Parts (van Galen, Wijers, Burrill, and Spence 1997) and it has been researched and written about extensively as it is used in this unit by Fosnot and Dolk (2002).
This story sets the stage for a series of investigations. First, students investigate whether the situation in the story was fair - was the quarreling justified? - thereby exploring the connection between division and fractions, as well as ways to compare fractional amounts. As the unit progresses, students explore other cases to determine fair sharing and then make a ratio table to ensure fair sharing during their future field trips. They also design a 60k bike course for a fund-raiser, a context that introduces a bar model for fractions and provides students with another opportunity to explore equivalent fractions.
Several minilessons for division of whole numbers using simplified equivalents are also included in the unit. These are structured using strings of related problems as a way to more explicitly guide learners toward computational fluency with whole number division and to build a connection to equivalent fractions.
Note: The context for this unit assumes that your students have had prior experience with arrays for multiplication and division, as well as partitive and quotative division with whole numbers. If this is not the case, you might find it helpful to first use The Teachers' Lounge and Minilessons Throughout the Year: Multiplication and Division from Investigations in Multiplication and Division: Grades 3 - 5.
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