Investigating Multiplication and Division (Grades 3–5)is organized around five classroom-tested units.
Groceries, Stamps, and Measuring Strips: Early Multiplication
by Frans van Galen and Catherine Twomey Fosnot
Groceries, Stamps, and Measuring Strips uses baker’s trays, patio tiles, and other real-world resources to introduce fundamental multiplication strategies. The careful arrangements of these resources invite repeated addition, skip-counting, and doubling strategies, as well as introduce the language of grouping. Measurement strips are used to explore the relationships between products.
The Big Dinner: Multiplication with the Ratio Table
by Catherine Twomey Fosnot
In The Big Dinner the preparation of a turkey dinner introduces early multiplication strategies and supports automatizing the facts, using the ratio table, and developing the distributive property with large numbers. Strings of problems guide learners toward computational fluency with whole-number multiplication and build automaticity with multiplication facts by focusing on relationships.
Muffles’ Truffles: Multiplication and Division with the Array
by Antonia Cameron and Catherine Twomey Fosnot
A chocolatier’s efforts to cope with the operational challenges of running a truffle shop (counting, pricing, and labeling assorted boxes of chocolates) in Muffles’ Truffles introduces students to the open array as a model for multiplication and division. A series of investigations explore place value—the multiplicative structure of our base-ten system and quotative division—and big ideas in multiplication, including the distributive, associative, and commutative properties.
The Teachers’ Lounge: Place Value and Division
by Chris Natale and Catherine Twomey Fosnot
The stocking of water and juice vending machines in The Teachers’ Lounge introduces big ideas related to division. As students consider different ways to inventory the contents of each machine, they employ a repertoire of strategies, including the use of the ten-times strategy, partial products and partial quotients, the associative property, and the distributive property of multiplication over addition— the basis for the long-division algorithm.
The Box Factory: Extending Multiplication with the Array
by Miki Jensen and Catherine Twomey Fosnot
The focus of The Box Factory is the deepening and extending of students’ understanding of multiplication, specifically the associative and commutative properties and their use with computation; systematic factoring; and the extension of students’ understanding of two-dimensional rectangular arrays to three-dimensional arrays within rectangular prisms. The concepts are explored within the context of a box factory where boxes are designed to meet specific size and space requirements.
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