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The five units in Investigating Multiplication and Division (Grades 3-5) explore with increasing sophistication big ideas in multiplication and division including factoring and the distributive, associative, and commutative properties, as well as their use in computation.

  1. Groceries, Stamps, and Measuring Strips: Early Multiplication
    by Frans van Galen and Catherine Twomey Fosnot
    Using baker's trays, postage stamps, patio tiles, and other realistic contexts, Groceries, Stamps, and Measuring Strips introduces fundamental multiplication strategies. Carefully-crafted arrangements of real-world resources invite repeated addition, skip-counting, and doubling strategies as well as introducing the language of grouping.As the unit progresses, students make a set of measurement strips (for the multiplication tables) and use them to explore the relationships between the products.
  2. The Big Dinner: Multiplication with the Ratio Table
    by Catherine Twomey Fosnot
    In The Big Dinner, the context of preparing a turkey dinner highlights students' early multiplication strategies, and supports automatizing the facts, using the ratio table, and developing the distributive property with large numbers. Strings of related problems guide learners toward computational fluency with whole-number multiplication and build automaticity with multiplication facts by focusing on relationships.
  3. 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 explores and applies 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.
  4. 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.
  5. 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 against the context of a box factory where students design boxes to meet specific size and space requirements.

Grades K–3
Grades 3–5
Grades 4–6