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Building learning around rich, instructionally sound contexts was an overarching goal during the development of the Contexts for Learning Mathematics series. Throughout the series context is used to set the stage for learning. It establishes a terrain that will intrigue children and ignite their imaginations. The contexts are situations children can imagine—either realistic or fictional—that enable them to reflect on what they are doing and apply mathematical thinking to their own world. Contexts for investigations are typically developed with stories and pictures. These are carefully crafted to involve students in meaningful investigations of the big ideas, strategies, and models that shape mathematical thinking.
The contexts for the five units in Investigating Multiplication and Division (Grades 3-5) are established through 17 vibrant posters (15" x 24") that meld humor, intrigue, and good math sense.
- The images and texts are engaging and include age-appropriate children using mathematics to solve real-world problems.
- The numbers referenced represent landmark numbers or number relationships that are significant and telling.
- The models and metaphors within a context make relationships and strategies more tangible and explicit.
Groceries, Stamps, and Measuring Strips: Early Multiplication
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. As the unit progresses, formal notation and use of the language of "times" is introduced within the context of measuring buildings and other objects in a city in relation to the height of eight-year-old Antonio, who is four feet tall. For example, a tree is determined to be twelve feet high if it is three times the height of Antonio. Subsequently, making measuring strips invites children to discuss relationships that help them automatize the basic multiplication facts.
The Big Dinner: Multiplication with the Ratio Table
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
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 Teacher's Lounge: Place Value and Division
The stocking of water and juice vending machines in The Teachers' Lounge introduces big ideas related to division. In considering different ways to inventory the contents of each machine, students employ a repertoire of strategies, including the use of the ten-times strategy, partial products and partial quotients, and the distributive property of multiplication over addition-the basis for the long division algorithm. They also examine the relationship between partitive and quotative models of division and explore what to do with remainders in various contexts.
The Box Factory: Extending Multiplication with the Array
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.