## Muffles' Truffles: Multiplication and Division with the Array (Contexts for Learning Mathematics)

### Antonia Cameron; Catherine Twomey Fosnot

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Muffle's Truffles: Multiplication and Division with the Array is one of five units in the Contexts for Learning Mathematics' Investigating Multiplication and Division (3 - 5)    The focus of this unit is the development of the open array as a model for multiplication and division. This unit uses a series of investigations based on the context of Muffles' Truffles shop. The questions posed in the first investigation (how many boxes of ten can be made with a given quantity of truffles; how many leftovers will there be from a given quantity and how can they be combined to make assortment boxes; and what is the cost of a given quantity of truffles if they cost \$1 each) give students an opportunity to explore place value - the multiplicative structure of our base-ten system and quotative division. In the second and third investigations, students build two-dimensional blueprints of one-layer boxes and use these arrays to explore some of the big ideas in multiplication (the distributive, associative, and commutative properties). In the fourth and final investigation, students work with open arrays in the context of labeling and pricing wrapped boxes of truffles. To figure out the dimensions of the wrapped boxes (or open arrays) and the cost, students need to apply a number of big ideas previously developed in this unit.   There are three different kinds of minilessons for multiplication included in the unit as well: counting around the circle, strings of related problems, and quick images. The count-around is used to support the development of place value as it relates to multiplication. The strings of related problems are explicitly designed to guide learners toward computational fluency with whole number multiplication and to build automaticity with multiplication facts by focusing on relationships. The quick images use 2 x 5 and 1 x 5 arrays as units to build larger arrays. In the last days of the unit, more complex minilessons (double-digit multiplication problems) generate a wider range of student strategies that can be explored (and modeled) with the open array.   To learn more visit http://www.contextsforlearning.com

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Antonia Cameron is a Master Coach for K-6 Mathematics at Metamorphosis. Former co-director of Mathematics in the City, a national center for professional development at The City College of New York, Toni is coauthor of numerous facilitator guides and Contexts for Learning unit books. She is a nationally known mathematics "coaching coach" and speaker on professional development practices.

Catherine Twomey Fosnot is the Founding Director of Mathematics in the City and former Professor of Education at The City College of the City of New York. She has twice received the "best writing" award from AERA's Constructivist SIG and she was the recipient of the "young scholar" award by Educational Communication and Technology Journal. She is the lead author of the Contexts for Learning Mathematics series as well as the Young Mathematicians at Work series.

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## 1.Muffles Truffles: Multiplication and Division with the Array (Paperback)

ISBN 10: 0325010196 ISBN 13: 9780325010199
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Book Description Heinemann USA, United States, 2008. Paperback. Book Condition: New. Language: English . Brand New Book. Muffle s Truffles: Multiplication and Division with the Array is one of five units in the Contexts for Learning Mathematics Investigating Multiplication and Division (3 - 5) The focus of this unit is the development of the open array as a model for multiplication and division. This unit uses a series of investigations based on the context of Muffles Truffles shop. The questions posed in the first investigation (how many boxes of ten can be made with a given quantity of truffles; how many leftovers will there be from a given quantity and how can they be combined to make assortment boxes; and what is the cost of a given quantity of truffles if they cost \$1 each) give students an opportunity to explore place value - the multiplicative structure of our base-ten system and quotative division. In the second and third investigations, students build two-dimensional blueprints of one-layer boxes and use these arrays to explore some of the big ideas in multiplication (the distributive, associative, and commutative properties). In the fourth and final investigation, students work with open arrays in the context of labeling and pricing wrapped boxes of truffles. To figure out the dimensions of the wrapped boxes (or open arrays) and the cost, students need to apply a number of big ideas previously developed in this unit. There are three different kinds of minilessons for multiplication included in the unit as well: counting around the circle, strings of related problems, and quick images. The count-around is used to support the development of place value as it relates to multiplication. The strings of related problems are explicitly designed to guide learners toward computational fluency with whole number multiplication and to build automaticity with multiplication facts by focusing on relationships. The quick images use 2 x 5 and 1 x 5 arrays as units to build larger arrays. In the last days of the unit, more complex minilessons (double-digit multiplication problems) generate a wider range of student strategies that can be explored (and modeled) with the open array. To learn more visit //. Bookseller Inventory # AAC9780325010199

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## 2.Muffles' Truffles: Multiplication and Division with the Array

ISBN 10: 0325010196 ISBN 13: 9780325010199
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Book Description 2008. PAP. Book Condition: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Bookseller Inventory # IB-9780325010199

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## 3.Muffles Truffles: Multiplication and Division with the Array (Paperback)

ISBN 10: 0325010196 ISBN 13: 9780325010199
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Book Description Heinemann USA, United States, 2008. Paperback. Book Condition: New. Language: English . Brand New Book. Muffle s Truffles: Multiplication and Division with the Array is one of five units in the Contexts for Learning Mathematics Investigating Multiplication and Division (3 - 5) The focus of this unit is the development of the open array as a model for multiplication and division. This unit uses a series of investigations based on the context of Muffles Truffles shop. The questions posed in the first investigation (how many boxes of ten can be made with a given quantity of truffles; how many leftovers will there be from a given quantity and how can they be combined to make assortment boxes; and what is the cost of a given quantity of truffles if they cost \$1 each) give students an opportunity to explore place value - the multiplicative structure of our base-ten system and quotative division. In the second and third investigations, students build two-dimensional blueprints of one-layer boxes and use these arrays to explore some of the big ideas in multiplication (the distributive, associative, and commutative properties). In the fourth and final investigation, students work with open arrays in the context of labeling and pricing wrapped boxes of truffles. To figure out the dimensions of the wrapped boxes (or open arrays) and the cost, students need to apply a number of big ideas previously developed in this unit. There are three different kinds of minilessons for multiplication included in the unit as well: counting around the circle, strings of related problems, and quick images. The count-around is used to support the development of place value as it relates to multiplication. The strings of related problems are explicitly designed to guide learners toward computational fluency with whole number multiplication and to build automaticity with multiplication facts by focusing on relationships. The quick images use 2 x 5 and 1 x 5 arrays as units to build larger arrays. In the last days of the unit, more complex minilessons (double-digit multiplication problems) generate a wider range of student strategies that can be explored (and modeled) with the open array. To learn more visit //. Bookseller Inventory # AAC9780325010199

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## 4.Muffles' Truffles: Multiplication and Division with the Array (Contexts for Learning Mathematics)

ISBN 10: 0325010196 ISBN 13: 9780325010199
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Book Description FirstHand, 2008. Paperback. Book Condition: New. Never used!. Bookseller Inventory # 0325010196

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## 5.Mufflesandapos; Truffles: Multiplication and Division with the Array

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Book Description Heinemann USA, 2008. PAP. Book Condition: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Bookseller Inventory # IB-9780325010199

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## 6.Muffles' Truffles: Multiplication and Division With the Array

ISBN 10: 0325010196 ISBN 13: 9780325010199
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Book Description Firsthand, 2008. Paperback. Book Condition: Brand New. 64 pages. 10.60x8.20x0.70 inches. In Stock. Bookseller Inventory # x-0325010196

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## 7.Muffles' Truffles: Multiplication and Division with the Array (Paperback)

ISBN 10: 0325010196 ISBN 13: 9780325010199
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Book Description Paperback. Book Condition: New. Paperback. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 64 pages. 0.181. Bookseller Inventory # 9780325010199

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## 8.Muffles' Truffles: Multiplication and Division with the Array

ISBN 10: 0325010196 ISBN 13: 9780325010199
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Book Description Heinemann USA. Paperback / softback. Book Condition: new. BRAND NEW, Muffles' Truffles: Multiplication and Division with the Array, Antonia Cameron, Catherine Twomey Fosnot. Bookseller Inventory # B9780325010199

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## 9.Muffles' Truffles: Multiplication and Division with the Array (Contexts for Learning Mathematics)

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## 10.Muffles' Truffles: Multiplication and Division with the Array (Context for Learning Mathematics: Grade 3-5)

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Book Description FirstHand, 2008. Paperback. Book Condition: New. Bookseller Inventory # DADAX0325010196