A Division of Houghton Mifflin Harcourt Heinemann

Investigate Multiplication

Getting Started with Contexts for Learning Mathematics, Grades 3-5

Catherine Twomey Fosnot, City College of New York

ISBN 978-0-325-03748-6 / 0-325-03748-5 / 2010 / 144pp / Bundle
Imprint: FirstHand
Availability: In Stock
Grade Level: 3rd - 5th
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“The rich, open investigations we’ve developed allow children to engage in mathematizing in a variety of ways. We honor children’s initial attempts at structuring and modeling their world mathematically, while at the same time supporting and challenging them to ensure that important big ideas and strategies are being developed progressively.”
—Catherine Twomey Fosnot

Learn how to establish a vibrant, collaborative math workshop for students in grades 3 through 5 and how Catherine Fosnot and her colleagues introduce early multiplication strategies and show students how to work with the ratio table and the distributive property. Through 2 foundational books—Investigating Multiplication and Division: Overview and The Big Dinner: Multiplication with the Ratio Table —and nine online video clips, Cathy and her colleagues provide the strategies, lesson plans, and tools you’ll need to transform your classroom into a community of young mathematicians.

In the Overview book Cathy provides the professional understandings needed to establish a vibrant math workshop. After chronicling the motivations and ideals that inspire her work, Cathy describes how to help students construct the big ideas, strategies, and models that shape the landscape of learning. Ensuing sections describe the architecture of an investigation and explain how the predictability of this framework fosters independence and collaboration. In addition to describing the management systems that make these investigations rigorous and responsive, Cathy suggests ways to sequence instruction and highlight how units can be used to enhance your existing curriculum.

Like the other units in the Contexts for Learning Mathematics series, The Big Dinner: Multiplication with the Ratio Table provides a two-week sequence of investigations, minilessons, games, and other contexts for learning. In this unit 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.

The nine accompanying video clips include live from-the-classroom video footage of the unit in action and narrated slide shows that describe the ideals that shape the math workshop and the thinking behind the Contexts for Learning Mathematics series. (Video clips are free for 6 months upon registration. You must register within 6 months of purchase.)

Learn more about these resources and the series at www.contextsforlearning.com.

This pack is part of firsthand’s Getting Started series.

Bridging the gap between educational theory and practice, firsthand classroom materials model the carefully crafted techniques and language of master teachers in ways that help teachers refine their practice and reinvent their own teaching. The most comprehensive of these resources span more than a year of instruction. Firsthand’s Getting Started Packs were created for teachers in training and professional book study groups who want a compact, affordable way to study and tryout these transformative classroom materials. Each Getting Started Pack includes an overview book, a complete unit of study, online video clips provided free of charge for 6 months, and an accompanying study guide.

Getting Started packs include: Launch a Primary Writing Workshop, Grades K-2; Launch an Intermediate Writing Workshop, Grades 3-5; Launch an Intermediate Reading Workshop, Grades 3-5; Introduce the Qualities of Writing, Grades 3-6; Monitor Comprehension with Primary Students, Grades K-2; Monitor Comprehension with Intermediate Students, Grades 3-6; Investigate the Number System, Grades K-3; Investigate Multiplication, Grades 3-5; Investigate Fractions, Grades 4-6.


Investigating Multiplication and Division: Overview Book
Why We Wrote These Materials
• Mathematics or Mathematizing?
• The Role of Contexts
• The Importance of Emergent Modeling
• From Numeracy to Algebra
Our Teaching and Learning Philosophy
• Depth Versus Breadth
• The Landscape of Learning
— Strategies, Big Ideas, and Models
— Learning as Development
Using the Contexts for Learning Mathematics Materials
• Description of Components
— Overview
— Resources CD-ROM
— Unit Books with Companion Context Resources
— Resource Guides
• Using Contexts for Learning Mathematics with Your Curriculum
— Related Professional Development
Teaching and Learning in a Math Workshop
• Overview and Description
• Developing the Context
• Supporting the Investigation
• Preparing for Math Congress
• Facilitating Math Congress
• Integrating Minilessons, Games, or Routines
• Timeframe
• A Session Walkthrough

The Big Dinner: Multiplication with the Ratio Table
Day One: Pricing the Ingredients The context of preparing a turkey dinner highlights students' early multiplication strategies.
Day Two: Buying the Turkey A math congress gives students a chance to share and discuss their work from Day One.
Day Three: Charts for the Grocer—Turkey A minilesson supports automatization of the basic facts by highlighting number relationships. The investigation and math congress focus on the ratio table and grouping strategies based on distributivity.
Day Four: Charts for the Grocer—Apples and Carrots A minilesson further supports automatization of the basic facts by focusing on number relationships. The investigation offers more experience with the ratio table and grouping strategies based on distributivity.
Day Five: Charts for the Grocer—Apples and Carrots A minilesson provides more practice with automatizing the basic facts. A math congress focuses on ways to add partial products and generalize the distributive property.
Day Six: Charts for the Grocer—Potatoes A minilesson, investigation, and math congress all encourage use of the distributive property over subtraction.
Day Seven: Playing with Nines A minilesson, investigation, and math congress all focus on the patterns that emerge when calculating with the number nine.
Day Eight: Buying the Groceries A minilesson and investigation support students in becoming more flexible in using the distributive property over subtraction.
Day Nine: Cooking the Dinner A minilesson introduces doubling and halving as a helpful strategy for automatizing the basic facts. The investigation encourages the use of various strategies developed in the unit.
Day Ten: Cooking the Dinner A minilesson supports the generalization of the doubling and halving strategy. A math congress gives students a chance to share and discuss their work from Day Nine.
Reflections on the Unit

VIDEO clips from the Resources CD-ROM (9 clips with 6 months of free online access)
• The Thinking Behind Contexts for Learning Math (3:45)
• The Importance of Context (4:27)
• Teaching and Learning in a math Workshop (3:39)
• Establishing a Mathematical Community (4:57)
• Investigation Walkthrough (6:38)
Investigation in Action
• Big Dinner: The Context (2:11)
• Big Dinner: The Investigation (10:39)
• Big Dinner: The Math Congress (5:30)
• Big Dinner: The Teacher Interview (8:21)

In Depth

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Email planningservices@heinemann.com if you would like to contact Catherine Twomey Fosnot directly about professional development support.

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