Investigate the Number System by Catherine Twomey Fosnot. Getting
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Investigate the Number System

Investigate the Number System

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

By Catherine Twomey Fosnot

"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 primary students and how Catherine Fosnot and her colleagues introduce students to place value patterns and develop efficient addition strategies. Through 2 foundational...

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Full Description

"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 primary students and how Catherine Fosnot and her colleagues introduce students to place value patterns and develop efficient addition strategies. Through 2 foundational books—Investigating Number Sense, Addition, and Subtraction: Overview and Organizing and Collecting: The Number System—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 Overviewbook 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, Organizing and Collecting provides a two-week sequence of investigations, minilessons, games, and other contexts for learning. In this unit the hopelessly disorganized Masloppy family’s efforts to inventory their possessions create a context for investigating place value patterns and efficient ways to count with five- and ten-structures. As the unit progresses, children develop place value and addition strategies.

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.

Contents

Investigating Number Sense, Addition, and Subtraction: Overview
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
Establishing a Mathematical Community

Organizing and Collecting: The Number System
Unit Overview
Day One: Taking Inventory The context of organizing and taking inventory highlights children's early strategies for counting and keeping track.
Day Two: Continuing the Inventory The inventory investigation continues and the subsequent math congress gives children a chance to discuss and share their work.
Day Three: Making Packs of Ten A minilesson of quick images supports children in developing more efficient counting strategies. The investigation encourages children to consider grouping as a way to count more efficiently.
Day Four: Making the Class Inventory Chart?A math congress focuses on the place value patterns that occur when making groups of ten. The subsequent investigation gives children an opportunity to explore those patterns further.
Day Five: Adding to the Class Inventory Chart A math congress gives children a chance to discuss and share their work from Day Four. The investigation involves children in figuring out how to get to the next multiple of ten.
Day Six: Recording the Orders for Full Packs and Playing Tossing for Tens A math congress highlights some new place value patterns. The Tossing for Tens game helps children to learn and develop fluency with combinations of ten, using two or more addends.
Day Seven: Making Packs of Five The investigation and math congress highlight the relationship between the five- and the ten-structures of our number system.
Day Eight: Collecting Stamps?The Collecting Stamps game and subsequent math congress focus on helpful strategies for addition.
Day Nine: Completing the Inventory with New Orders A minilesson of quick images builds on the place value patterns children have explored during their inventory work. The investigation and math congress explore using place value patterns when adding multiples of ten.
Day Ten: Games?A minilesson of quick images focuses on adding ten to a number. The Collecting Stamps game provides further opportunities to employ strategies developed throughout the unit.

VIDEO clips from the Resources CD-ROM (9 clips with 6 months of free online access)

Introduction
• 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
• Organizing and Collecting: The Context (2:09)
• Organizing and Collecting: The Investigation (9:37)
• Organizing and Collecting: The Math Congress (8:17)
• Organizing and Collecting: The Teacher Interview (12:51)