Investigate Fractions by Catherine Twomey Fosnot. Getting Started
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Investigate Fractions

Investigate Fractions

Getting Started with Contexts for Learning Mathematics, Grades 4-6

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 students in grades 4 through 6 and how Catherine Fosnot and her colleagues introduce fractions and compare fractional amounts. Through 2 foundational books—Investigating...

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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 students in grades 4 through 6 and how Catherine Fosnot and her colleagues introduce fractions and compare fractional amounts. Through 2 foundational books—Investigating Fractions, Decimals, and Percents: Overview and Field Trips and Fund-Raisers: Introducing Fractions—and eight 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, Field Trips and Fund-Raisers: Introducing Fractions provides a two-week sequence of investigations, minilessons, games, and other contexts for learning. The fair-sharing of submarine sandwiches on a school field trip provides the context for exploring big ideas related to fractions in this unit. In attempting to settle arguments about the fair distribution of sandwiches, students explore the connection between division and fractions as well as ways to compare fractional amounts. As the unit progresses, students use the double number line as a model and explore equivalent fractions.

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 Fractions, Decimals, and Percents: 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

Field Trips and Fund-Raisers: Introducing Fractions
Day One: The Field Trip
The context of fair-sharing submarine sandwiches supports the development of several big ideas related to fractions.
Day Two: The Field Trip A math congress gives students a chance to share and discuss their work from Day One.
Day Three: Redistribution A minilesson encourages the use of partial products and the fair-sharing context extends to an investigation that involves redistributing.
Day Four: Redistribution A minilesson highlights a common misconception about adding fractions. A math congress gives students a chance to share and discuss their work from Day Three.
Day Five: Working with Landmarks The fair-sharing context extends to an investigation that involves using landmark fractions to judge the magnitude of other fractional amounts.
Day Six: Discussing Strategies A math congress gives students a chance to share and discuss their work from Day Five.
Day Seven: Developing Equivalence A minilesson focuses on fractions as operators and the ratio table helps students develop strategies to make equivalent fractions.
Day Eight: The Fund-Raiser A minilesson encourages simplifying when dividing. The context of designing a bike course supports the development of a measurement model for fractions.
Day Nine: The Fund-Raiser A minilesson revisits simplifying when dividing. The bike course investigation concludes with an exploration of equivalent relationships.
Day Ten: Fraction Bar Capture The Fraction Bar Capture game gives students more experience with determining equivalent relations.
Reflections on the Unit

VIDEO clips from the Resources CD-ROM (8 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
• Field Trips: The Context (13:52)
• Field Trips: The Investigation (10:05)
• Field Trips: The Math Congress (17:10)