Developing essential understanding of rational numbers for teaching mathematics in grades 3-5 / Carne Barnett-Clarke, WestEd, Oakland, California, William Fisher, California State University, Chico, California, Rick Marks, Sonoma State University, Rohnert Park, California, Sharon Ross, California State University, Chico, California ; Randall I. Charles, volume editor , Carmel California.

By: Barnett-Clarke, Carne [author.]Contributor(s): Fisher, William [author.] | Marks, Rick [author.] | Ross, Sharon [author.] | I. Charles, Randall [editor.]Material type: TextTextLanguage: English Series: A Series for Teaching Mathematics | Essential Understanding SeriesPublisher: Reston : National Council of Teachers of Mathematics, 2017Edition: Fifth printing 2017Description: x, 83 pages : illustrations ; 26 cmContent type: text Media type: unmediated Carrier type: volumeISBN: 9780873536301 (paperback)Other title: Developing essential understanding of rational numbers for teaching mathematics in grades three through fiveSubject(s): Numbers, Rational -- Study and teaching (Elementary) | Mathematics -- Study and teaching (Elementary)LOC classification: QA135.6 .D48 2017Subject: By Carne Clarke, William Fisher, Rick Marks, Sharon Ross, Rose Mary Zbiek What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently. https://www.nctm.org/Store/Products/Developing-Essential-Understanding-of-Rational-Numbers-for-Teaching-Mathematics-in-Grades-3-5-(Download)/
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Includes bibliographical references (pages 81-83).

By Carne Clarke, William Fisher, Rick Marks, Sharon Ross, Rose Mary Zbiek

What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades?

How much do you know… and how much do you need to know?

Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean?

This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic.

Focus on the ideas that you need to understand thoroughly to teach confidently.

https://www.nctm.org/Store/Products/Developing-Essential-Understanding-of-Rational-Numbers-for-Teaching-Mathematics-in-Grades-3-5-(Download)/