Putting Essential Understanding Of Multiplication And Division Into Practice In Grades 3 5

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Putting Essential Understanding of Multiplication and Division Into Practice in Grades 3-5

John Lannin,Kathryn Bouchard Chval,Dusty Jones
Putting Essential Understanding of Multiplication and Division Into Practice in Grades 3 5 Book PDF

Author : John Lannin,Kathryn Bouchard Chval,Dusty Jones
Publisher : Unknown
Page : 173 pages
File Size : 47,9 Mb
Release : 2013-01-01
Category : Division
ISBN : 0873537157

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Putting Essential Understanding of Multiplication and Division Into Practice in Grades 3-5 by John Lannin,Kathryn Bouchard Chval,Dusty Jones Pdf

Do your students believe that division "doesn't make sense" if the divisor is greater than the dividend? Explore rich, researched-based strategies and tasks that show how students are reasoning about and making sense of mulitplication and division. This book focuses on the specialised pedagogical content knowledge that you need to teach multiplication and division effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level maths and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of multiplication and division. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning. About the Series: You have essential understanding. It’s time to put it into practise in your teaching. The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practises for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life and questions for reader reflection open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, understanding into practise, instructional strategies and assessment that pedagogical content knowledge entails. Maximise the potential of student-centred learning and teaching by putting essential understanding into practise.

Putting Essential Understanding of Fractions Into Practice in Grades 3-5

Kathryn Bouchard Chval,John Lannin,Dusty Jones
Putting Essential Understanding of Fractions Into Practice in Grades 3 5 Book PDF

Author : Kathryn Bouchard Chval,John Lannin,Dusty Jones
Publisher : Unknown
Page : 148 pages
File Size : 48,8 Mb
Release : 2013
Category : Fractions
ISBN : 0873537327

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Putting Essential Understanding of Fractions Into Practice in Grades 3-5 by Kathryn Bouchard Chval,John Lannin,Dusty Jones Pdf

Do your students suppose that 1/3 is greater than 1/2, since 3 is greater than 2? Do they believe that having “halves” means having two, and only two, congruent “pieces” of a whole? What tasks can you offer—what questions can you ask—to determine what your students know or don’t know—and move them forward in their thinking? This book focuses on the specialised pedagogical content knowledge that you need to teach fractions effectively in grades 3–5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with fractions—not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of fractions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.

Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5

Albert Dean Otto
Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3 5 Book PDF

Author : Albert Dean Otto
Publisher : National Council of Teachers of English
Page : 84 pages
File Size : 41,9 Mb
Release : 2011
Category : Division
ISBN : 0873536673

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Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5 by Albert Dean Otto Pdf

Unpacking"" the ideas related to multiplication and division is a critical step in developing a deeper understanding. To those without specialised training, many of these ideas might appear to be easy to teach. But those who teach in grades 3-5 are aware of their subtleties and complexities. This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3–5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modelled by multiplication have an element that represents the scalar and an element that represents the quantity to which the scalar applies. Big Idea 2 relates to the algorithms that problem solvers have invented - some of which have become “standard” - for multiplying and dividing. The authors examine the ways in which counting, adding and subtracting lead to multiplication and division, as well as the role that these operations play in algebraic expressions and other advanced topics. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Putting Essential Understanding of Addition and Subtraction Into Practice in Prekindergarten-grade 2

Janet H. Caldwell,Beth McCord Kobett,Karen S. Karp
Putting Essential Understanding of Addition and Subtraction Into Practice in Prekindergarten grade 2 Book PDF

Author : Janet H. Caldwell,Beth McCord Kobett,Karen S. Karp
Publisher : Unknown
Page : 152 pages
File Size : 50,6 Mb
Release : 2014
Category : Addition
ISBN : 0873537300

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Putting Essential Understanding of Addition and Subtraction Into Practice in Prekindergarten-grade 2 by Janet H. Caldwell,Beth McCord Kobett,Karen S. Karp Pdf

Do your students have the incorrect idea that addition “makes numbers bigger” and subtraction “makes numbers smaller”? Do they believe that subtraction is always “taking away”? What tasks can you offer - what questions can you ask - to determine what your students know or don’t know - and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge that you need to teach addition and subtraction effectively in prekindergarten–grade 2. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of addition and subtraction. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning. You have essential understanding. It’s time to put it into practice in your teaching. The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practices for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life, and questions for reader reaction open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at nctm.org/more4U.

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5

Carne Barnett-Clarke
Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3 5 Book PDF

Author : Carne Barnett-Clarke
Publisher : National Council of Teachers of English
Page : 83 pages
File Size : 40,7 Mb
Release : 2010
Category : Mathematics
ISBN : 0873536304

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Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5 by Carne Barnett-Clarke Pdf

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 organised 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.

Teaching Numeracy

Margie Pearse,K. M. Walton
Teaching Numeracy Book PDF

Author : Margie Pearse,K. M. Walton
Publisher : Corwin Press
Page : 241 pages
File Size : 41,7 Mb
Release : 2011-03-23
Category : Education
ISBN : 9781452224404

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Teaching Numeracy by Margie Pearse,K. M. Walton Pdf

Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.

Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2

Barbara J. Dougherty
Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten grade 2 Book PDF

Author : Barbara J. Dougherty
Publisher : Unknown
Page : 60 pages
File Size : 46,7 Mb
Release : 2010
Category : Number concept
ISBN : 0873536290

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Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2 by Barbara J. Dougherty Pdf

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organised around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world. Essential Understanding series topics include: Number and Numeration for Grades Pre-K-2 Addition and Subtraction for Grades Pre-K-2 Geometry for Grades Pre-K-2 Reasoning and Proof for Grades Pre-K-8 Multiplication and Division for Grades 3-5 Rational Numbers for Grades 3-5 Algebraic Ideas and Readiness for Grades 3-5 Geometric Shapes and Solids for Grades 3-5 Ratio, Proportion and Proportionality for Grades 6-8 Expressions and Equations for Grades 6-8 Measurement for Grades 6-8 Data Analysis and Statistics for Grades 6-8 Function for Grades 9-12 Geometric Relationships for Grades 9-12 Reasoning and Proof for Grades 9-12 Statistics for Grades 9-12

Answers to Your Biggest Questions About Teaching Elementary Math

John J. SanGiovanni,Susie Katt,Latrenda D. Knighten,Georgina Rivera
Answers to Your Biggest Questions About Teaching Elementary Math Book PDF

Author : John J. SanGiovanni,Susie Katt,Latrenda D. Knighten,Georgina Rivera
Publisher : Corwin Press
Page : 198 pages
File Size : 53,8 Mb
Release : 2021-09-09
Category : Education
ISBN : 9781071861233

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Answers to Your Biggest Questions About Teaching Elementary Math by John J. SanGiovanni,Susie Katt,Latrenda D. Knighten,Georgina Rivera Pdf

Your guide to grow and learn as a math teacher! Let’s face it, teaching elementary math can be hard. So much about how we teach math today may look and feel different from how we learned it. Today, we recognize placing the student at the center of their learning increases engagement, motivation, and academic achievement soars. Teaching math in a student-centered way changes the role of the teacher from one who traditionally “delivers knowledge” to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity. Whether you are a brand new teacher or a veteran, if you find teaching math to be quite the challenge, this is the guide you want by your side. Designed for just-in-time learning and support, this practical resource gives you brief, actionable answers to your most pressing questions about teaching elementary math. Written by four experienced math educators representing diverse experiences, these authors offer the practical advice they wish they received years ago, from lessons they′ve learned over decades of practice, research, coaching, and through collaborating with teams, teachers and colleagues—especially new teachers—every day. Questions and answers are organized into five areas of effort that will help you most thrive in your elementary math classroom: 1. How do I build a positive math community? 2. How do I structure, organize, and manage my math class? 3. How do I engage my students in math? 4. How do I help my students talk about math? 5. How do I know what my students know and move them forward? Woven throughout, you′ll find helpful sidebar notes on fostering identity and agency; access and equity; teaching in different settings; and invaluable resources for deeper learning. The final question—Where do I go from here?— offers guidance for growing your practice over time. Strive to become the best math educator you can be; your students are counting on it! What will be your first step on the journey?

Your Mathematics Standards Companion, Grades 3-5

Linda M. Gojak,Ruth Harbin Miles
Your Mathematics Standards Companion Grades 3 5 Book PDF

Author : Linda M. Gojak,Ruth Harbin Miles
Publisher : Corwin Press
Page : 360 pages
File Size : 47,6 Mb
Release : 2017-05-17
Category : Education
ISBN : 9781544302331

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Your Mathematics Standards Companion, Grades 3-5 by Linda M. Gojak,Ruth Harbin Miles Pdf

Transforming the standards into learning outcomes just got a lot easier In this expansion of the original popular Common Core Mathematics Companions, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, showing which of your standards are the same as CCSS-M, which differ and how—and which page number to turn to for standards-based teaching ideas. It’s all here, page by page: The mathematics embedded in each standard for a deeper understanding of the content Examples of what effective teaching and learning look like in the classroom Connected standards within each domain so teachers can better appreciate how they relate Priorities within clusters so teachers know where to focus their time The three components of rigor: conceptual understanding, procedural skills, and applications Vocabulary and suggested materials for each grade-level band with explicit connections to the standards Common student misconceptions around key mathematical ideas with ways to address them Sample lesson plans and lesson planning templates Cross-referenced index listing the standards in the following states, explaining what is unique to the standards of each state Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5

Linda M. Gojak,Ruth Harbin Miles
The Common Core Mathematics Companion The Standards Decoded Grades 3 5 Book PDF

Author : Linda M. Gojak,Ruth Harbin Miles
Publisher : Corwin Press
Page : 320 pages
File Size : 49,8 Mb
Release : 2015-05-28
Category : Education
ISBN : 9781483381596

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The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5 by Linda M. Gojak,Ruth Harbin Miles Pdf

This book is modeled after Jim Burke’s successful Common Core Companion Series. It is the second of two books (K-2, 3-5) in the series. The book will include a clear explanation of the mathematics within each domain, cluster, and standard and suggested grade level appropriate visual models and representations. It is a book for math teachers who may or may not be math specialists. As teachers plan and develop their curriculum, this book will help them determine important mathematics in a cluster and how that mathematics connects from one grade to the next as well as within a grade.

Mastering the Basic Math Facts in Multiplication and Division

Susan O'Connell,John SanGiovanni
Mastering the Basic Math Facts in Multiplication and Division Book PDF

Author : Susan O'Connell,John SanGiovanni
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 46,5 Mb
Release : 2011
Category : Arithmetic
ISBN : 0325029628

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Mastering the Basic Math Facts in Multiplication and Division by Susan O'Connell,John SanGiovanni Pdf

Presents an approach to teaching basic math facts to young students, featuring instructional strategies, tips, and classroom activities. Includes a CD-ROM with customizable activities, templates, recording sheets, and teacher tools.

Helping Children Learn Mathematics

National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Helping Children Learn Mathematics Book PDF

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee
Publisher : National Academies Press
Page : 52 pages
File Size : 46,7 Mb
Release : 2002-07-31
Category : Education
ISBN : 9780309131988

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Helping Children Learn Mathematics by National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Mathematics Learning Study Committee Pdf

Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we’re teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre--kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Teaching Multiplication with Lesson Study

Masami Isoda,Raimundo Olfos
Teaching Multiplication with Lesson Study Book PDF

Author : Masami Isoda,Raimundo Olfos
Publisher : Springer Nature
Page : 302 pages
File Size : 44,5 Mb
Release : 2020-11-23
Category : Education
ISBN : 9783030285616

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Teaching Multiplication with Lesson Study by Masami Isoda,Raimundo Olfos Pdf

This open access book is intended to assist teachers, teacher trainers, curriculum designers, editors and authors of textbooks in developing strategies to teach the multiplication of natural numbers based on the experience of the Lesson Study in Japan. This approach to mathematics education dates back to the 1870s and reconciles the emphasis on problem solving with the treatment of the curricular contents. It has gained international recognition since the 1990s and thanks to it mathematics education in Japan has been recognized as one of the most efficient and innovative in the world. This growing international awareness has led to an effort to apply the principles of Lesson Study to other parts of the world and this book shows how experienced authors from Brazil, Chile, Mexico, Spain and Portugal have worked to adapt some of these methods and techniques to the Portuguese and Spanish speaking countries of Ibero-America. Drawing on the impact of Lesson Study on government curriculum decisions and teacher behavior in Japanese classrooms; offering examples of lessons, lesson plans and suggestions for teaching; and presenting examples of the good reception of the principles of Lesson Study in Ibero-America, Teaching Multiplication with Lesson Study – Japanese and Ibero-American Theories for Mathematics Education shows how an efficient and cutting-edge experience in mathematics education can travel the world and help teachers in many different countries.

Modeling Mathematical Ideas

Jennifer M. Suh,Padmanabhan Seshaiyer
Modeling Mathematical Ideas Book PDF

Author : Jennifer M. Suh,Padmanabhan Seshaiyer
Publisher : Rowman & Littlefield
Page : 227 pages
File Size : 49,5 Mb
Release : 2016-12-27
Category : Education
ISBN : 9781475817607

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Modeling Mathematical Ideas by Jennifer M. Suh,Padmanabhan Seshaiyer Pdf

Modeling Mathematical Ideas combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students’ common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students’ strategic competence in modeling mathematical ideas.

Teaching Math to Multilingual Students, Grades K-8

Kathryn B. Chval,Erin Smith,Lina Trigos-Carrillo,Rachel J. Pinnow
Teaching Math to Multilingual Students Grades K 8 Book PDF

Author : Kathryn B. Chval,Erin Smith,Lina Trigos-Carrillo,Rachel J. Pinnow
Publisher : Corwin Press
Page : 317 pages
File Size : 43,8 Mb
Release : 2021-01-07
Category : Education
ISBN : 9781071810835

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Teaching Math to Multilingual Students, Grades K-8 by Kathryn B. Chval,Erin Smith,Lina Trigos-Carrillo,Rachel J. Pinnow Pdf

Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.