Developing Essential Understanding Of Multiplication And Division For Teaching Mathematics In Grades 3 5

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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 : 49,5 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 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 : 54,8 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.

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 : 43,9 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.

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 : 52,7 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.

Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5

Maria L. Blanton
Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3 5 Book PDF

Author : Maria L. Blanton
Publisher : Unknown
Page : 102 pages
File Size : 54,5 Mb
Release : 2011
Category : Algebra
ISBN : 0873536681

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Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5 by Maria L. Blanton Pdf

Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten-grade 2

Janet H. Caldwell
Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten grade 2 Book PDF

Author : Janet H. Caldwell
Publisher : National Council of Teachers of English
Page : 85 pages
File Size : 48,5 Mb
Release : 2011
Category : Addition
ISBN : 0873536649

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Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten-grade 2 by Janet H. Caldwell Pdf

What is the relationship between addition and subtraction? How do you know whether an algorithm will always work? Can you explain why order matters in subraction but not in addition or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organised around two big ideas and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining an understanding about addition and subtraction is essential as they are the foundation for students’ later learning of multiplication and division. 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

Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8

Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Developing Essential Understanding of Ratios Proportions and Proportional Reasoning for Teaching Mathematics in Grades 6 8 Book PDF

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 47,5 Mb
Release : 2010
Category : Curriculum planning
ISBN : 0873536223

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Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 by Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles Pdf

"A series for teaching mathematics."--P. [1] of cover.

Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5

Cheryl Rose Tobey,Emily R. Fagan
Uncovering Student Thinking About Mathematics in the Common Core Grades 3 5 Book PDF

Author : Cheryl Rose Tobey,Emily R. Fagan
Publisher : Corwin Press
Page : 249 pages
File Size : 47,6 Mb
Release : 2013-11-27
Category : Education
ISBN : 9781483340203

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Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5 by Cheryl Rose Tobey,Emily R. Fagan Pdf

Take the guesswork out of grades 3-5 math assessment! Quickly pinpoint and reverse your students’ common math difficulties with this detailed and easy-to-follow resource from best-selling authors Cheryl Tobey and Carolyn Arline. Twenty research-based assessment probes help you ask the right questions to uncover just where your students get confused – while learning is already underway. These CCSM-aligned probes eliminate all guesswork and will help you: Systematically address conceptual and procedural mistakes Plan targeted instruction and remediation in multiplication and division, problem solving, the four operations, factorization, and beyond Master essential CCSM mathematical processes and proficiencies for Grades 3-5

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 : 46,5 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

Math Fact Fluency

Jennifer Bay-Williams,Gina Kling
Math Fact Fluency Book PDF

Author : Jennifer Bay-Williams,Gina Kling
Publisher : ASCD
Page : 206 pages
File Size : 45,8 Mb
Release : 2019-01-14
Category : Education
ISBN : 9781416627227

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Math Fact Fluency by Jennifer Bay-Williams,Gina Kling Pdf

This approach to teaching basic math facts, grounded in years of research, will transform students' learning of basic facts and help them become more confident, adept, and successful at math. Mastering the basic facts for addition, subtraction, multiplication, and division is an essential goal for all students. Most educators also agree that success at higher levels of math hinges on this fundamental skill. But what's the best way to get there? Are flash cards, drills, and timed tests the answer? If so, then why do students go into the upper elementary grades (and beyond) still counting on their fingers or experiencing math anxiety? What does research say about teaching basic math facts so they will stick? In Math Fact Fluency, experts Jennifer Bay-Williams and Gina Kling provide the answers to these questions—and so much more. This book offers everything a teacher needs to teach, assess, and communicate with parents about basic math fact instruction, including The five fundamentals of fact fluency, which provide a research-based framework for effective instruction in the basic facts. Strategies students can use to find facts that are not yet committed to memory. More than 40 easy-to-make, easy-to-use games that provide engaging fact practice. More than 20 assessment tools that provide useful data on fact fluency and mastery. Suggestions and strategies for collaborating with families to help their children master the basic math facts. Math Fact Fluency is an indispensable guide for any educator who needs to teach basic math facts.

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 : 43,6 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.

Lessons for Extending Multiplication

Maryann Wickett,Marilyn Burns
Lessons for Extending Multiplication Book PDF

Author : Maryann Wickett,Marilyn Burns
Publisher : Math Solutions
Page : 224 pages
File Size : 40,7 Mb
Release : 2001
Category : Education
ISBN : 9780941355315

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Lessons for Extending Multiplication by Maryann Wickett,Marilyn Burns Pdf

Lessons, games and activities to increase children's multiplication skills.

Number Talks

Sherry Parrish
Number Talks Book PDF

Author : Sherry Parrish
Publisher : Math Solutions
Page : 434 pages
File Size : 43,8 Mb
Release : 2010
Category : Education
ISBN : 9781935099116

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Number Talks by Sherry Parrish Pdf

"A multimedia professional learning resource"--Cover.

Classroom-Ready Rich Math Tasks, Grades 4-5

Beth McCord Kobett,Francis (Skip) Fennell,Karen S. Karp,Delise Andrews,Sorsha-Maria T. Mulroe
Classroom Ready Rich Math Tasks Grades 4 5 Book PDF

Author : Beth McCord Kobett,Francis (Skip) Fennell,Karen S. Karp,Delise Andrews,Sorsha-Maria T. Mulroe
Publisher : Corwin Press
Page : 348 pages
File Size : 40,9 Mb
Release : 2021-04-14
Category : Education
ISBN : 9781071841068

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Classroom-Ready Rich Math Tasks, Grades 4-5 by Beth McCord Kobett,Francis (Skip) Fennell,Karen S. Karp,Delise Andrews,Sorsha-Maria T. Mulroe Pdf

Detailed plans for helping elementary students experience deep mathematical learning Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don’t have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! Classroom Ready-Rich Math Tasks for Grades 4-5 details more than 50 research- and standards-aligned, high-cognitive-demand tasks that will have your students doing deep-problem-based learning. These ready-to-implement, engaging tasks connect skills, concepts and practices, while encouraging students to reason, problem-solve, discuss, explore multiple solution pathways, connect multiple representations, and justify their thinking. They help students monitor their own thinking and connect the mathematics they know to new situations. In other words, these tasks allow students to truly do mathematics! Written with a strengths-based lens and an attentiveness to all students, this guide includes: • Complete task-based lessons, referencing mathematics standards and practices, vocabulary, and materials • Downloadable planning tools, student resource pages, and thoughtful questions, and formative assessment prompts • Guidance on preparing, launching, facilitating, and reflecting on each task • Notes on access and equity, focusing on students’ strengths, productive struggle, and distance or alternative learning environments. With concluding guidance on adapting or creating additional rich tasks for your students, this guide will help you give all of your students the deepest, most enriching and engaging mathematics learning experience possible.

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 : 53,7 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.