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
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Author : Albert Dean Otto
language : en
Publisher: National Council of Teachers of English
Release Date : 2011
Developing Essential Understanding Of Multiplication And Division For Teaching Mathematics In Grades 3 5 written by Albert Dean Otto and has been published by National Council of Teachers of English this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Division categories.
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 Multiplication And Division Into Practice In Grades 3 5
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Author : John Lannin
language : en
Publisher:
Release Date : 2013-01-01
Putting Essential Understanding Of Multiplication And Division Into Practice In Grades 3 5 written by John Lannin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Division categories.
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 Addition And Subtraction For Teaching Mathematics In Prekindergarten Grade 2
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Author : Janet H. Caldwell
language : en
Publisher: National Council of Teachers of English
Release Date : 2011
Developing Essential Understanding Of Addition And Subtraction For Teaching Mathematics In Prekindergarten Grade 2 written by Janet H. Caldwell and has been published by National Council of Teachers of English this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Addition categories.
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
Putting Essential Understanding Of Fractions Into Practice In Grades 3 5
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Author : Kathryn Bouchard Chval
language : en
Publisher:
Release Date : 2013
Putting Essential Understanding Of Fractions Into Practice In Grades 3 5 written by Kathryn Bouchard Chval and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Fractions categories.
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 Number And Numeration For Teaching Mathematics In Prekindergarten Grade 2
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Author : Barbara J. Dougherty
language : en
Publisher:
Release Date : 2010
Developing Essential Understanding Of Number And Numeration For Teaching Mathematics In Prekindergarten Grade 2 written by Barbara J. Dougherty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Number concept categories.
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
Planting The Seeds Of Algebra 3 5
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Author : Monica Neagoy
language : en
Publisher: Corwin Press
Release Date : 2014-12-23
Planting The Seeds Of Algebra 3 5 written by Monica Neagoy and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-23 with Education categories.
'Planting the Seeds of Algebra, 3-5' will empower teachers with theoretical and practical knowledge about both the content and pedagogy of algebraic instruction, and shows them the different faces of algebra as it appears in the early grades.
Numeracy And Learning Difficulties
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Author : Peter Westwood
language : en
Publisher: ACER Press
Release Date : 2016-09-01
Numeracy And Learning Difficulties written by Peter Westwood and has been published by ACER Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-01 with Education categories.
Drawing on research from the fields of developmental and cognitive psychology, Peter Westwood presents a case for high-quality 'first teaching' to prevent students failing in the initial acquisition of numeracy skills.
Investigate Multiplication
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Author : Catherine Twomey Fosnot
language : en
Publisher: Firsthand
Release Date : 2010-10
Investigate Multiplication written by Catherine Twomey Fosnot and has been published by Firsthand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10 with Education categories.
"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 3 through 5 and how Catherine Fosnot and her colleagues introduce early multiplication strategies and show students how to work with the ratio table and the distributive property. Through 2 foundational books-Investigating Multiplication and Division: Overview and The Big Dinner: Multiplication with the Ratio Table -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 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, The Big Dinner: Multiplication with the Ratio Table provides a two-week sequence of investigations, minilessons, games, and other contexts for learning. In this unit the preparation of a turkey dinner introduces early multiplication strategies and supports automatizing the facts, using the ratio table, and developing the distributive property with large numbers. Strings of problems guide learners toward computational fluency with whole-number multiplication and build automaticity with multiplication facts by focusing on relationships. 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.
Unpacking Fractions
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Author : Monica Neagoy
language : en
Publisher: ASCD
Release Date : 2017-03-10
Unpacking Fractions written by Monica Neagoy and has been published by ASCD this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-10 with Education categories.
For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.
Modeling Mathematical Ideas
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Author : Jennifer M. Suh
language : en
Publisher: Rowman & Littlefield
Release Date : 2016-12-27
Modeling Mathematical Ideas written by Jennifer M. Suh and has been published by Rowman & Littlefield this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-27 with Education categories.
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.