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.
The Mathematics Lesson Planning Handbook Grades 3 5
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Author : Ruth Harbin Miles
language : en
Publisher: Corwin Press
Release Date : 2018-07-13
The Mathematics Lesson Planning Handbook Grades 3 5 written by Ruth Harbin Miles and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-13 with Education categories.
"This book brings together the best of Visible Learning and the teaching of mathematics. The chapters on learning intentions, success criteria, misconceptions, formative evaluation, and knowing thy impact are stunning. Rich in exemplars, grounded in research about practice, and with the right balance about the surface and deep learning in math, it′s a great go-to book for all who teach mathematics." —John Hattie, Laureate Professor, Deputy Dean of MGSE, Director of the Melbourne Education Research Institute, Melbourne Graduate School of Education YOU are the architect in the mathematics classroom. When it comes to mathematics lessons, do you sometimes feel overly beholden to the required texts from which you teach? Do you wish you could break the mold, but feel like you get conflicting guidance on the "right" things to do? How often do you find yourself in the last-minute online scramble for a great task activity that will capture your students′ interest and align to your state standards? In The Mathematics Lesson-Planning Handbook, Grades 3–5: Your Blueprint for Building Cohesive Lessons, you’ll learn the streamlined decision-making processes that will help you plan the focused, research-based, standards-aligned lessons your students need. This daily reference offers practical guidance for when and how to pull together mathematics routines, resources, and effective teaching techniques into a coherent and manageable set of lesson plans. This resource will Lead teachers through a process of lesson planning based on various learning objectives Set the stage for lesson planning using relatable vignettes Offer sample lesson plans for Grades 3–5 Create opportunities to reflect on each component of a mathematics lesson Suggest next steps for building a unit from the lessons Provide teachers the space and tools to create their own lesson plans going forward Based on years of classroom experience from seasoned mathematics educators, this book brings together the just-in-time resources and practical advice you need to make lesson planning simple, practical, and doable. From laying a solid foundation to choosing the right materials, you’ll feel confident structuring lessons that lead to high student achievement.
Developing Essential Understanding Of Proof And Proving For Teaching Mathematics In Grades 9 12
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Author : Amy B. Ellis
language : en
Publisher: National
Release Date : 2012
Developing Essential Understanding Of Proof And Proving For Teaching Mathematics In Grades 9 12 written by Amy B. Ellis and has been published by National this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Education categories.
Focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students...and teachers.
Planting The Seeds Of Algebra 3 5
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Author : Monica Neagoy
language : en
Publisher: Corwin Press
Release Date : 2014-12-05
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 2014-12-05 with Education categories.
Give your students a foundation of algebra for math success – now and in the future! Algebra is not something to be feared, but something to be embraced with a sense of wonder. Planting the Seeds of Algebra, 3-5, introduces algebra as an accessible way of seeing the world that is necessary to our students’ futures. Students and teachers must become friendly with algebraic foundations, as they have increasingly become the gateway to careers in the STEM fields. Monica Neagoy empowers teachers with theoretical and practical ways to introduce Algebra to 3-5 grade students, making vital connections to concepts they will encounter in middle school and beyond. You’ll discover Four explorations to help you weave key algebraic ideas into everyday mathematics Step-by-step lessons from real classrooms that will guide you in teaching concepts and in establishing their relevance and applicability New teaching methods that break down difficult algebraic concepts and build a critical foundation for higher math Awaken new awareness and change attitudes by sowing the seeds for a vibrant, useful, and rich experience with mathematics. "While reading this book I experienced the sense of wonder and aha moments alongside the students themselves. This book will move your faculty to new depths of understanding about mathematics and will instill the passion to explore a myriad of algebraic concepts." — Bob Weiman, Director St. Stephen’s & St. Agnes School "She’s done it again! Monica Neagoy has authored another book that deftly presents important foundations of algebra while celebrating mathematics through carefully crafted explorations, all of which include student and teacher vignettes and comments about the mathematics they have learned and are teaching. Wow. When I read this book I felt like I was in a classroom!" — Francis (Skip) Fennell, McDaniel College Past President of the National Council of Teachers of Mathematics
Developing Essential Understanding Of Rational Numbers For Teaching Mathematics In Grades 3 5
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Author : Carne Barnett-Clarke
language : en
Publisher: National Council of Teachers of English
Release Date : 2010
Developing Essential Understanding Of Rational Numbers For Teaching Mathematics In Grades 3 5 written by Carne Barnett-Clarke 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 2010 with Mathematics categories.
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.
Your Mathematics Standards Companion Grades 3 5
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Author : Linda M. Gojak
language : en
Publisher: Corwin Press
Release Date : 2017-05-17
Your Mathematics Standards Companion Grades 3 5 written by Linda M. Gojak and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with Education categories.
Transforming the standards into learning outcomes just got a lot easier In this resource, 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, allowing you to see and understand 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.
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 Algebraic Thinking For Teaching Mathematics In Grades 3 5
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Author : Maria L. Blanton
language : en
Publisher:
Release Date : 2011
Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5 written by Maria L. Blanton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Algebra categories.
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.
Understanding The Math We Teach And How To Teach It K 8
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Author : Small Marian
language : en
Publisher: Taylor & Francis
Release Date : 2025-08-26
Understanding The Math We Teach And How To Teach It K 8 written by Small Marian and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-26 with Education categories.
Dr. Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach. Comprehensive and Readable: Dr. Small helps all teachers deepen their content knowledge by illustrating core mathematical themes with sample problems, clear visuals, and plain language Big Focus on Student Thinking: The book's tools, models. and discussion questions are designed to understand student thinking and nudge it forward. Particularly popular features include charts listing common student misconceptions and ways to address them, a table of suggested manipulatives for each topic, and a list of related children's book Implementing Standards That Make Sense: By focusing on key mathematics principles, Understanding the Math We Teach and How to Teach It, K-8 helps to explain the "whys" of state standards and provides teachers with a deeper understanding of number sense, operations, algebraic thinking, geometry, and other critical topics Dr. Small, a former dean with more than 40 years in the field, conceived the book as an essential guide for teachers throughout their career: "Many teachers who teach at the K-8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help."
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.
Numeracy and Learning Difficulties provides guidance on how to develop flexible teaching methods and strategies to improve mathematical skills of students. It discusses common areas of learning difficulty in mathematics and looks at ways teachers can determine gaps in students' knowledge, as well as how to develop curricula and problem-solving strategies to address these gaps.