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| concrete models in math: Guided Math Workshop Laney Sammons, Donna Boucher, 2017-03-01 This must-have resource helps teachers successfully plan, organize, implement, and manage Guided Math Workshop. It provides practical strategies for structure and implementation to allow time for teachers to conduct small-group lessons and math conferences to target student needs. The tested resources and strategies for organization and management help to promote student independence and provide opportunities for ongoing practice of previously mastered concepts and skills. With sample workstations and mathematical tasks and problems for a variety of grade levels, this guide is sure to provide the information that teachers need to minimize preparation time and meet the needs of all students. |
| concrete models in math: A Concrete Approach to Mathematical Modelling Mike Mesterton-Gibbons, 2007-05-18 Critical praise for A Concrete Approach to Mathematical Modelling ...a treasure house of material for students and teachers alike...can be dipped into regularly for inspiration and ideas. It deserves to become a classic.--London Times Higher Education Supplement The author succeeds in his goal of serving the needs of the undergraduate population who want to see mathematics in action, and the mathematics used is extensive and provoking.--SIAM Review Each chapter discusses a wealth of examples ranging from old standards...to novelty ... Each model is developed critically, analyzed critically, and assessed critically.--Mathematical Reviews Mike Mesterton-Gibbons has done what no author before him could: he has written an in-depth, systematic guide to the art and science of mathematical modelling that's a great read from first page to last. With an abundance of both wit and common sense, he shows readers exactly how the modelling process works, using fascinating real-life examples from virtually every realm of human, machine, natural, and cosmic activity. You'll find models for determining how fast cars drive through a tunnel; how many workers industry should employ; the length of a supermarket checkout line; how birds should select worms; the best methods for avoiding an automobile accident; and when a barber should hire an assistant; just to name a few. Offering more examples, more detailed explanations, and by far, more sheer enjoyment than any other book on the subject, A Concrete Approach to Mathematical Modelling is the ultimate how-to guide for students and professionals in the hard sciences, social sciences, engineering, computers, statistics, economics, politics, business management, and every other discipline in which mathematical modelling plays a role. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department. Cover Design / Illustration: Keithley Associates, Inc. |
| concrete models in math: Concrete Mathematics Ronald L. Graham, Donald E. Knuth, Oren Patashnik, 1994-02-28 This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. More concretely, the authors explain, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. |
| concrete models in math: Statistical Mechanics of Lattice Systems Sacha Friedli, Yvan Velenik, 2017-11-23 A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail. |
| concrete models in math: Conceptual Model-Based Problem Solving Yan Ping Xin, 2013-02-11 Are you having trouble in finding Tier II intervention materials for elementary students who are struggling in math? Are you hungry for effective instructional strategies that will address students’ conceptual gap in additive and multiplicative math problem solving? Are you searching for a powerful and generalizable problem solving approach that will help those who are left behind in meeting the Common Core State Standards for Mathematics (CCSSM)? If so, this book is the answer for you. • The conceptual model-based problem solving (COMPS) program emphasizes mathematical modeling and algebraic representation of mathematical relations in equations, which are in line with the new Common Core. • “Through building most fundamental concepts pertinent to additive and multiplicative reasoning and making the connection between concrete and abstract modeling, students were prepared to go above and beyond concrete level of operation and be able to use mathematical models to solve more complex real-world problems. As the connection is made between the concrete model (or students’ existing knowledge scheme) and the symbolic mathematical algorithm, the abstract mathematical models are no longer “alien” to the students.” As Ms. Karen Combs, Director of Elementary Education of Lafayette School Corporation in Indiana, testified: “It really worked with our kids!” • “One hallmark of mathematical understanding is the ability to justify,... why a particular mathematical statement is true or where a mathematical rule comes from” (http://illustrativemathematics.org/standards). Through making connections between mathematical ideas, the COMPS program makes explicit the reasoning behind math, which has the potential to promote a powerful transfer of knowledge by applying the learned conception to solve other problems in new contexts. • Dr. Yan Ping Xin’s book contains essential tools for teachers to help students with learning disabilities or difficulties close the gap in mathematics word problem solving. I have witnessed many struggling students use these strategies to solve word problems and gain confidence as learners of mathematics. This book is a valuable resource for general and special education teachers of mathematics. - Casey Hord, PhD, University of Cincinnati |
| concrete models in math: Guided Math: A Framework for Mathematics Instruction Sammons, Laney, 2017-03-01 Use a practical approach to teaching mathematics that integrates proven literacy strategies for effective instruction. This professional resource will help to maximize the impact of instruction through the use of whole-class instruction, small-group instruction, and Math Workshop. Incorporate ideas for using ongoing assessment to guide your instruction and increase student learning, and use hands-on, problem-solving experiences with small groups to encourage mathematical communication and discussion. Guided Math supports the College and Career Readiness and other state standards. |
| concrete models in math: A History of Mathematics Education in the United States and Canada National Council of Teachers of Mathematics, National Council of Teachers of Mathematics Staff, 1970 |
| concrete models in math: Powerful Problem Solving Max Ray, 2013 How can we break the cycle of frustrated students who drop out of math because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say problem solved, by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the big picture of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking What do you notice? What do you wonder? we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be over and done, but to realize the many different ways to approach problems. Read a sample chapter. |
| concrete models in math: Educational Assessment of Students Anthony J. Nitko, Susan M. Brookhart, 2013-11-01 For a wide variety of courses in classroom assessment. This highly respected text offers the most comprehensive discussion of traditional and alternative assessments of any classroom assessment text-explaining, giving examples, discussing pros and cons, and showing how to construct virtually all of the traditional and alternative assessments teachers use in the classroom. The author explores assessment theories and research findings as they affect teaching and learning, and examines why, when, and how teachers should use assessment in the classroom. To the text's hundreds of practical examples are added checklists to aid in evaluating assessment vehicles and scores of strategies for assessing higher-order thinking, critical-thinking, and problem-solving skills. |
| concrete models in math: Mathematics Education Lyn D. English, Graeme S. Halford, 1995 First Published in 1995. Routledge is an imprint of Taylor & Francis, an informa company. |
| concrete models in math: Number Talks Sherry Parrish, 2010 A multimedia professional learning resource--Cover. |
| concrete models in math: The Teaching of Fractions Edward Wildeman, 1923 |
| concrete models in math: Mathematical Models for Teaching Ann Kajander, Tom Boland, 2014-01-01 Students of mathematics learn best when taught by a teacher with a deep and conceptual understanding of the fundamentals of mathematics. In Mathematical Models for Teaching, Ann Kajander and Tom Boland argue that teachers must be equipped with a knowledge of mathematics for teaching, which is grounded in modelling, reasoning, and problem-based learning. A comprehensive exploration of models and concepts, this book promotes an understanding of the material that goes beyond memorization and recitation, which begins with effective teaching. This vital resource is divided into 15 chapters, each of which addresses a specific mathematical concept. Focusing on areas that have been identified as problematic for teachers and students, Mathematical Models for Teaching equips teachers with a different type of mathematical understanding-one that supports and encourages student development. Features: grounded in the most current research about teachers' learning contains cross-chapter connections that identify common ideas includes chapter concluding discussion questions that encourage critical thinking incorporates figures and diagrams that simplify and solidify important mathematical concepts offers further reading suggestions for instructors seeking additional information |
| concrete models in math: Every Math Learner, Grades K-5 Nanci N. Smith, 2017-02-01 Differentiation that shifts your instruction and boosts ALL student learning! Nationally recognized math differentiation expert Nanci Smith debunks the myths surrounding differentiated instruction, revealing a practical approach to real learning differences. Theory-lite and practice-heavy, this book provides a concrete and manageable framework for helping all students know, understand, and even enjoy doing mathematics. Busy K-5 mathematics educators learn to Provide practical structures for assessing how students learn and process mathematical concepts Design, implement, manage, and formatively assess and respond to learning in a standards-aligned differentiated classroom; and Adjust current instructional materials to better meet students' needs Includes classroom videos and a companion website. |
| concrete models in math: Building Thinking Classrooms in Mathematics, Grades K-12 Peter Liljedahl, 2020-09-28 A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling non-thinking student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before. |
| concrete models in math: Mathematize It! [Grades K-2] Kimberly Morrow-Leong, Sara Delano Moore, Linda M. Gojak, 2020-04-23 This book is a must-have for anyone who has faced the challenge of teaching problem solving. The ideas to be learned are supported with a noticeably rich collection of classroom-ready problems, examples of student thinking, and videos. Problem solving is at the center of learning and doing mathematics. And so, Mathematize It! should be at the center of every teacher’s collection of instructional resources. John SanGiovanni Coordinator, Elementary Mathematics Howard County Public School System, Ellicott City, MD Help students reveal the math behind the words I don’t get what I’m supposed to do! This is a common refrain from students when asked to solve word problems. Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution. Many students often pluck numbers from the problem and plug them into an equation using the first operation they can think of (or the last one they practiced). Students also tend to choose an operation by solely relying on key words that they believe will help them arrive at an answer, which without careful consideration of what the problem is actually asking of them. Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades K-2 shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. Through the process of mathematizing, the authors provide an explanation of a consistent method—and specific instructional strategies—to take the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the problem. Sure to enhance teachers’ own operation sense, this user-friendly resource for Grades K-2 · Offers a systematic mathematizing process for students to use when solving word problems · Gives practice opportunities and dozens of problems to leverage in the classroom · Provides specific examples of questions and explorations for addition and subtraction of whole numbers as well as early thinking for multiplication and division · Demonstrates the use of concrete manipulatives to model problems with dozens of short videos · Includes end-of-chapter activities and reflection questions How can you help your students understand what is happening mathematically when solving word problems? Mathematize it! |
| concrete models in math: Scientific Models and Decision Making Eric Winsberg, Stephanie Harvard, 2024-02-08 This Element introduces the philosophical literature on models, with an emphasis on normative considerations relevant to models for decision-making. Chapter 1 gives an overview of core questions in the philosophy of modeling. Chapter 2 examines the concept of model adequacy for purpose, using three examples of models from the atmospheric sciences to describe how this sort of adequacy is determined in practice. Chapter 3 explores the significance of using models that are not adequate for purpose, including the purpose of informing public decisions. Chapter 4 provides a basic framework for values in modelling, using a case study to highlight the ethical challenges in building models for decision making. It concludes by establishing the need for strategies to manage value judgments in modelling, including the potential for public participation in the process. |
| concrete models in math: Response to Intervention in Math Paul J. Riccomini, Bradley S. Witzel, 2010 Provides educators with instructions on applying response-to-intervention (RTI) while teaching and planning curriculum for students with learning disabilities. |
| concrete models in math: Every Math Learner, Grades 6-12 Nanci N. Smith, 2017-02-02 Differentiation that shifts your instruction and boosts ALL student learning! Nationally recognized math differentiation expert Nanci Smith debunks the myths surrounding differentiated instruction, revealing a practical approach to real learning differences. Theory-lite and practice-heavy, this book provides a concrete and manageable framework for helping all students know, understand, and even enjoy doing mathematics. Busy secondary mathematics educators learn to Provide practical structures for assessing how students learn and process mathematical concepts information Design, implement, manage, and formatively assess and respond to learning in a standards-aligned differentiated classroom Adjust current materials to better meet students' needs Includes classroom videos and a companion website. |
| concrete models in math: Models and Modeling in the Sciences Stephen M. Downes, 2020-07-09 Biologists, climate scientists, and economists all rely on models to move their work forward. In this book, Stephen M. Downes explores the use of models in these and other fields to introduce readers to the various philosophical issues that arise in scientific modeling. Readers learn that paying attention to models plays a crucial role in appraising scientific work. This book first presents a wide range of models from a number of different scientific disciplines. After assembling some illustrative examples, Downes demonstrates how models shed light on many perennial issues in philosophy of science and in philosophy in general. Reviewing the range of views on how models represent their targets introduces readers to the key issues in debates on representation, not only in science but in the arts as well. Also, standard epistemological questions are cast in new and interesting ways when readers confront the question, What makes for a good (or bad) model? All examples from the sciences and positions in the philosophy of science are presented in an accessible manner. The book is suitable for undergraduates with minimal experience in philosophy and an introductory undergraduate experience in science. Key features: The book serves as a highly accessible philosophical introduction to models and modeling in the sciences, presenting all philosophical and scientific issues in a nontechnical manner. Students and other readers learn to practice philosophy of science by starting with clear examples taken directly from the sciences. While not comprehensive, this book introduces the reader to a wide range of views on key issues in the philosophy of science. |
| concrete models in math: International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives Patricia S. Moyer-Packenham, 2016-06-21 This book explores terminology, frameworks, and research being conducted worldwide on virtual manipulatives. It brings together international authors who provide their perspectives on virtual manipulatives in research and teaching. By defining terminology, explaining conceptual and theoretical frameworks, and reporting research, the authors provide a comprehensive foundation on the study and use of virtual manipulatives for mathematics teaching and learning. This foundation provides a common way for researchers to communicate about virtual manipulatives and build on the major works that have been conducted on this topic. By discussing these big ideas, the book advances knowledge for future research on virtual manipulatives as these dynamic tools move from computer platforms to hand-held, touch-screen, and augmented platforms. |
| concrete models in math: High Leverage Practices for Inclusive Classrooms James McLeskey, Lawrence Maheady, Bonnie Billingsley, Mary T. Brownell, Timothy J. Lewis, 2022-03-30 High Leverage Practices for Inclusive Classrooms, Second Edition offers a set of practices that are integral to the support of student learning, and that can be systematically taught, learned, and implemented by those entering the teaching profession. In this second edition, chapters have been fully updated to reflect changes in the field since its original publication, and feature all new examples illustrating the use of HLPs and incorporating culturally responsive practices. Focused primarily on Tiers 1 and 2—or work that mostly occurs with students with mild to moderate disabilities in general education classrooms—this powerful, research-based resource provides rich, practical information highly suitable for teachers, and additionally useful for teacher educators and teacher preparation programs. |
| concrete models in math: Math in Focus Sta , 2017-08-10 |
| concrete models in math: Transforming Mathematics Instruction Yeping Li, Edward A. Silver, Shiqi Li, 2014-07-05 This book surveys and examines different approaches and practices that contribute to the changes in mathematics instruction, including (1) innovative approaches that bring direct changes in classroom instructional practices, (2) curriculum reforms that introduce changes in content and requirements in classroom instruction, and (3) approaches in mathematics teacher education that aim to improve teachers’ expertise and practices. It also surveys relevant theory and methodology development in studying and assessing mathematics instruction. Classroom instruction is commonly seen as one of the key factors contributing to students’ learning of mathematics, but much remains to be understood about teachers’ instructional practices that lead to the development and enactment of effective classroom instruction, and approaches and practices developed and used to transform classroom instruction in different education systems. Transforming Mathematics Instruction is organized to help readers learn not only from reading individual chapters, but also from reading across chapters and sections to explore broader themes, including: - Identifying what is important in mathematics for teaching and learning emphasized in different approaches; - Exploring how students’ learning is considered and facilitated through different approaches and practices; - Understanding the nature of various approaches that are valued in different systems and cultural contexts; - Probing culturally valued approaches in identifying and evaluating effective instructional practices. The book brings new research and insights into multiple approaches and practices for transforming mathematics instruction to the international community of mathematics education, with 25 chapters and four section prefaces contributed by 56 scholars from 10 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, teacher educators, curriculum developers, and graduate students interested in learning about different instructional practices, approaches for instructional transformation, and research in different education systems. It will help readers to reflect on approaches and practices that are useful for instructional changes in their own education systems, and also inspire them to identify and further explore new areas of research and program development in improving mathematics teaching and learning. |
| concrete models in math: Modeling Students' Mathematical Modeling Competencies Richard Lesh, Peter L. Galbraith, Christopher R. Haines, Andrew Hurford, 2013-03-17 Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects. |
| concrete models in math: Modeling Mathematical Ideas Jennifer M. Suh, Padmanabhan Seshaiyer, 2016-12-27 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. |
| concrete models in math: Model and Mathematics: From the 19th to the 21st Century Michael Friedman, Karin Krauthausen, 2022-08-08 This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license. |
| concrete models in math: Authentic Opportunities for Writing about Math in High School Tammy L. Jones, Leslie A Texas, 2024-10-30 Teach students to write about math so they can improve their conceptual understanding in authentic ways. This resource offers hands-on strategies you can use to help students in grades 9–12 discuss and articulate mathematical ideas, use correct vocabulary, and compose mathematical arguments. Part One discusses the importance of emphasizing language to make students’ thinking visible and to sharpen communication skills, while attending to precision. Part Two provides a plethora of writing prompts and activities: Visual Prompts; Compare and Contrast; The Answer Is; Topical Questions; Writing About; Journal Prompts; Poetry/Prose; Cubing and Think Dots; RAFT; Question Quilt; and Always, Sometimes, and Never. Each activity is accompanied by a clear overview plus a variety of examples. Part Three offers a crosswalk of writing strategies and math topics to help you plan, as well as a sample anchor task and lesson plan to demonstrate how the strategies can be integrated. Throughout each section, you’ll also find Blackline Masters that can be downloaded for classroom use. With this book’s engaging, standards-based activities, you’ll have your high school students communicating like fluent mathematicians in no time! |
| concrete models in math: Eureka Math Grade 5 Study Guide Great Minds, 2015-11-09 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 5 provides an overview of all of the Grade 5 modules, including Place Value and Decimal Fractions; Multi-Digit Whole Number and Decimal Fraction Operations; Addition and Subtraction of Fractions; Multiplication and Division of Fractions and Decimal Fractions; Addition and Multiplication with Volume and Areal; Problem Solving with the Coordinate Plane. |
| concrete models in math: Eureka Math Grade 4 Study Guide Great Minds, 2015-11-09 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 4 provides an overview of all of the Grade 4 modules, including Place Value, Rounding, and Algorithms for Addition and Subtraction; Unit Conversions and Problem Solving with Metric Measurement; Multi-Digit Multiplication and Division; Angle Measure and Plane Figures; Fraction Equivalence, Ordering, and Operations; Decimal Fractions; and Exploring Measurement with Multiplication. |
| concrete models in math: Eureka Math Grade K Study Guide Great Minds, 2015-09-18 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade K provides an overview of all of the Kindergarten modules, including Numbers to 10; Two-Dimensional and Three-Dimensional Shapes; Comparison of Length, Weight, Capacity, and Numbers to 10; Number Pairs, Addition and Subtraction to 10; Numbers 10–20 and Counting to 10; and Analyzing Comparing and Composing Shapes. |
| concrete models in math: Eureka Math Grade 2 Study Guide Great Minds, 2015-09-18 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 2 provides an overview of all of the Grade 2 modules, including Sums and Differences to 20; Addition and Subtraction of Length Units; Place Value, Counting, and Comparison of Numbers to 1,000; Addition and Subtraction Within 200 with Word Problems to 100; Addition and Subtraction Within 1,000 with Word Problems to 100; Foundations of Multiplication and Division; Problem Solving with Length, Money, and Data; and Time, Shapes, and Fractions as Equal Parts of Shapes. |
| concrete models in math: Eureka Math Pre-K Study Guide Great Minds, 2016-08-02 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade PK provides an overview of all of the Pre-Kindergarten modules, including Counting to 5; Shapes; Counting to 10; Comparison of Length, Weight, Capacity, and Numbers to 5; and Addition and Subtraction Stories and Counting to 20. |
| concrete models in math: Eureka Math Grade 1 Study Guide Great Minds, 2015-09-18 Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 1 provides an overview of all of the Grade 1 modules, including Sums and Differences to 10; Introduction to Place Value Through Addition and Subtraction Within 20; Ordering and Comparing Length Measurements as Numbers; Place Value, Comparison, Addition and Subtraction to 40; Identifying, Composing, and Partitioning Shapes; and Place Value, Comparison, Addition and Subtraction to 100. |
| concrete models in math: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| concrete models in math: RtI in Math Linda Forbringer, Wendy Weber, 2014-01-03 Learn how to help K–8 students who struggle in math. This book provides a variety of clear, practical strategies that can be implemented right away to boost student achievement. You will find out how to design lessons that work with struggling learners, implement the recommendations for math intervention from the What Works Clearinghouse, use praise and self-motivation more effectively, develop number sense and computational fluency, teach whole numbers and fractions, increase students’ problem-solving abilities, and more! Extensive examples are provided for each strategy, as well as lesson plans, games, and resources. |
| concrete models in math: A Focus on Addition and Subtraction Caroline B. Ebby, Elizabeth T. Hulbert, Rachel M. Broadhead, 2020-11-23 This innovative text offers a unique approach to making mathematics education research on addition, subtraction, and number concepts readily accessible and understandable to pre-service and in-service teachers of grades K–3. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book provides educators with the knowledge and tools needed to modify their lessons and improve student learning of additive reasoning in the primary grades. Based on research gathered in the Ongoing Assessment Project (OGAP), this engaging, easy-to-use resource features practical resources such as: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding; A focus on the OGAP Addition, Subtraction, and Base Ten Number Progressions, based on research conducted with hundreds of teachers and thousands of pieces of student work; In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research; End-of-chapter questions to allow teachers to analyze student thinking and consider instructional strategies for their own students; Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs; An accompanying eResource, available online, offers an answer key to Looking Back questions, as well as a copy of the OGAP Additive Framework and the OGAP Number Line Continuum. A Focus on Addition and Subtraction marks the fourth installment of the popular A Focus on... collection, designed to aid the professional development of pre-service and in-service mathematics teachers. Following from previous volumes on ratios and proportions, multiplication and division, and fractions, this newest addition is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions. |
| concrete models in math: Math Instruction for Students with Learning Problems Susan Perry Gurganus, 2017-02-24 Math Instruction for Students with Learning Problems, Second Edition provides a research-based approach to mathematics instruction designed to build confidence and competence in pre- and in-service PreK–12 teachers. This core textbook addresses teacher and student attitudes toward mathematics, as well as language issues, specific mathematics disabilities, prior experiences, and cognitive and metacognitive factors. The material is rich with opportunities for class activities and field extensions, and the second edition has been fully updated to reference both NCTM and CCSSM standards throughout the text and includes an entirely new chapter on measurement and data analysis. |
| concrete models in math: Factorization and Model Theory for Contraction Operators with Unitary Part Joseph A. Ball, 1978 |
| concrete models in math: The Math Pact, Middle School Sarah B. Bush, Karen S. Karp, Barbara J. Dougherty, 2020-09-19 A schoolwide solution for students’ mathematics success! Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When rules seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular Rules that Expire series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid rules that expire—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · Practical templates and checklists · PLC prompts and discussion points When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics! |
Concrete - Wikipedia
Concrete is a composite material composed of aggregate bound together with a fluid cement that cures to a solid over time. It is the second-most-used substance (after water), [1] the …
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Concrete structures boast some great qualities: In its most common form, concrete consists of aggregate (sand and stone), Portland cement, and water. The cement and water create a …
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ACI offers numerous certifications, training programs, workbooks, free online learning presentations, and technical resources specifically designed for concrete contractors. Learn …
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Concrete is made up of three basic components: water, aggregate (rock, sand, or gravel) and Portland cement. Cement, usually in powder form, acts as a binding agent when mixed with …
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In its simplest form, concrete is a mixture of paste and aggregates. The paste, composed of portland cement and water, coats the surface of the fine and coarse aggregates. Through a …
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Concrete is a material comprised of a number of coarse aggregates (particulate materials such as sand, gravel, crushed stone, and slag) bonded with cement. Cement is a substance that is …
Concrete - Wikipedia
Concrete is a composite material composed of aggregate bound together with a fluid cement that cures to a solid over time. It is the second-most-used substance (after water), [1] the …
Types of Concrete Mix for Any Project - The Home Depot
May 16, 2025 · Concrete is a common material used in a wide range of construction projects. It is used in setting fence posts, pouring driveways and even laying the foundation for a home. …
Concrete | Definition, Composition, Uses, Types, & Facts ...
Jun 6, 2025 · concrete, in construction, structural material consisting of a hard, chemically inert particulate substance, known as aggregate (usually sand and gravel), that is bonded together …
Best Concrete Paving near Fort Ashby, WV - Yelp
Top 10 Best Concrete Paving near you in Fort Ashby, WV - December 2024 - Yelp - Liller Paving & Excavating, Haggerty Bros, All-Star Landscaping & Services, Bullfrog Contracting, Rock …
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BBB Directory of Concrete Contractors near Fort Ashby, WV. BBB Start with Trust ®. Your guide to trusted BBB Ratings, customer reviews and BBB Accredited businesses.
Concrete 101 - American Concrete
Concrete structures boast some great qualities: In its most common form, concrete consists of aggregate (sand and stone), Portland cement, and water. The cement and water create a …
American Concrete Institute
ACI offers numerous certifications, training programs, workbooks, free online learning presentations, and technical resources specifically designed for concrete contractors. Learn …
What is Concrete? Concrete Defined - Concrete Network
Concrete is made up of three basic components: water, aggregate (rock, sand, or gravel) and Portland cement. Cement, usually in powder form, acts as a binding agent when mixed with …
Concrete Basics - ConcreteState
In its simplest form, concrete is a mixture of paste and aggregates. The paste, composed of portland cement and water, coats the surface of the fine and coarse aggregates. Through a …
Concrete Calculator
Concrete is a material comprised of a number of coarse aggregates (particulate materials such as sand, gravel, crushed stone, and slag) bonded with cement. Cement is a substance that is …
