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| first in math k2: Mine the Gap for Mathematical Understanding, Grades K-2 John SanGiovanni, 2016-10-31 Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our young learners’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time, and multiplication and division. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality taskwhat you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct gap commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see. |
| first in math k2: Big Ideas Math Ron Larson, Laurie Boswell, 2019 |
| first in math k2: Math Fact Fluency Jennifer Bay-Williams, Gina Kling, 2019-01-14 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. |
| first in math k2: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| first in math k2: Five Practices for Orchestrating Productive Mathematics Discussions Margaret Schwan Smith, Mary Kay Stein, 2011 Describes five practices for productive mathematics discussions, including anticipating, monitoring, selecting, sequencing, and connecting. |
| first in math k2: High-Dimensional Probability Roman Vershynin, 2018-09-27 An integrated package of powerful probabilistic tools and key applications in modern mathematical data science. |
| first in math k2: Making Math Accessible to Students With Special Needs (Grades K2) r4Educated Solutions, 2011-12-30 The purpose of Making Math Accessible to Students With Special Needs is to support everyone involved in mathematics education to become confident and competent with mathematics instruction and assessment so that 99% of students will be able to access enrolled grade-level mathematics. This resource actively engages readers through reflections and tasks in each chapter and can be used as a self-study professional development or as a group book study. Sample answers to tasks and reflections are found in the appendix, along with additional supports. Making Math Accessible to Students With Special Needs is designed for all teachers involved with mathematics instruction and is a unique resource for alternatively certified teachers and adjunct professionals. |
| first in math k2: Making Sense of Mathematics for Teaching Juli K. Dixon, Edward C. Nolan, Thomasenia Lott Adams, Lisa A. Brooks, Tashana D. Howse, 2016 With Making sense of mathematics for teaching grades K-2: the TQE process, participants have the opportunity to engage in mathematics as learners. This unscripted video program addresses three specific goals: (1) to explore meaningful tasks as learners of mathematics for teaching, (2) to make sense of the TQE process (tasks, questioning, and evidence), and (3) to create a shared vision of classrooms where teachers are supporting the TQE process and students are engaged in meaningful mathematics learning experiences. The program accomplishes these goals through the use of challenging tasks for teachers, effective questions related to classroom content, and classroom video showing tasks modeled during instruction.--Container |
| first in math k2: 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. |
| first in math k2: Making Sense of Mathematics for Teaching, Grades 3-5 Juli K. Dixon, Edward C. Nolan, 2016-04-11 Develop a deep understanding of mathematics. This user-friendly resource presents grades 3–5 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Focus on an understanding of and procedural fluency with multiplication and division. Address how to learn and teach fraction concepts and operations with depth. Thoroughly teach plane and solid geometry. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Use charts and diagrams for classifying shapes, which can engage students in important mathematical practices. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Place Value, Addition, and Subtraction 2 Multiplication and Division 3 Fraction Concepts 4 Fraction Operations 5 Geometry 6 Measurement Epilogue Next Steps Appendix A Completed Classification of Triangles Chart Appendix B Completed Diagram for Classifying Quadrilaterals |
| first in math k2: Teaching Student-Centered Mathematics Pearson Etext Access Code John a. Van De Walle, Jennifer M. Bay-Williams, LouAnn H. Lovin, Karen S Karp, 2017-01-28 NOTE: Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the Enhanced Pearson eText may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. This access code card provides access to the Enhanced Pearson eText. Helping students make connections between mathematics and their worlds-and helping them feel empowered to use math in their lives-is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM's teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions. Invigorate learning with the Enhanced Pearson eText This access code card provides access to the new Enhanced Pearson eText, a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features: NEW! Embedded videos. The Enhanced Pearson eText now includes links to videos throughout the text that provide examples of students' misconceptions, expand on key concepts, and demonstrate how to implement strategies and techniques in real classrooms. NEW! Downloadable Teacher Resource and Activity Pages that support teaching activities such as formative assessment and team-building are now available in the Enhanced Pearson eText at the point of use. NEW! Downloadable Blackline Masters in Part 2 Chapters. Readers may download Blackline Masters that support the activities and Expanded Lessons by clicking on hyperlinks embedded in the Enhanced Pearson eText. Appendix E includes a list of the Blackline Masters and a thumbnail version of each. *The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads. *The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7 or 10 tablet, or iPad iOS 5.0 or later. |
| first in math k2: The Mathematics of Chip-Firing Caroline J. Klivans, 2018-11-15 The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics. |
| first in math k2: Street-Fighting Mathematics Sanjoy Mahajan, 2010-03-05 An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license. |
| first in math k2: How People Learn National Research Council, Division of Behavioral and Social Sciences and Education, Board on Behavioral, Cognitive, and Sensory Sciences, Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice, 2000-08-11 First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methodsâ€to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education. |
| first in math k2: Probability Rick Durrett, 2010-08-30 This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject. |
| first in math k2: Advanced Calculus (Revised Edition) Lynn Harold Loomis, Shlomo Zvi Sternberg, 2014-02-26 An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds. |
| first in math k2: The Common Core Companion: The Standards Decoded, Grades K-2 Sharon Taberski, Jim Burke, 2014-04-28 With the click of a mouse, anyone has access to the standards. So aligning our instruction should be a snap. If only it were that simple . . . Jim Burke anticipated the challenges and developed the Common Core Companion series for K-12. In his next smart move, he deferred to the talents of Sharon Taberski to be author of the K-2 volume. What makes Sharon Taberski’s Common Core Companion that version of the standards you wish you had? It’s the way Sharon translates each and every standard for reading, writing, speaking and listening, language, and foundational skills into the day-to-day what you do: lesson ideas, best literacy practices, grouping configurations, adaptations for ELLs, anchor charts, and so much more. It’s all here, page by page: The standards for literature and informational texts put side by side for easier planning More than a dozen teaching ideas for each standard Recommendations on how to cultivate the habits of mind that are critical to meeting the standards, including interpersonal skills, collaboration, and perseverance A glossary of academic language for each standard Teaching suggestions for how to support ELL students Developmental debriefs to signal how you may need to adapt expectations to meet students where they’re at An online bank of graphic organizers, student reproducibles, sample classroom charts, rubrics, and photos Reproducible planning templates for each standard to help you map out lessons, select books, generate key questions, and more With more than 30 years of classroom experience in the primary grades and years of consulting in schools nationwide, Sharon Taberski has a depth of knowledge about what both students and teachers in this country need in order to cultivate the win-win of high expectations and high engagement in K-2. She is a nationally recognized educator, author, and presenter, and a leader in the field of early reading instruction. Her professional books and teaching materials have revolutionized the way primary teachers approach reading and remain classics in the field. |
| first in math k2: The Magic of Maths Arthur Benjamin, 2015-09-08 The world's greatest mental mathematical magician takes us on a spellbinding journey through the wonders of numbers (and more) Arthur Benjamin ... joyfully shows you how to make nature's numbers dance.--Bill Nye (the science guy) The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the mathemagician, Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike. A positively joyful exploration of mathematics. -Publishers Weekly, starred review Each [trick] is more dazzling than the last. -Physics World |
| first in math k2: Proofs from THE BOOK Martin Aigner, Günter M. Ziegler, 2013-06-29 According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such perfect proofs, those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics. |
| first in math k2: The Knot Book Colin Conrad Adams, 2004 Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics. |
| first in math k2: Integral Closure of Ideals, Rings, and Modules Craig Huneke, Irena Swanson, 2006-10-12 Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure. |
| first in math k2: An Invitation to Abstract Mathematics Béla Bajnok, 2020-10-27 This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH |
| first in math k2: K2 Heidi Howkins, 2001 The tales of a single mother who has climbed K2, just a little lower than Everest, but steeper, tougher, and deadlier.--Jacket. |
| first in math k2: The Mathematics Lesson-Planning Handbook, Grades 6-8 Lois A. Williams, Beth McCord Kobett, Ruth Harbin Miles, 2018-12-28 Your blueprint to planning Grades 6-8 math lessons that lead to achievement for all learners When it comes to planning mathematics lessons, do you sometimes feel burdened? Have you ever scrambled for an activity to engage your students that aligns with your state standards? Do you ever look at a recommended mathematics lesson plan and think, This will never work for my students? The Mathematics Lesson-Planning Handbook: Your Blueprint for Building Cohesive Lessons, Grades 6–8 walks you step by step through the process of planning focused, research-based mathematics lessons that enhance the coherence, rigor, and purpose of state standards and address the unique learning needs of your individual students. This resource deepens the daily lesson-planning process for middle school teachers and offers practical guidance for merging routines, resources, and effective teaching techniques into an individualized and manageable set of lesson plans. The effective planning process helps you Identify learning intentions and connect goals to success criteria Select resources and worthwhile tasks that make the best use of instructional materials Structure lessons differently for traditional and block middle school schedules Anticipate student misconceptions and evaluate understanding using a variety of formative assessment techniques Facilitate questioning, encourage productive struggle, and close lessons with reflection techniques This author team of seasoned mathematics educators make lesson planning practical and doable with a useful lesson-planning template and real-life examples from Grades 6–8 classrooms. Chapter by chapter, the decision-making strategies empower teachers to plan mathematics lessons strategically, to teach with intention and confidence, and to build purposeful, rigorous, coherent lessons that lead to mathematics achievement for all learners. |
| first in math k2: Visible Learning for Mathematics, Grades K-12 John Hattie, Douglas Fisher, Nancy Frey, Linda M. Gojak, Sara Delano Moore, William Mellman, 2016-09-15 Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in visible learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning. |
| first in math k2: Discrete Mathematics Oscar Levin, 2016-08-16 This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the introduction to proof course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. |
| first in math k2: Foundations of Analysis Joseph L. Taylor, 2012 Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover. |
| first in math k2: The Mathematics of Diffusion John Crank, 1979 Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained. |
| first in math k2: Differential Geometry Erwin Kreyszig, 2013-04-26 An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations. |
| first in math k2: Mindset Mathematics Jo Boaler, Jen Munson, Cathy Williams, 2017-08-28 Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the first-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum. |
| first in math k2: An Introduction to Abstract Mathematics Robert J. Bond, William J. Keane, 2007-08-24 Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments. |
| first in math k2: Number Talks Sherry Parrish, 2010 A multimedia professional learning resource--Cover. |
| first in math k2: Lectures on K3 Surfaces Daniel Huybrechts, 2016-09-26 K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers. |
| first in math k2: Counterexamples in Analysis Bernard R. Gelbaum, John M. H. Olmsted, 2012-07-12 These counterexamples deal mostly with the part of analysis known as real variables. Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition. |
| first in math k2: Combinatorics: The Art of Counting Bruce E. Sagan, 2020-10-16 This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular. |
| first in math k2: CRC Concise Encyclopedia of Mathematics Eric W. Weisstein, 2002-12-12 Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d |
| first in math k2: Earlybird Kindergarten Mathematics: Textbook A Ban Har Yeap, Winnie Tan, Marshall Cavendish Education, 2014 Earlybird Kindergarten Mathematics Common Core Edition helps kindergarten students build a strong foundation in mathematics through fun-filled lessons and activities. ...updated to align with the Common Core State Standards--Cover, p. [4]. |
| first in math k2: Math and Art Sasho Kalajdzievski, 2011-04-28 Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. With downloadable resources and a 16-page full-color insert, it includes numerous illustrations, computer-generated graphics, photographs, and art reproductions to demonstrate how mathematics can inspire art. Basic Math Topics and Their Visual Aspects Focusing on accessible, visually interesting, and mathematically relevant topics, the text unifies mathematics subjects through their visual and conceptual beauty. Sequentially organized according to mathematical maturity level, each chapter covers a cross section of mathematics, from fundamental Euclidean geometry, tilings, and fractals to hyperbolic geometry, platonic solids, and topology. For art students, the book stresses an understanding of the mathematical background of relatively complicated yet intriguing visual objects. For science students, it presents various elegant mathematical theories and notions. Comprehensive Material for a Math in Art Course Providing all of the material for a complete one-semester course on mathematics in art, this self-contained text shows how artistic practice with mathematics and a comprehension of mathematical concepts are needed to logically and creatively appreciate the field of mathematics. |
| first in math k2: Teaching Student-Centered Mathematics Access Code John a Van De Walle, 2017-01-28 NOTE: Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the Enhanced Pearson eText may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. This access code card provides access to the Enhanced Pearson eText. For courses in Elementary Mathematics Methods and for classroom teachers. A practical, comprehensive, student-centered approach to effective mathematical instruction for grades Pre-K-2. Helping students make connections between mathematics and their worlds-and helping them feel empowered to use math in their lives-is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM's teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions. This book is part of the Student-Centered Mathematics Series, which is designed with three objectives: to illustrate what it means to teach student-centered, problem-based mathematics, to serve as a reference for the mathematics content and research-based instructional strategies suggested for the specific grade levels, and to present a large collection of high quality tasks and activities that can engage students in the mathematics that is important for them to learn. Improve mastery and retention with the Enhanced Pearson eText* This access code card provides access to the new Enhanced Pearson eText, a rich, interactive learning environment designed to improve student mastery of content. The Enhanced Pearson eText is: Engaging. The new interactive, multimedia learning features were developed by the authors and other subject-matter experts to deepen and enrich the learning experience. Convenient. Enjoy instant online access from your computer or download the Pearson eText App to read on or offline on your iPad(R) and Android(R) tablet.* Affordable. Experience the advantages of the Enhanced Pearson eText along with all the benefits of print for 40% to 50% less than a print bound book. *The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads. *The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7- or 10- tablet, or iPad iOS 5.0 or later. |
| first in math k2: Beginning and Intermediate Algebra Tyler Wallace, 2018-02-13 Get Better Results with high quality content, exercise sets, and step-by-step pedagogy! Tyler Wallace continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate Algebra. The text reflects the compassion and insight of its experienced author with features developed to address the specific needs of developmental level students. Throughout the text, the author communicates to students the very points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. The exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor. |
First In Math K2 [PDF] - netsec.csuci.edu
First in Math K2 is a dynamic online math program designed to make learning fun and effective for second-grade students. It utilizes a game-based approach, motivating children to master fundamental math concepts through engaging challenges and rewarding achievements. The
First In Math K2 (PDF) - archive.ncarb.org
The book will furnish comprehensive and in-depth insights into First In Math K2, encompassing both the fundamentals and more intricate discussions. 1. This book is structured into several …
First In Math K2 (book) - archive.ncarb.org
Teachers makes learning basic math facts and number sense a breeze This book helps students in grades K 2 meet current math fluency standards for their age group Beyond teaching speed …
First In Math K2 [PDF] - archive.ncarb.org
Teachers makes learning basic math facts and number sense a breeze This book helps students in grades K 2 meet current math fluency standards for their age group Beyond teaching speed …
First in Math Instructions for Students - SharpSchool
First in Math Instructions for Students 1. Log in to BCPS One. 2. Click Digital Content Tab. 3. Locate and click First in Math Tab. (you do not have to log in) 4. Kindergarten to Grade 2 …
FIRST IN MATH
Use K-2 games as guided practice to motivate young stu-dents. Introduce basic math skills, improve focus and help students understand the importance of setting and achiev-ing short …
First In Math® Online Program
First In Math® Online Program Alignment To Mathematics Standards First Grade Introduction (1) The desire to achieve educational excellence is the driving force behind the Texas essential …
Performance Level Descriptors (PLD) for Grades K-2 …
The Performance Level Descriptor (PLD) document was created to provide details on the content progressions of the mathematics areas of focus at the kindergarten through grade 2 levels. …
FAST K–2 Sample Test Materials Star Math - flfast.org
These sample test materials are intended to introduce the item types that may be seen on Star Math tests. By using these materials, students will become familiar with the types of items they …
2024–25 Florida Assessment of Student Thinking (FAST) Fact …
FAST for students in grades K–2 is administered three times a year using Renaissance Learning’s Star assessments, as shown in the table below. Students who earn a scale score of 852 or …
Mathematics programmes of study: key stages 1 and 2 - GOV.UK
The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should …
Numeracy and Mathematics Benchmarks (Word version)
Benchmarks have been developed to provide clarity on the national standards expected within each curriculum area at each level. They set out clear lines of progression in literacy and …
First In Math K2 (PDF) - archive.ncarb.org
extraordinary book, aptly titled "First In Math K2," written by a highly acclaimed author, immerses readers in a captivating exploration of the significance of language and its profound effect on …
2023 national curriculum tests Key stage 2 - GOV.UK
This test has been developed to meet the specification set out in the test framework1 for mathematics at key stage 2. A new test and new mark schemes will be produced each year. …
K–2 Standards and Targets - EL Education
This document breaks down the Common Core State Standards for Reading Foundations, plus Language Standard 2 (spelling) into sub-standards and learning targets. The purpose of this …
Learning Mathematics K2_CTP_375U R spot merge.pdf
Count and write the numbers and words. Match the words to the numbers. Count and circle the correct answer. Colour the correct number of apples. Count and circle the correct answer.
Kindergarten Word Problems Worksheet - K5 Learning
Solve the word problems. Mini ate 6 ice-creams. Sam ate 2 ice-creams. How many ice-creams did they eat in total? Martin plucked 4 apples. Later he. plucked 5 more. How many apples did he …
Algebraic K-Theory and Quadratic Forms - School of Mathematics
Inventiones math. 9, 318-344 (1970) Algebraic K-Theory and Quadratic Forms JOHN MILNOR (Cambridge, Massachusetts) The first section of this paper defines and studies a graded ring …
Grade 1 Addition Worksheet - Number Bonds - sums with 8 - K5 …
What number should be added to the first number to make 8?
First In Math K2 [PDF] - netsec.csuci.edu
First in Math K2 is a dynamic online math program designed to make learning fun and effective for second-grade students. It utilizes a game-based approach, motivating children to master fundamental math concepts through engaging challenges and rewarding achievements. The
Skill Set & Games Guide - First In Math
DOWNLOAD & PRINT AS CLASSROOM POSTER! Easily assess Fact Fluency. Student takes a Pre-Test to determine fluency, repeats as a Post-Test to review growth. Focus: Whole Numbers; Decimals; Integers & Fractions. Test only takes five mi-nutes.
First In Math K2 (PDF) - archive.ncarb.org
The book will furnish comprehensive and in-depth insights into First In Math K2, encompassing both the fundamentals and more intricate discussions. 1. This book is structured into several chapters, namely: Chapter 1: Introduction to First In Math K2 Chapter 2: Essential Elements of First In Math K2 Chapter 3: First In Math K2 in Everyday Life ...
First In Math K2 (book) - archive.ncarb.org
Teachers makes learning basic math facts and number sense a breeze This book helps students in grades K 2 meet current math fluency standards for their age group Beyond teaching speed accuracy and memorization this book focuses on getting students to apply math in a variety of real life situations Inside you ll find Current fluency standards ...
First In Math K2 [PDF] - archive.ncarb.org
Teachers makes learning basic math facts and number sense a breeze This book helps students in grades K 2 meet current math fluency standards for their age group Beyond teaching speed accuracy and memorization this book focuses on getting students to apply math in a variety of real life situations Inside you ll find Current fluency standards ...
First in Math Instructions for Students - SharpSchool
First in Math Instructions for Students 1. Log in to BCPS One. 2. Click Digital Content Tab. 3. Locate and click First in Math Tab. (you do not have to log in) 4. Kindergarten to Grade 2 students click EARLY (K2). 5. Click Purple K-2. 6. Choose an activity to play: Numbers, Shapes and Logic or Know and Show
FIRST IN MATH
Use K-2 games as guided practice to motivate young stu-dents. Introduce basic math skills, improve focus and help students understand the importance of setting and achiev-ing short-term goals. Most games require no reading and make math …
First In Math® Online Program
First In Math® Online Program Alignment To Mathematics Standards First Grade Introduction (1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards.
Performance Level Descriptors (PLD) for Grades K-2 Mathematics
The Performance Level Descriptor (PLD) document was created to provide details on the content progressions of the mathematics areas of focus at the kindergarten through grade 2 levels. The performance level descriptors in the table below describe the evidence needed to identify student proficiency along a progression of learning within each domain.
FAST K–2 Sample Test Materials Star Math - flfast.org
These sample test materials are intended to introduce the item types that may be seen on Star Math tests. By using these materials, students will become familiar with the types of items they may see on their test.
2024–25 Florida Assessment of Student Thinking (FAST) Fact Sheet
FAST for students in grades K–2 is administered three times a year using Renaissance Learning’s Star assessments, as shown in the table below. Students who earn a scale score of 852 or higher on Star Early Literacy are considered “probable readers.”
Mathematics programmes of study: key stages 1 and 2 - GOV.UK
The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working...
Numeracy and Mathematics Benchmarks (Word version)
Benchmarks have been developed to provide clarity on the national standards expected within each curriculum area at each level. They set out clear lines of progression in literacy and English and numeracy and mathematics, and across all other curriculum areas from Early to Fourth Levels (First to Fourth Levels in Modern Languages).
First In Math K2 (PDF) - archive.ncarb.org
extraordinary book, aptly titled "First In Math K2," written by a highly acclaimed author, immerses readers in a captivating exploration of the significance of language and its profound effect on our existence.
2023 national curriculum tests Key stage 2 - GOV.UK
This test has been developed to meet the specification set out in the test framework1 for mathematics at key stage 2. A new test and new mark schemes will be produced each year. Key stage 2 tests...
K–2 Standards and Targets - EL Education
This document breaks down the Common Core State Standards for Reading Foundations, plus Language Standard 2 (spelling) into sub-standards and learning targets. The purpose of this document is twofold.
Learning Mathematics K2_CTP_375U R spot merge.pdf
Count and write the numbers and words. Match the words to the numbers. Count and circle the correct answer. Colour the correct number of apples. Count and circle the correct answer.
Kindergarten Word Problems Worksheet - K5 Learning
Solve the word problems. Mini ate 6 ice-creams. Sam ate 2 ice-creams. How many ice-creams did they eat in total? Martin plucked 4 apples. Later he. plucked 5 more. How many apples did he pluck in total? Alice brought 2 pencils. Her dad brought 7 more pencils for her. How many total pencils are there ? Mini ate 6 ice-creams. Sam ate 2 ice-creams.
Algebraic K-Theory and Quadratic Forms - School of Mathematics
Inventiones math. 9, 318-344 (1970) Algebraic K-Theory and Quadratic Forms JOHN MILNOR (Cambridge, Massachusetts) The first section of this paper defines and studies a graded ring K. F associated to any field F. By definition, K~F is the target …
Grade 1 Addition Worksheet - Number Bonds - sums with 8 - K5 Learning
What number should be added to the first number to make 8?
