Download or read book Rational Numbers written by Thomas P. Carpenter and published by Routledge. This book was released on 2012-10-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment. The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain. Integrating a number of different research perspectives is a complex task, and ways must be found to reduce the complexity without sacrificing the integration. The research discussed in this volume is tied together because it deals with a common content strand. During the last ten years specific content domains have served as focal points for research on the development of mathematical concepts in children. The areas of addition and subtraction, algebra, rational numbers, and geometry are notable examples. Whether a similar organizational structure will prevail for programs of research that integrate the study of teaching, learning, curriculum, and assessment is an open question. The perspectives presented in this volume illustrate the potential for adopting this perspective.
Download or read book Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3 5 written by Carne Barnett-Clarke and published by National Council of Teachers of English. This book was released on 2010 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Download or read book Rational Numbers to Linear Equations written by Hung-Hsi Wu and published by American Mathematical Soc.. This book was released on 2020-06-18 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and grade-level appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject. The present volume begins with fractions, then rational numbers, then introductory geometry that can make sense of the slope of a line, then an explanation of the correct use of symbols that makes sense of “variables”, and finally a systematic treatment of linear equations that explains why the graph of a linear equation in two variables is a straight line and why the usual solution method for simultaneous linear equations “by substitutions” is correct. This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.
Download or read book Numbers written by Ivan Morton Niven and published by . This book was released on 1979 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Figuring Out Fluency Operations With Rational Numbers and Algebraic Equations written by Jennifer M. Bay-Williams and published by Corwin Press. This book was released on 2022-07-25 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is awesome! What stood out to me was the deep understanding I was able to have about what fluency actually means. Too often the message has been fluency and accuracy, especially at the middle school level. By providing teachers with tools for building fluency with integers, expressions, and algebra, this book shifts that message to also focus on flexibility and strategy selection." Lindsey Henderson Secondary Mathematics Specialist, Utah State Board of Education Salt Lake City, UT Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. Now, teachers have the chance to apply that inspiration through explicit instruction and practice every day with the classroom companion Figuring Out Fluency—Operations With Rational Numbers and Algebraic Equations. With this book, teachers can Dive deeper into the Significant Strategies for fluency explained in the anchor book as they apply to rational number operations Explore how these strategies can be applied for proportional reasoning, solving equations for unknowns, and solving systems of linear equations Access over 100 classroom-ready activities, including worked examples, routines, and games. Find activities to explicitly teach students how to use and choose strategies to operate on rational numbers and solve algebraic equations Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.
Download or read book Prealgebra written by Lynn Marecek and published by . This book was released on 2015-09-25 with total page 1138 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Prealgebra follows a nontraditional approach in its presentation of content. The beginning, in particular, is presented as a sequence of small steps so that students gain confidence in their ability to succeed in the course. The order of topics was carefully planned to emphasize the logical progression throughout the course and to facilitate a thorough understanding of each concept. As new ideas are presented, they are explicitly related to previous topics."--BC Campus website.
Download or read book Prealgebra 2e written by Lynn Marecek and published by . This book was released on 2020-03-11 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The images in this book are in color. For a less-expensive grayscale paperback version, see ISBN 9781680923254. Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Students who are taking basic mathematics and prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi.
Download or read book Rational Quadratic Forms written by J. W. S. Cassels and published by Courier Dover Publications. This book was released on 2008-08-08 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.
Download or read book Introduction to Rational Numbers written by Adrian Harrison and published by . This book was released on 2019-10-03 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Rational numbers This book includes a brief explanation part, example with solutions and multiple-choice questions with answer sheet and it has been prepared for the beginners to help them understand the basic concepts of rational numbers. RATIONAL NUMBERS DECIMAL NUMBERS REOCCURING DECIMALS TEST WITH SOLUTIONS QUESTIONS
Download or read book Numbers Rational and Irrational written by Ivan Niven and published by . This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-study guide on the classification of numbers and the standards used to determine whether a number is rational or irrational.
Download or read book Mathematics of Choice written by Ivan Niven and published by MAA. This book was released on 1965 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rational Numbers with Integers and Reals written by John F. LeBlanc and published by Addison Wesley Publishing Company. This book was released on 1976 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unit is 1 of 12 developed for the university classroom portion of the Mathematics-Methods Program (MMP), created by the Indiana University Mathematics Education Development Center (MEDC) as an innovative program for the mathematics training of prospective elementary school teachers (PSTs). Each unit is written in an activity format that involves the PST in doing mathematics with an eye toward application of that mathematics in the elementary school. This document is one of four units that are devoted to the basic number work in the elementary school. In addition to an introduction to the unit, the text has sections on integers in the elementary school, rational numbers in the elementary school, mathematics of the rational numbers, rational numbers as decimals, the real number system, and appendices that cover self-test answers, the properties of number systems, and skill builder exercises. (MP)
Download or read book Understanding Mathematics 8 written by C. Sailaja, Smita Ratish, Lata Wishram and published by Vikas Publishing House. This book was released on with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Mathematics is a carefully written series of mathematics to help students encourage the study of mathematics in the best interactive form. It contains ample practice material, attractive illustrations and real-life examples for the students to relate the topics with their everyday life. Special care has been taken while teaching topics like geometry and probability to the students. Keeping in mind the development status and comprehension level of students, the text has been presented in a well graded manner.
Download or read book Understanding Numbers 7 written by C. Sailaja, Smita Ratish, Lata Wishram and published by Vikas Publishing House. This book was released on with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Numbers is a carefully written series of mathematics to help students encourage the study of mathematics in the best interactive form. It contains ample practice material, attractive illustrations and real-life examples for the students to relate the topics with their everyday life. Special care has been taken while teaching topics like geometry and probability to the students. Keeping in mind the development status and comprehension level of students, the text has been presented in a well graded manner.
Download or read book Number Game 8 written by Khurana Rohit and published by Pearson Education India. This book was released on 2007-09 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Analysis written by Bernd S. W. Schröder and published by John Wiley & Sons. This book was released on 2008-01-28 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
