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Fibonacci and Lucas Numbers with Applications, Volume 1

by Thomas Koshy

Praise for the First Edition “ …beautiful and well worth the reading … with many exercises and a good bibliography, this book will fascinate both students and teachers.” Mathematics Teacher Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: • A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio • Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication • Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers • A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers. Thomas Koshy, PhD, is Professor Emeritus of Mathematics at Framingham State University in Massachusetts and author of several books and numerous articles on mathematics. His work has been recognized by the Association of American Publishers, and he has received many awards, including the Distinguished Faculty of the Year. Dr. Koshy received his PhD in Algebraic Coding Theory from Boston University. “Anyone who loves mathematical puzzles, number theory, and Fibonacci numbers will treasure this book. Dr. Koshy has compiled Fibonacci lore from diverse sources into one understandable and intriguing volume, [interweaving] a historical flavor into an array of applications.” Marjorie Bicknell-Johnson

Field Experiments and Their Critics

by Dawn Langan Teele

In recent years, social scientists have engaged in a deep debate over the methods appropriate to their research. Their long reliance on passive observational collection of information has been challenged by proponents of experimental methods designed to precisely infer causal effects through active intervention in the social world. Some scholars claim that field experiments represent a new gold standard and the best way forward, while others insist that these methods carry inherent inconsistencies, limitations, or ethical dilemmas that observational approaches do not. This unique collection of essays by the most influential figures on every side of this debate reveals its most important stakes and will provide useful guidance to students and scholars in many disciplines.

Field Guide to Compelling Analytics (Chapman and Hall/CRC Focus Case Studies in Analytics and OR)

by Walter DeGrange Lucia Darrow

Field Guide to Compelling Analytics is written for Analytics Professionals (APs) who want to increase their probability of success in implementing analytical solutions. In the past, soft skills such as presentation and persuasive writing techniques have been the extent of teaching junior APs how to effectively communicate the value of analytical products. However, there are other aspects to success such as trust and experience that may play a more important role in convincing fellow APs, clients, advisors, and leadership groups that their analytic solutions will work. This book introduces the formula ‘Analytics + Trust + Communication + Experience > Convince Them’ to illustrate an AP’s ability to convince a stakeholder. The ‘Convince Me’ stakeholders might be an analytics team member, team lead, decision-maker, or senior leader that are either internal or external to the AP’s organization. Whoever they are, this formula represents a concise, digestible, and above all practical means to increase the likelihood that you will be able to persuade them of the value of your analytical product. Features Includes insight questions to support class discussion. Written in broadly non-mathematical terms, designed to be accessible to any level of student or practicing AP to read, understand, and implement the concepts. Each section introduces the ideas through real-life case studies.

Field Solutions on Computers

by Stanley Humphries Jr.

Field Solutions on Computers covers a broad range of practical applications involving electric and magnetic fields. The text emphasizes finite-element techniques to solve real-world problems in research and industry. After introducing numerical methods with a thorough treatment of electrostatics, the book moves in a structured sequence to advanced topics. These include magnetostatics with non-linear materials, permanent magnet devices, RF heating, eddy current analysis, electromagnetic pulses, microwave structures, and wave scattering. The mathematical derivations are supplemented with chapter exercises and comprehensive reviews of the underlying physics. The book also covers essential supporting techniques such as mesh generation, interpolation, sparse matrix inversions, and advanced plotting routines.

Field Theoretic Method in Phase Transformations

by Alexander Umantsev

The main subject of the book is the continuum, field theoretic method of study of phase transformations in material systems. The method, also known as "phase field", allows one to analyze different stages of transformations on the unified platform. It has received significant attention in the materials science community recently due to many successes in solving or illuminating important problems. The book will address fundamentals of the method starting from the classical theories of phase transitions, the most important theoretical and computational results, and some of the most advanced recent applications.

Field-based Tests for Soccer Players: Methodological Concerns and Applications (SpringerBriefs in Applied Sciences and Technology)

by Filipe Manuel Clemente José Afonso Hugo Sarmento Bruno Silva Rafael Oliveira Rui Silva Zeki Akyildiz Halil Ibrahim Ceylan Javier Raya González Francisco Tomás Fernández Rui Araújo Ricardo Lima Sérgio Matos Yung-Sheng Chen

This book systematically summarizes the accuracy, precision, and repeatability levels of field-based tests applied in soccer. It considers such details as the effectiveness of tests for different age categories and sexes. In this book, the readers will be able to check all the field-based tests conceived for fitness assessment in soccer through a large systematic review made to the literature. In addition a brief characterization of each test and presentation of the concurrent validity and repeatability levels for each test will be provided. Finally, the book contains a general discussion of the implications of the tests for different methodological approaches to training. It will be use to sports scientists and practitioners.

Fiesta!

by Ginger Foglesong Guy

Bilingual text describes a children's party and provides practice counting in English and Spanish.

Fifth Grade Math with Confidence Instructor Guide (Math with Confidence)

by Kate Snow

Teach Fifth Grade Math with Confidence! This scripted, open-and-go program from math educator Kate Snow will give you the tools you need to teach math with confidence–even if it’s been years since you learned these concepts yourself. Engaging, hands-on lessons will help your child develop a strong understanding of math, step by step. This scripted, open-and-go program from math educator Kate Snow will give you the tools you need to teach math with confidence–even if it’s been years since you learned these concepts yourself. Engaging, hands-on lessons will help your child develop a strong understanding of math, step by step. adding, subtracting, multiplying, and dividing decimals adding and subtracting fractions with different denominators multiplying and dividing fractions and mixed numbers multi-step fraction and decimal word problems solving measurement problems with fractions and decimals line graphs and the coordinate plane geometry and volume mean and median Your child will develop strong math skills and a positive attitude toward math with fun games and real-world applications. All you’ll need are this Instructor Guide, the two Student Workbooks (Part A and Part B), and a few simple manipulatives (like base-ten blocks and fraction tiles) to make math come alive for your child. Hands-on, incremental lessons that steadily build conceptual understanding Daily review to ensure children retain what they’ve learned and master essential skills Step-by-step examples help your child develop math study skills and greater independence Games and real-world applications make math fun and relevant Clear directions and explanatory notes make teaching straightforward for the parent Optional extension activities and enrichment book recommendation link math lessons with everyday life WHAT PARENTS ARE SAYING: "Math with Confidence has made math the favorite subject in our homeschool. My kids love it, and are learning the 'why' behind every new skill they learn. As a self-proclaimed math-phobic person, I feel completely supported by the teacher's guide to present the material and help my children." –Stephanie E. "The Instructor Guide is well-thought out, extremely easy to follow, and doesn't require the instructor to be good at math - it enables you to learn alongside your student!" --Angela M.

Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics)

by Frederick Mosteller

Can you solve the problem of "The Unfair Subway"? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics. Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them.

Fifty Years of Fuzzy Logic and its Applications

by Dan E. Tamir Naphtali D. Rishe Abraham Kandel

This book presents a comprehensive report on the evolution of Fuzzy Logic since its formulation in Lotfi Zadeh's seminal paper on "fuzzy sets," published in 1965. In addition, it features a stimulating sampling from the broad field of research and development inspired by Zadeh's paper. The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Conceived by the editors as an academic celebration of the fifty years' anniversary of the 1965 paper, this work is a must-have for students and researchers willing to get an inspiring picture of the potentialities, limitations, achievements and accomplishments of Fuzzy Logic-based systems.

Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Future of AWM (Association for Women in Mathematics Series #28)

by Cathy Kessel Janet L. Beery Sarah J. Greenwald

The Assocation for Women in Mathematics (AWM), the oldest organization in the world for women in mathematics, had its fiftieth anniversary in 2021. This collection of refereed articles, illustrated by color photographs, reflects on women in mathematics and the organization as a whole. Some articles focus on the situation for women in mathematics at various times and places, including other countries. Others describe how individuals have shaped AWM, and, in turn, how the organization has impacted individuals as well as the broader mathematical community. Some are personal stories about careers in mathematics. Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Future of AWM covers a span from AWM’s beginnings through the following fifty years. The volume celebrates AWM and its successes but does not shy away from its challenges.The book is designed for a general audience. It provides interesting and informative reading for people interested in mathematics, gender equity, or organizational structures; teachers of mathematics; students at the high school, college, and graduate levels; and members of more recently established organizations for women in mathematics and related fields or prospective founders of such organizations.

Fighting the Silent Killer: How Men and Women Can Prevent and Cope with Heart Disease Today

by Dr Peter Cohn Dr Joan Cohn

Americais number-one killer, heart disease, can exist in the absence of symptoms. Calledlent heart disease,�ts first manifestations can be catastrophic. This no-nonsense guide now addresses this and other new issues in a clear, non-technical way and examines old concerns from a fresh perspective. The text moves easily from the role of smoking, st

Figure It Out, Henri Weldon

by Tanita S. Davis

Tanita S. Davis, author of Partly Cloudy and Serena Says, has written another funny, warm story featuring middle school and family life—all about the complex calculations it takes for everyone to balance the equations of their lives and what it takes to be part of a team while handling a learning disability. This middle grade novel is perfect for fans of From the Desk of Zoe Washington and A Good Kind of Trouble.Seventh grader Henrietta Weldon gets to switch schools—finally! She’ll be “mainstreaming” into public school, leaving her special education school behind. She can’t wait for her new schedule, new friends, and new classes.Henri’s dyscalculia, a learning disability that makes math challenging to process and understand, is what she expects to give her problems. What she doesn’t expect is a family feud with her sister over her new friends, joining the girls’ soccer team, and discovering poetry. Henri’s tutor and new friend, Vinnie, reminds her to take it slow. One problem at a time.If Henri Weldon has twenty-four hours in a day, and she has two siblings who dislike her four new friends, two hours of soccer practice, seven hours of classes, and three hours of homework . . . she has:A. No free timeB. No idea how to make everyone happyC. No time to figure it out, Henri Weldon!

Figures for Fun: Stories, Puzzles and Conundrums

by Yakov Perelman

"Does your brain need a workout? Are you wondering what to do? Well this could be the book for you! This is a great book for anyone who is looking for a challenge and, if you get too stuck, the author kindly also provided the answers at the end of each chapter!" -- Splashes Into BooksGive your mind a playful workout with this collection of more than 100 inventive puzzles. Finding the solutions requires only minimal mathematical knowledge and will test your imagination as well as your brainpower. The motley collection ranges from conundrums and mathematical stunts to practical situations involving counting and measuring. Chess problems, magic squares, and a host of other intriguing scenarios will amuse and challenge puzzle enthusiasts and fans of recreational mathematics. Answers appear at the end of each chapter.These puzzles are the inventions of a gifted Soviet mathematician, Yakov Perelman, whose popular science books on astronomy, physics, and mathematics inspired generations of readers. Perelman's distinctive style, abounding in wit and ingenuity, adds a special flair to his timeless riddles and brainteasers.

Figures of the Future: Latino Civil Rights and the Politics of Demographic Change

by Michael Rodríguez-Muñiz

An in-depth look at how U.S. Latino advocacy groups are using ethnoracial demographic projections to bring about political change in the presentFor years, newspaper headlines, partisan speeches, academic research, and even comedy routines have communicated that the United States is undergoing a profound demographic transformation—one that will purportedly change the “face” of the country in a matter of decades. But the so-called browning of America, sociologist Michael Rodríguez-Muñiz contends, has less to do with the complexion of growing populations than with past and present struggles shaping how demographic trends are popularly imagined and experienced. Offering an original and timely window into these struggles, Figures of the Future explores the population politics of national Latino civil rights groups.Based on eight years of ethnographic and qualitative research, spanning both the Obama and Trump administrations, this book investigates how several of the most prominent of these organizations—including UnidosUS (formerly NCLR), the League of United Latin American Citizens, and Voto Latino—have mobilized demographic data about the Latino population in dogged pursuit of political recognition and influence. In census promotions, get-out-the-vote campaigns, and policy advocacy, this knowledge has been infused with meaning, variously serving as future-oriented sources of inspiration, emblems for identification, and weapons for contestation. At the same time, Rodríguez-Muñiz considers why these political actors have struggled to translate this demographic growth into tangible political gain and how concerns about white backlash have affected how they forecast demographic futures.Figures of the Future looks closely at the politics surrounding ethnoracial demographic changes and their rising influence in U.S. public debate and discourse.

Figurierte Zahlen: Veranschaulichung als heuristische Strategie

by Jochen Ziegenbalg

Dieses Buch behandelt die Visualisierung als Methode des mathematischen Problemlösens, Begründens und Beweisens: Konkrete Beispiele zur Veranschaulichung durch mathematische Figuren und Bilder bieten einen faszinierenden Einblick in das Argumentieren anhand strukturierter und strukturierender Figuren zur Betrachtung von Zahlen und Zahlenfolgen. Die historischen Wurzeln dieses mathematischen Handwerkszeugs werden dabei so weit wie möglich einbezogen. Die Beispiele sind in der Regel konstruktiver Natur; gelegentlich wird, wo angebracht, die algorithmische Erschließung durch Hinweise auf die Programmierung mit Hilfe von Computeralgebra Systemen ergänzt. Das Buch richtet sich an Studierende und Lehrende an Schulen und Hochschulen, sowie an alle an der Elementarmathematik interessierten Nichtspezialisten, die das mathematische Arbeiten einmal außerhalb der von den Bildungsinstitutionen vorgezeichneten Pfade kennenlernen wollen. Es liefert insbesondere Lehrkräften und Lehramtsstudierenden wertvolle Anregungen, etwa zur Förderung mathematisch interessierter Schülerinnen und Schüler. In der 2. Auflage ist mit den mathematisch fundamentalen und historisch bedeutsamen Themen Wechselwegnahme, Teilbarkeit, Euklidischer Algorithmus, Inkommensurabilität und Kettenbrüche ein neues, für Visualisierungen gut geeignetes Kapitel hinzugekommen. Bereits bestehende Kapitel wurde durch Abschnitte über Trapezzahlen, ungerade Quadratzahlen und zentrierte Polygonalzahlen ergänzt.

Figuring It Out

by Nuno Crato

This is a book of mathematical stories -- funny and puzzling mathematical stories. They tell of villains who try to steal secrets, heroes who encode their messages, and mathematicians who spend years on end searching for the best way to pile oranges. There are also stories about highway confusions occurring when the rules of Cartesian geometry are ignored, small-change errors due to ignorance of ancient paradoxes, and mistakes in calendars arising from poor numerical approximations. This book is about the power and beauty of mathematics. It shows mathematics in action, explained in a way that everybody can understand. It is a book for enticing youngsters and inspiring teachers. Nuno Crato is a leading science writer and mathematician, whose entertaining essays have won a number of international awards.

Figuring Out Fluency - Addition and Subtraction With Fractions and Decimals: A Classroom Companion (Corwin Mathematics Series)

by John J. SanGiovanni Jennifer M. Bay-Williams Sherri L. Martinie Jennifer Suh

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: Addition and Subtraction with Fractions and Decimals. With this book, teachers can: Dive deeper into the Significant Strategies for fluency explained in the anchor book Learn how these strategies grow from and relate to the basic fact strategies children learn Access over 100 strategy-aligned and classroom-ready activities for fluency instruction and practice in adding and subtracting fractions and decimals, including worked examples, routines, games, and centers Find activities for assessing all components of addition and subtraction fluency for fractions and decimals, plus support for engaging families 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.

Figuring Out Fluency - Addition and Subtraction With Fractions and Decimals: A Classroom Companion (Corwin Mathematics Series)

by John J. SanGiovanni Jennifer M. Bay-Williams Sherri L. Martinie Jennifer Suh

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: Addition and Subtraction with Fractions and Decimals. With this book, teachers can: Dive deeper into the Significant Strategies for fluency explained in the anchor book Learn how these strategies grow from and relate to the basic fact strategies children learn Access over 100 strategy-aligned and classroom-ready activities for fluency instruction and practice in adding and subtracting fractions and decimals, including worked examples, routines, games, and centers Find activities for assessing all components of addition and subtraction fluency for fractions and decimals, plus support for engaging families 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.

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8: Moving Beyond Basic Facts and Memorization (Corwin Mathematics Series)

by Jennifer M. Bay-Williams John J. SanGiovanni

Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers 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. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8: Moving Beyond Basic Facts and Memorization (Corwin Mathematics Series)

by Jennifer M. Bay-Williams John J. SanGiovanni

Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers 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. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.

FileMaker Pro 13: The Missing Manual

by Susan Prosser Stuart Gripman

You don’t need a technical background to build powerful databases with FileMaker Pro 13. This crystal-clear guide covers all new FileMaker Pro 13 features, such as its improved layout tools and enhanced mobile support. Whether you’re running a business, printing a catalog, or planning a wedding, you’ll learn how to customize your database to run on a PC, Mac, Web browser, or iOS device.The important stuff you need to know:Get started. Tour FileMaker Pro’s features and create your first database in minutes.Access data anywhere. Use FileMaker Go on your iPad or iPhone—or share data on the Web.Dive into relational data. Solve problems quickly by connecting and combining data tables.Create professional documents. Publish reports, invoices, catalogs, and other documents with ease.Harness processing power. Use calculations and scripts to crunch numbers, search text, and automate tasks.Add visual power and clarity. Create colorful charts to illustrate and summarize your data.Share your database on a secure server. Add the high-level features of FileMaker Pro Advanced and FileMaker Pro Server.

Filling and Wrapping, Three-Dimensional Measurement

by Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis Phillips

NIMAC-sourced textbook

Filling and Wrapping: Three-Dimensional Measurement

by Glenda Lappan James T. Fey Susan N. Friel Elizabeth Difanis Phillips

NIMAC-sourced textbook

Filling and Wrapping: Three-Dimensional Measurement

by Phillips Fey Friel Lappan

Glenda Lap pan is a University Distinguished Professor in the Program in Mathematics Education (PRIME) and the Department of Mathematics at Michigan State University. Her research and development interests are in the connected areas of students' learning of mathematics and mathematics teachers' professional growth and change related to the development and enactment of K-12 curriculum materials. Elizabeth Difanis Phillips is a Senior Academic Specialist in the Program in Mathematics Education (PRIME) and the Department of Mathematics at Michigan State University. She is interested in teaching and learning mathematics for both teachers and students. These interests have led to curriculum and professional development projects at the middle school and high school levels, as well as projects related to the teaching and learning of algebra across the grades.

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Showing 9,701 through 9,725 of 28,279 results