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| discovering geometry an investigative approach answer key: Discovering Geometry Michael Serra, Key Curriculum Press Staff, 2003-03-01 |
| discovering geometry an investigative approach answer key: Discovering Advanced Algebra Jerald Murdock, Ellen Kamischke, 2010 Changes in society and the workplace require a careful analysis of the algebra curriculum that we teach. The curriculum, teaching, and learning of yesterday do not meet the needs of today's students. |
| discovering geometry an investigative approach answer key: Discovering Geometry: An Inductive Approach Michael Serra, 2002 |
| discovering geometry an investigative approach answer key: Patty Paper Geometry Michael Serra, 1994 |
| discovering geometry an investigative approach answer key: Discovering Geometry Michael Serra, 2007-02-27 |
| discovering geometry an investigative approach answer key: Democracy and Education John Dewey, 1916 . Renewal of Life by Transmission. The most notable distinction between living and inanimate things is that the former maintain themselves by renewal. A stone when struck resists. If its resistance is greater than the force of the blow struck, it remains outwardly unchanged. Otherwise, it is shattered into smaller bits. Never does the stone attempt to react in such a way that it may maintain itself against the blow, much less so as to render the blow a contributing factor to its own continued action. While the living thing may easily be crushed by superior force, it none the less tries to turn the energies which act upon it into means of its own further existence. If it cannot do so, it does not just split into smaller pieces (at least in the higher forms of life), but loses its identity as a living thing. As long as it endures, it struggles to use surrounding energies in its own behalf. It uses light, air, moisture, and the material of soil. To say that it uses them is to say that it turns them into means of its own conservation. As long as it is growing, the energy it expends in thus turning the environment to account is more than compensated for by the return it gets: it grows. Understanding the word control in this sense, it may be said that a living being is one that subjugates and controls for its own continued activity the energies that would otherwise use it up. Life is a self-renewing process through action upon the environment. |
| discovering geometry an investigative approach answer key: Fostering Children's Mathematical Power Arthur J. Baroody, Ronald T. Coslick, 1998-09-01 Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics. |
| discovering geometry an investigative approach answer key: Smart Moves: Developing Mathematical Reasoning with Games and Puzzles Michael Serra, 2013-02-14 Smart Moves: Developing Mathematical Reasoning with Games and Puzzles is designed to improve your sequential reasoning, explore some mathematics, and have fun along the way. The games and puzzles were created to encourage perseverance and logical thinking. The Mathematical Connections highlight key math concepts. The Game of Racetrack is the perfect introduction to vectors, Tour Puzzles lead to graph theory and Euler paths, and the mathematics behind Magic Squares is revealed. Smart Moves is a very effective way to support mathematical learning and reduce the anxiety that often accompanies the subject.Each chapter is designed to strengthen sequential reasoning, which is necessary for everyday living and problem solving. Whether you are nine or ninety, in the classroom or at home, I invite you to make a smart move and discover how much fun math can be! |
| discovering geometry an investigative approach answer key: Statistical Power Analysis for the Behavioral Sciences Jacob Cohen, 2013-05-13 Statistical Power Analysis is a nontechnical guide to power analysis in research planning that provides users of applied statistics with the tools they need for more effective analysis. The Second Edition includes: * a chapter covering power analysis in set correlation and multivariate methods; * a chapter considering effect size, psychometric reliability, and the efficacy of qualifying dependent variables and; * expanded power and sample size tables for multiple regression/correlation. |
| discovering geometry an investigative approach answer key: Transforming the Workforce for Children Birth Through Age 8 National Research Council, Institute of Medicine, Board on Children, Youth, and Families, Committee on the Science of Children Birth to Age 8: Deepening and Broadening the Foundation for Success, 2015-07-23 Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children. |
| discovering geometry an investigative approach answer key: Learning to Think Spatially National Research Council, Division on Earth and Life Studies, Board on Earth Sciences and Resources, Geographical Sciences Committee, Committee on Support for Thinking Spatially: The Incorporation of Geographic Information Science Across the K-12 Curriculum, 2005-02-03 Learning to Think Spatially examines how spatial thinking might be incorporated into existing standards-based instruction across the school curriculum. Spatial thinking must be recognized as a fundamental part of Kâ€12 education and as an integrator and a facilitator for problem solving across the curriculum. With advances in computing technologies and the increasing availability of geospatial data, spatial thinking will play a significant role in the information-based economy of the twenty-first century. Using appropriately designed support systems tailored to the Kâ€12 context, spatial thinking can be taught formally to all students. A geographic information system (GIS) offers one example of a high-technology support system that can enable students and teachers to practice and apply spatial thinking in many areas of the curriculum. |
| discovering geometry an investigative approach answer key: On What We Know We Don't Know Sylvain Bromberger, 1992 In this collection of essays, Bromberger explores the centrality of questions and predicaments they create in scientific research. He discusses the nature of explanation, theory, and the foundations of linguistics. |
| discovering geometry an investigative approach answer key: Introduction to Educational Research W. Newton Suter, 2012 W. Newton Suter argues that what is important in a changing education landscape is the ability to think clearly about research methods, reason through complex problems and evaluate published research. He explains how to evaluate data and establish its relevance. |
| discovering geometry an investigative approach answer key: College Geometry Howard Whitley Eves, Howard Eves, 1995 College Geometry is divided into two parts. Part I is a sequel to basic high school geometry and introduces the reader to some of the important modern extensions of elementary geometry- extension that have largely entered into the mainstream of mathematics. Part II treats notions of geometric structure that arose with the non-Euclidean revolution in the first half of the nineteenth century. |
| discovering geometry an investigative approach answer key: Geometry: Euclid and Beyond Robin Hartshorne, 2013-11-11 This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. |
| discovering geometry an investigative approach answer key: Precalculus Jay P. Abramson, Valeree Falduto, Rachael Gross (Mathematics teacher), David Lippman, Melonie Rasmussen, Rick Norwood, Nicholas Belloit, Jean-Marie Magnier, Harold Whipple, Christina Fernandez, 2017 Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives and includes worked examples that demonstrate problem-solving approaches in an accessible way. |
| discovering geometry an investigative approach answer key: A Fuller Explanation Amy C. Edmondson, 2012-12-06 In a broad sense Design Science is the grammar of a language of images rather than of words. Modern communication techniques enable us to transmit and reconstitute images without the need of knowing a specific verbal sequential language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at differ ent altitudes representing a stack of floor plans. Such renderings make it difficult to imagine buildings containing ramps and other features which disguise the separation between floors; consequently, they limit the creativity of the architect. Analogously, we tend to analyze natural structures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. |
| discovering geometry an investigative approach answer key: Problems and Solutions in Euclidean Geometry M. N. Aref, William Wernick, 2010-01-01 Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition. |
| discovering geometry an investigative approach answer key: Discovering Geometry Serra, 2015-07-31 |
| discovering geometry an investigative approach answer key: Architectural Research Methods Linda N. Groat, David Wang, 2013-04-03 A practical guide to research for architects and designers—now updated and expanded! From searching for the best glass to prevent glare to determining how clients might react to the color choice for restaurant walls, research is a crucial tool that architects must master in order to effectively address the technical, aesthetic, and behavioral issues that arise in their work. This book's unique coverage of research methods is specifically targeted to help professional designers and researchers better conduct and understand research. Part I explores basic research issues and concepts, and includes chapters on relating theory to method and design to research. Part II gives a comprehensive treatment of specific strategies for investigating built forms. In all, the book covers seven types of research, including historical, qualitative, correlational, experimental, simulation, logical argumentation, and case studies and mixed methods. Features new to this edition include: Strategies for investigation, practical examples, and resources for additional information A look at current trends and innovations in research Coverage of design studio–based research that shows how strategies described in the book can be employed in real life A discussion of digital media and online research New and updated examples of research studies A new chapter on the relationship between design and research Architectural Research Methods is an essential reference for architecture students and researchers as well as architects, interior designers, landscape architects, and building product manufacturers. |
| discovering geometry an investigative approach answer key: Decolonizing Methodologies Linda Tuhiwai Smith, 2016-03-15 'A landmark in the process of decolonizing imperial Western knowledge.' Walter Mignolo, Duke University To the colonized, the term 'research' is conflated with European colonialism; the ways in which academic research has been implicated in the throes of imperialism remains a painful memory. This essential volume explores intersections of imperialism and research - specifically, the ways in which imperialism is embedded in disciplines of knowledge and tradition as 'regimes of truth.' Concepts such as 'discovery' and 'claiming' are discussed and an argument presented that the decolonization of research methods will help to reclaim control over indigenous ways of knowing and being. Now in its eagerly awaited second edition, this bestselling book has been substantially revised, with new case-studies and examples and important additions on new indigenous literature, the role of research in indigenous struggles for social justice, which brings this essential volume urgently up-to-date. |
| discovering geometry an investigative approach answer key: Report of the Presidential Commission on the Space Shuttle Challenger Accident DIANE Publishing Company, Southgate Publishers, 1995-07 |
| discovering geometry an investigative approach answer key: Pirate Math Michael Serra, 2014-02-25 Ahoy matey! Fear not mathematics. Build ye thinking skills, learn ye coordinates, and a smarter pirate ye will be! Michael Serra combines the challenge of mathematics with the fun adventure of pirates and buried treasure. Play the Buried Treasure game using a rectangle coordinate plane, a polar coordinate system, a spherical surface, and with three-dimensional areas. Use the chapter on cryptography to help solve hidden messages to uncover the pirate loot. Take a journey to sun-drenched tropical islands in search of pirate booty. With a map in your hand, follow clues and solve puzzles, developing your mathematical reasoning skills along the way. Argh, what glorious adventures, the thrill of using math to find pirate treasure! |
| discovering geometry an investigative approach answer key: Digital Communications John G. Proakis, 1995-01-01 This text provides an introduction to the analysis and design of digital communication systems. The third edition has been updated with a discussion of modern technological advances, providing coverage of such topics as digital modulation and demodulation techniques, source coding, channel coding and decoding, spread spectrum signals, channel equilization, multiuser communications, and modulation and coding for fading multipath channels. In addition, the book has been reorganized so that each chapter builds on previous material, begins with an introduction to the history and classification of channel models and reviews important topics in probability and stochastic processes. |
| discovering geometry an investigative approach answer key: Mathematics Framework for California Public Schools California. Curriculum Development and Supplemental Materials Commission, 1999 |
| discovering geometry an investigative approach answer key: Advanced Algebra Anthony W. Knapp, 2007-10-11 Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole. |
| discovering geometry an investigative approach answer key: Technology in Mathematics Teaching Gilles Aldon, Jana Trgalová, 2019-07-01 This book comprises chapters featuring a state of the art of research on digital technology in mathematics education. The chapters are extended versions of a selection of papers from the Proceedings of the 13th International Conference on Technology in Mathematics Teaching (ICTMT-13), which was held in Lyon, France, from July 3rd to 6th. ICTMT-13 gathered together over one hundred participants from twenty countries sharing research and empirical results on the topical issues of technology and its potential to improve mathematics teaching and learning. The chapters are organised into 4 themed parts, namely assessment in mathematics education and technology, which was the main focus of the conference, innovative technology and approaches to mathematics education, teacher education and professional development toward the technology use, and mathematics teaching and learning experiences with technology. In 13 chapters contained in the book, prominent mathematics educators from all over the world present the most recent theoretical and practical advances on these themes This book is of particular interest to researchers, teachers, teacher educators and other actors interested in digital technology in mathematics education. |
| discovering geometry an investigative approach answer key: Shaping Written Knowledge Charles Bazerman, 1988 The forms taken by scientific writing help to determine the very nature of science itself. In this closely reasoned study, Charles Bazerman views the changing forms of scientific writing as solutions to rhetorical problems faced by scientists arguing for their findings. Examining such works as the early Philosophical Transactions and Newton's optical writings as well as Physical Review, Bazerman views the changing forms of scientific writing as solutions to rhetorical problems faced by scientists. The rhetoric of science is, Bazerman demonstrates, an embedded part of scientific activity that interacts with other parts of scientific activity, including social structure and empirical experience. This book presents a comprehensive historical account of the rise and development of the genre, and views these forms in relation to empirical experience. |
| discovering geometry an investigative approach answer key: Task Design In Mathematics Education Anne Watson, Minoru Ohtani, 2015-10-26 *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* This open access book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student. |
| discovering geometry an investigative approach answer key: Knowing What Students Know National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Board on Testing and Assessment, Committee on the Foundations of Assessment, 2001-10-27 Education is a hot topic. From the stage of presidential debates to tonight's dinner table, it is an issue that most Americans are deeply concerned about. While there are many strategies for improving the educational process, we need a way to find out what works and what doesn't work as well. Educational assessment seeks to determine just how well students are learning and is an integral part of our quest for improved education. The nation is pinning greater expectations on educational assessment than ever before. We look to these assessment tools when documenting whether students and institutions are truly meeting education goals. But we must stop and ask a crucial question: What kind of assessment is most effective? At a time when traditional testing is subject to increasing criticism, research suggests that new, exciting approaches to assessment may be on the horizon. Advances in the sciences of how people learn and how to measure such learning offer the hope of developing new kinds of assessments-assessments that help students succeed in school by making as clear as possible the nature of their accomplishments and the progress of their learning. Knowing What Students Know essentially explains how expanding knowledge in the scientific fields of human learning and educational measurement can form the foundations of an improved approach to assessment. These advances suggest ways that the targets of assessment-what students know and how well they know it-as well as the methods used to make inferences about student learning can be made more valid and instructionally useful. Principles for designing and using these new kinds of assessments are presented, and examples are used to illustrate the principles. Implications for policy, practice, and research are also explored. With the promise of a productive research-based approach to assessment of student learning, Knowing What Students Know will be important to education administrators, assessment designers, teachers and teacher educators, and education advocates. |
| discovering geometry an investigative approach answer key: The Crest of the Peacock George Gheverghese Joseph, 1992 |
| discovering geometry an investigative approach answer key: The Art and Craft of Problem Solving Paul Zeitz, 2017 This text on mathematical problem solving provides a comprehensive outline of problemsolving-ology, concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective. |
| discovering geometry an investigative approach answer key: Young Mathematicians at Work Catherine Twomey Fosnot, Maarten Ludovicus Antonius Marie Dolk, 2001 Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction. |
| discovering geometry an investigative approach answer key: Discovering Algebra Murdock et al, 2015-01-14 |
| discovering geometry an investigative approach answer key: Guidelines for Early Learning in Child Care Home Settings John McLean, Tom Cole, 2010 |
| discovering geometry an investigative approach answer key: Jesus Christ Michael Pennock, 2010 (© 2010) The Subcommittee on the Catechism, United States Conference of Catholic Bishops, has found that this catechetical high school text is in conformity with the Catechism of the Catholic Church and fulfills the requirements of Core Course I of the Doctrinal Elements of a Curriculum Framework for the Development of Catechetical Materials for Young People of High School Age.Jesus Christ: God's Revelation to the World provides a map for high school students to navigate the salvific work of God--Father, Son, and Spirit--in forming a People, giving a Law, and preparing for the Messiah. The one-semester course gives students a general knowledge and appreciation of Sacred Scripture through which they encounter Jesus Christ.Tracing the stages of Salvation History, this text introduces key figures, events, vocabulary, and doctrine that will appear continuously throughout a four-year curriculum. While this text is a study of both the Old and New Testaments, it begins by centering on the nature of God and a person's natural instinct to search for God.Jesus Christ: God's Revelation to the World is a versatile text that follows the first course of the new curriculum framework but is also suitable for schools teaching a one-semester scripture course or an Introduction to the Catholic faith course in both high schools and parish religious education programs. |
| discovering geometry an investigative approach answer key: Mathematical Reasoning Theodore A. Sundstrom, 2007 Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom |
| discovering geometry an investigative approach answer key: The Ideal Problem Solver John Bransford, Barry S. Stein, 1993 Provocative, challenging, and fun, The Ideal Problem Solver offers a sound, methodical approach for resolving problems based on the IDEAL (Identify, Define, Explore, Act, Look) model. The authors suggest new strategies for enhancing creativity, improving memory, criticizing ideas and generating alternatives, and communicating more effectively with a wider range of people. Using the results of laboratory research previously available only in a piece-meal fashion or in scientific journals, Bransford and Stein discuss such issues as Teaming new information, overcoming blocks to creativity, and viewing problems from a variety of perspectives. |
| discovering geometry an investigative approach answer key: A First Course in Design and Analysis of Experiments Gary W. Oehlert, 2000-01-19 Oehlert's text is suitable for either a service course for non-statistics graduate students or for statistics majors. Unlike most texts for the one-term grad/upper level course on experimental design, Oehlert's new book offers a superb balance of both analysis and design, presenting three practical themes to students: • when to use various designs • how to analyze the results • how to recognize various design options Also, unlike other older texts, the book is fully oriented toward the use of statistical software in analyzing experiments. |
| discovering geometry an investigative approach answer key: SpringBoard Mathematics , 2015 |
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May 27, 2025 · The meaning of DISCOVER is to make known or visible : expose.
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Definition of discover verb in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, …
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DISCOVER Definition & Meaning - Merriam-Webster
May 27, 2025 · The meaning of DISCOVER is to make known or visible : expose.
DISCOVERING | definition in the Cambridge English Dictionary
DISCOVERING meaning: 1. present participle of discover 2. to find information, a place, or an object, especially for the…. Learn more.
discover verb - Definition, pictures, pronunciation and usage …
Definition of discover verb in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
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Find 107 different ways to say DISCOVERING, along with antonyms, related words, and example sentences at Thesaurus.com.
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Define discovering. discovering synonyms, discovering pronunciation, discovering translation, English dictionary definition of discovering. tr.v. dis·cov·ered , dis·cov·er·ing , dis·cov·ers 1. To …
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Scientists claim to have discovered [= found] a new way of controlling high blood pressure. It took her several weeks to discover the solution. The autopsy discovered [= revealed, uncovered] …
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Discovery is the act of detecting something new, or something previously unrecognized as meaningful.
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DISCOVERING definition: 1. present participle of discover 2. to find information, a place, or an object, especially for the…. Learn more.
