Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on in school curriculums. The triangle, one of the basic instruments in geometry, has a plethora of unexpected curiosities. Geometric Gems presents one of the largest collections of triangle curiosities currently available, which the authors discuss in an easily understood fashion, requiring nothing more of readers other than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating triangle properties.

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on in school curriculums. The triangle, one of the basic instruments in geometry, has a plethora of unexpected curiosities. Geometric Gems presents one of the largest collections of triangle curiosities currently available, which the authors discuss in an easily understood fashion, requiring nothing more of readers other than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating triangle properties.

Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.

Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics - from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses - this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics - from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses - this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

We see numbers on automobile license plates, addresses, weather reports, and, of course, on our smartphones. Yet we look at these numbers for their role as descriptors, not as an entity in and unto themselves. Each number has its own history of meaning, usage, and connotation in the larger world. The Secret Lives of Numbers takes readers on a journey through integers, considering their numerological assignments as well as their significance beyond mathematics and in the realm of popular culture. Of course we all know that the number 13 carries a certain value of unluckiness with it. The phobia of the number is called Triskaidekaphobia; Franklin Delano Roosevelt was known to invite and disinvite guests to parties to avoid having 13 people in attendance; high-rise buildings often skip the 13th floor out of superstition. There are many explanations as to how the number 13 received this negative honor, but from a mathematical point of view, the number 13 is also the smallest prime number that when its digits are reversed is also a prime number. It is honored with a place among the Fibonacci numbers and integral Pythagorean triples, as well as many other interesting and lesser-known occurrences. In The Secret Lives of Numbers, popular mathematician Alfred S. Posamentier provides short and engaging mini-biographies of more than 100 numbers, starting with 1 and featuring some especially interesting numbers -like 6,174, a number with most unusual properties -to provide readers with a more comprehensive picture of the lives of numbers both mathematically and socially.

We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren't told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird. Mathematicians call it a transcendental number because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction. In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review pi's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi (including an attempt to legislate its exact value), and useful applications of pi in everyday life, including statistics. This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.

Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, . oo, , , and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.

There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units - ranging from grades 7 through 12 - that can be used to enhance the mathematics curriculum. Each unit presents a preassessment, instructional objectives, and a detailed description of the topic as well as teaching suggestions. Each unit has a post-assessment. This is the sort of instructional intervention that can make students love mathematics!

There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units - ranging from grades 7 through 12 - that can be used to enhance the mathematics curriculum. Each unit presents a preassessment, instructional objectives, and a detailed description of the topic as well as teaching suggestions. Each unit has a post-assessment. This is the sort of instructional intervention that can make students love mathematics!

Innovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world - and beyond - are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of 'noise.' With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business - and beyond - and recombine these resources for appropriate use in the classroom.

Innovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world - and beyond - are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of 'noise.' With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business - and beyond - and recombine these resources for appropriate use in the classroom.

The primary aim of this book is to provide teachers of mathematics with all the tools they would need to conduct most effective mathematics instruction. The book guides teachers through the all-important planning process, which includes short and long-term planning as well as constructing most effective lessons, with an emphasis on motivation, classroom management, emphasizing problem-solving techniques, assessment, enriching instruction for students at all levels, and introducing relevant extracurricular mathematics activities. Technology applications are woven throughout the text.A unique feature of this book is the second half, which provides 125 highly motivating enrichment units for all levels of secondary school mathematics. Many years of proven success makes this book essential for both pre-service and in-service mathematics teachers.

'The physical form of this new title is pleasing, including good paper, readable font, and durable binding ... The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.Summing Up: Recommended. General readers.'CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics - to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics - something most general readers will not initially find possible, but we hope will be an end product of this book.

'The physical form of this new title is pleasing, including good paper, readable font, and durable binding ... The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.Summing Up: Recommended. General readers.'CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics - to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics - something most general readers will not initially find possible, but we hope will be an end product of this book.

Parents need to take an ever-increasing role in their child's learning experience. However, what to do and how to do it is often not prescribed to the parents. This book offers a wide variety of aspects related to the parent's role as a support to their child's learning of mathematics, and above all appreciation for the subject.The uniqueness of this book is that we provide the parent the information they need about how mathematics is taught in today's early grades. We then provide a plethora of ideas that can motivate children with information beyond that which is taught in the classroom.

Making Pre-Algebra Come Alive! provides versatile enrichment exercises for teaching a broad range of mathematical topic. The book includes guidelines and notes.

Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.

Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.

"The authors have provided a unique, strategy-focused resource supported by a wealth of engaging examples that mathematics teachers can readily use to help students develop a more purposeful, systematic, and successful approach to problem solving." -Howard W. Smith, Superintendent Public Schools of the Tarrytowns, Sleepy Hollow, NY "Helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. The authors present in very simple terms the strategies that are the backbone of mathematics instruction. This indispensable material is useful at all levels, from basic stages to advanced student work to the development of top problem solvers." -Daniel Jaye, Principal Bergen County Academies, Hackensack, NJ Help students become skilled and confident problem solvers! Demonstrating there is always more than one approach to solving a problem, well-known authors and educators Alfred S. Posamentier and Stephen Krulik present ten basic strategies that are effective for finding solutions to a wide range of mathematics problems. These tried-and-true methods-including working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, and making a visual representation-make problem solving easier, neater, and more understandable for students as well as teachers. Providing numerous sample problems that illustrate how mathematics teachers and specialists can incorporate these techniques into their mathematics curriculum, this updated edition also includes: A variety of new problems that show how to use the strategies References to current NCTM standards Solutions to the problems in each chapter Extensive discussions of the empowering strategies used to solve sample problems The second edition of Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12 helps teachers develop students' creative problem-solving skills for success in and out of school.

Help students succeed as problem solvers in mathematics and in real-life situations! Based on the premise that problem solving is a key mathematics skill and an essential life skill, this book is designed to help teachers at all grade levels engage students in active problem solving. This resource presents ten easy-to-use strategies that offer elegant alternate approaches for resolving many types of mathematics problems. The authors demonstrate how you can: Apply the strategies to problems at different grade levels Incorporate the strategies into your mathematics program Use the strategies in real-life situations Make each strategy a part of your thinking processes

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.