• Mathematics

Counting

Math for Gifted Students
Author: Xing Zhou
Publisher: CreateSpace
ISBN: 9781506119151
Category: Mathematics
Page: 156
View: 9435
Welcome to the Math All Star series! These books are for middle school and high school students who are motivated to participate in math competitions such as MathCounts, AMC, and AIME. Their coaches may also find these books useful. The website, www.mathallstar.com, provides extra practice problems and serves as a highly recommended supplemental learning resource. Counting You think everybody can count? Take a look at some counting problems available on the aforementioned website, and you might just think differently. Counting problems appear in all levels of math competitions. It is one type of problems that senior students and even adults may not necessarily do better on than well-trained junior students. This is because counting problems usually do not involve complex theorems or formulas. Rather, they demand a systematic and analytical approach, which can be mastered with the structured training that this book offers. The first half of the book teaches essential counting principles and formulas by going over easy-to-follow examples. After identifying hidden pitfalls and common misunderstandings, this book offers tips on how to avoid those traps. The second half covers well-established patterns in counting problems and introduces different ways to tackle each type. Mastering these techniques has proven to be very powerful and effective in improving problem solving skills. Each chapter starts with examples and progresses with inspiring questions, followed by detailed, step-by-step reasoning. When there are multiple solutions, their similarities and differences are examined to provide students with greater insights. Each chapter contains practice problems with full solutions provided at the end of the book. Upon completing this book, students will be able to: Analyze and approach problems like trained pros Identify common pitfalls in problem solving, and Recognize frequently used patterns and apply appropriate techniques

Art of Thinking

Math for Gifted Students
Author: Xing Zhou
Publisher: Createspace Independent Publishing Platform
ISBN: 9781548989729
Category:
Page: 152
View: 7764
Official site with more information and practice: www.mathallstar.org.Competition math is not about complicated theorems and formulas. It is more about how to analyze in order to solve challenging problems. Thus, merely remembering hundreds of theorems and formulas is far from sufficient to win math competitions. Students must be able to think effectively.This book aims to help students understand some frequently used methods of proof and improve their ability to think effectively. Contents in this book are organized based on methodologies rather than specific subjects. Consequently, examples and practice problems presented in each chapter may cover many different subjects. For example, the chapter Symmetry contains problems relating to polynomial factorization, equation, counting, and so on. Despite of being belong to different subjects, all of these problems can be solved by exploiting their intrinsic symmetric properties. Readers should focus on learning how to identify and utilize such properties. This analysis skill is a critical one to develop in addition to specific subject math knowledge.All the methodologies discussed in this book are intuitive and easy to understand. Some of them may be taught in classroom such as mathematical induction and proof by contradiction. Others may be not. Regardlessly, all of them are powerful to solve many competition problems. In addition, mastering the art of thinking not only is helpful for improving students' contest performance during school years, but also has positive impacts on their future. For example, some problems in this book originate from various job interviews. Being able to think effectively in order to solve such interview and other practical problems is certainly beneficial to their future.More information can be found at www.mathallstar.org.

    • Mathematics

Introduction to Functional Equations

Theory and Problem-solving Strategies for Mathematical Competitions and Beyond
Author: Costas Efthimiou
Publisher: American Mathematical Soc.
ISBN: 0821853147
Category: Mathematics
Page: 363
View: 6032
Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Geometry Techniques

Math for Gifted Students
Author: Xing Zhou
Publisher: Createspace Independent Publishing Platform
ISBN: 9781534790629
Category:
Page: 168
View: 2452
Solving competition geometry problems is challenging. It requires students not only to remember lots of geometry theorems, but also to master various related techniques. Though related, these two skills are not the same. Many geometry techniques are intuitive to apply and do not involve complex theorems. However, it can be surprisingly more effective to utilize these techniques than to solely rely on a bunch of theorems. Therefore, being proficient in employing appropriate techniques will boost a one's problem solving ability in a meaningful way. That being said, it appears that the vast majority of math trainings and materials focus on teaching students geometry theorems. This book will introduce a collection of geometry techniques which can be readily used to solve many competition geometry problems at various levels. Mastering them is a must for anyone who wants to be a strong contender in math competitions. More information about this book, including pre-assessment exercise, can be found at http: //www.mathallstar.org/

Practice Counting

Level 1 (Ages 7 to 9)
Author: Cleo Borac,Silviu Borac
Publisher: N.A
ISBN: 9780692241158
Category:
Page: 78
View: 5278
2nd Edition - 2014 About "Competitive Mathematics for Gifted Students" This series provides practice materials and short theory reminders for students who aim to excel at problem solving. Material is introduced in a structured manner: each new concept is followed by a problem set that explores the content in detail. Each book ends with a problem set that reviews both concepts presented in the current volume and related topics from previous volumes. The series forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. Full solutions explain both reasoning and execution. Often, several solutions are contrasted. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Ready to participate in a math competition such as MOEMS, Math Kangaroo in USA, or Noetic Math? This series will open the doors to consistent performance. About Level 1 This level of the series is designed for students who know addition and subtraction with multi-digit numbers as well as simple multiplications of one-digit numbers. Some of the problems, however, involve advanced concepts and may be useful for older students. About Volume 1 - Counting This book starts a foundation for good skills for discrete counting and probability. Age appropriate examples introduce elementary counting concepts and inductive reasoning. We focus on establishing a solid strategy for each problem, even when using a brute force solution, such as listing all possibilities, is an option. Similar problem statements with strikingly different solutions familiarize the student with the subtle details in wording that can make counting problems difficult.

    • Mathematics

Trigonometry

A Clever Study Guide
Author: James Tanton
Publisher: The Mathematical Association of America
ISBN: 0883858363
Category: Mathematics
Page: 232
View: 7351
This guide covers the story of trigonometry. It is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject you may have taken or are currently taking. (These notes will be tough going for those encountering trigonometry for the very first time!)

Geometry Theorems

Math for Gifted Students
Author: Xing Zhou
Publisher: Createspace Independent Publishing Platform
ISBN: 9781539827986
Category:
Page: 142
View: 7910
There are hundreds of, if not more, geometry theorems. It is nearly impossible and definitely not necessary to remember all of them. Instead, students should focus on those must know theorems. In addition to remembering these theorems themselves, it is also important to study their typical applications. This book covers both areas. Each chapter of this book introduces a collection of related theorems. Those essential ones are discussed in the body contents. Students must remember all of them. Some additional theorems are included in the practice. They are good to know and remember. Practices are intended to demonstrate these theorems' typical applications. Many of them are classical problems. Some conclusion are well-known and can be practically treated as theorems. As such, students are encouraged to remember such conclusions as well. More information can be found at http: //www.mathallstar.org/

    • Juvenile Nonfiction

Math for All Seasons


Author: Greg Tang
Publisher: Scholastic Inc.
ISBN: 1338193740
Category: Juvenile Nonfiction
Page: 40
View: 827
Your challenge is to find the sum Without counting one by one Why not count? It's much too slow -- Adding is the way to go! Make clever groups before you start -- Then add them in a way that's smart! MATH FOR ALL SEASONS will challenge every kid -- and every parent -- to open their minds and solve problems in new and unexpected ways. By looking for patterns, symmetries, and familiar number combinations within eye-catching pictures, math will become easier, quicker, and more fun than anyone could have imagined!

Competition Algebra

Math for Gifted Students
Author: Xing Zhou
Publisher: Createspace Independent Publishing Platform
ISBN: 9781542567121
Category:
Page: 144
View: 6511
Algebra is taught from elementary school to college and beyond. Algebraic problems present a significant portion in all math competitions including MathCounts, AMC, AIME, USAMO and so on. Therefore, solving competition level algebraic problems is a must-master skills for every contest contender. Algebra includes a wide range of topics and techniques. Some of them may be related to advanced mathematical theorems and tools. Therefore, it is impossible to cover all of them in one book. However, middle school and high school level competitions usually do not require advanced mathematics. Instead, the emphasis is on the applications of basic algebraic skills in a flexible and effective way to solve complex problems. As a result, it is a wise strategy to thoroughly understand the most important topics and drill down into details of related solving techniques in order to improve one's skill and test performance. This book covers three basic but important topics: equation, sequence and function. While these topics are all taught in schools, there are some competition specific techniques which deserve a systematic discussion. Taking Vieta's theorem as an example. While polynomial transformation is a well known method to evaluate expressions such as $x_1 DEGREES2+x_2 DEGREES2$, there are several other powerful techniques. They can be used to evaluate some complex expressions in a more efficient and less error-prone way. These expressions can have high power such as $x_1 DEGREES{7}+x_2 DEGREES{7}$, or are asymmetric such as $5x_1 DEGREES3 + 3 x_2 DEGREES5$. In fact, the latter asymmetric expression can present a challenge to many students who only know the polynomial transformation method. In addition to expression evaluation, Vieta's theorem can also be used to solve some seemingly unrelated problems. Such problems are among top hits in various math competitions. Sequence is another good example. Most students understand the two basic types of sequences, namely, arithmetic and geometric. Though the vast majority of sequence related problems in math contests can be converted to these basic types, finding such conversion may be a demanding task which is usually not discussed in classrooms. Meanwhile, in order to become a strong competitor, one must also understand a few additional more complex sequences especially those defined recursively. They are beyond the scope of school textbooks, but are discussed in this book. The goal of this book is to give an organized in-depth discussion on competition level techniques. Fully understanding these techniques will help students to quickly recognize and solve these types of problems. It will also lay down a solid foundation for them to solve other problems whose solutions require these algebraic techniques as critical stepping stones. Please visit http: //www.ma


Competitive Mathematics for Gifted Students - Level 1 Combo

Ages 7-9
Author: Cleo Borac,Silviu Borac
Publisher: N.A
ISBN: 9780692240076
Category:
Page: 294
View: 8413
This is a combo volume that incorporates all four volumes for level 1. The interior of the 4 in 1 volume is always updated to contain the latest edition of the individual volumes. About "Competitive Mathematics for Gifted Students" This series provides practice materials and short theory reminders for students who aim to excel at problem solving. Material is introduced in a structured manner: each new concept is followed by a problem set that explores the content in detail. Each book ends with a problem set that reviews both concepts presented in the current volume and related topics from previous volumes. The series forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. Full solutions explain both reasoning and execution. Often, several solutions are contrasted. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Ready to participate in a math competition such as MOEMS, Math Kangaroo in USA, or Noetic Math? This series will open the doors to consistent performance. About Level 1 This level of the series is designed for students who know addition and subtraction with multi-digit numbers as well as simple multiplications of one-digit numbers. Some of the problems, however, involve advanced concepts and may be useful for older students.

    • Education

Alien Math


Author: Marya Washington Tyler
Publisher: PRUFROCK PRESS INC.
ISBN: 188266471X
Category: Education
Page: 148
View: 1218
Go shopping through an intergalactic mall...ride on a subterranean hover module...converse with creatures who know your every thought...and eat exotic food at an alien restaurant (if you can keep it from crawling away).

    • Education

Identifying, Describing, and Developing Teachers Who Are Gifted and Talented


Author: Van Sickle, Meta L.,Swanson, Julie D.,Bazler, Judith A.,Lubniewski, Kathryn L.
Publisher: IGI Global
ISBN: 1522558802
Category: Education
Page: 302
View: 6164
Much of the research about teachers focuses on “those who can’t/don’t/aren’t good” in the classroom. However, teachers who are gifted and talented exist, but there has been little attention to date on the characteristics and practices of such teachers in the classroom. While few, the examples of research on positive teacher attributes include work on the “expert,” “authentic,” and “creative,” as well as examples of research on eminent adults. Identifying, Describing, and Developing Teachers Who Are Gifted and Talented is an essential reference source that discusses behaviors and traits in teachers who are considered gifted and talented as well as case studies on the identification and preparation of teachers who fall into this category. Featuring research on topics such as creative innovation, emotional intelligence, and skill development, this book is ideally designed for educators, administrators, researchers, and academicians.

Practice Tests in Math Kangaroo Style for Students in Grades 1-2


Author: Cleo Borac,Silviu Borac
Publisher: N.A
ISBN: 9780692235287
Category:
Page: 100
View: 5563
A companion series to our "Competitive Mathematics for Gifted Students," the series "Math Challenges for Gifted Students" offers additional material in practice test form. The workbooks are useful for assessment and for development of testing skills. In full color and with fully detailed solutions, the workbooks may be used as a fun introduction to competitive problem solving. However, the problems are a bit more difficult than actual Kangaroo problems, exploring a large number of known 'tips and tricks.' One could say it is much more concentrated in that, unlike actual exams, it has less 'filler' - almost every problem is 'tricky' and embodies a specific strategy. The material is excellent for training purposes and has been used by the authors in seminars with hundreds of the most gifted students in the Bay Area. The workbook contains six 24-question tests. After each test there is an answer key. The tests are followed by detailed solutions. The recommended time limit for each test is of 75 minutes. Students who have not been exposed to competitive problem solving will find this book extremely difficult and will need help from an adult. Without preparation, students who get 'A' in school generally score about 50 points out of 96 possible on Kangaroo level 1-2.

    • Education

Math Basics 4


Author: Barbara Bando Irvin
Publisher: School Zone Publishing Company
ISBN: 9780887431401
Category: Education
Page: 64
View: 5203
Math Basics 4 includes the most important elements of the fourth grade math curriculum and the skills that cause children the most difficulty. This workbook may be used to introduce maintain or review skills. Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics (NCTM) was used as a guide in writing this book. Ages 8-9

    • Juvenile Nonfiction

Counting on Frank


Author: Rod Clement
Publisher: Gareth Stevens Publishing LLLP
ISBN: 9780836803587
Category: Juvenile Nonfiction
Page: 32
View: 6782
A boy and his dog present amusing counting, size comparison, and mathematical facts.

    • Juvenile Nonfiction

Singapore Math Challenge, Grades 5 - 8


Author: N.A
Publisher: Carson-Dellosa Publishing
ISBN: 1624424996
Category: Juvenile Nonfiction
Page: 352
View: 3396
Get ready to take the Math Challenge! Singapore Math Challenge will provide fifth grade students with skill-building practice based on the leading math program in the world, Singapore Math! Common Core Standards accelerate math expectations for all students, creating a need for challenging supplementary math practice. Singapore Math Challenge is the ideal solution, with problems, puzzles, and brainteasers that strengthen mathematical thinking. Step-by-step strategies are clearly explained for solving problems at varied levels of difficulty. A complete, worked solution is also provided for each problem. Singapore Math Challenge includes the tools and practice needed to provide a strong mathematical foundation and ongoing success for your students. The Common Core State Standards cite Singapore math standards as worldwide benchmarks for excellence in mathematics.

    • Education

Mathematical Mindsets

Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Author: Jo Boaler
Publisher: John Wiley & Sons
ISBN: 1118418271
Category: Education
Page: 320
View: 4334
Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

    • Education

The Math Olympian


Author: Richard Hoshino
Publisher: FriesenPress
ISBN: 1460258738
Category: Education
Page: 496
View: 8629
BETHANY MACDONALD HAS TRAINED SIX LONG YEARS FOR THIS MOMENT. SHE'LL TRY TO SOLVE FIVE QUESTIONS IN THREE HOURS, FOR ONE IMPROBABLE DREAM. THE DREAM OF REPRESENTING HER COUNTRY, AND BECOMING A MATH OLYMPIAN. As a small-town girl in Nova Scotia bullied for liking numbers more than boys, and lacking the encouragement of her unsupportive single mother who frowns at her daughter's unrealistic ambition, Bethany's road to the International Math Olympiad has been marked by numerous challenges. Through persistence, perseverance, and the support of innovative mentors who inspire her with a love of learning, Bethany confronts these challenges and develops the creativity and confidence to reach her potential. In training to become a world-champion "mathlete," Bethany discovers the heart of mathematics - a subject that's not about memorizing formulas, but rather about problem-solving and detecting patterns to uncover truth, as well as learning how to apply the deep and unexpected connections of mathematics to every aspect of her life, including athletics, spirituality, and environmental sustainability. As Bethany reflects on her long journey and envisions her exciting future, she realizes that she has shattered the misguided stereotype that only boys can excel in math, and discovers a sense of purpose that through mathematics, she can and she will make an extraordinary contribution to society....

Practice Arithmetic

Level 2 (ages 9 To 11)
Author: Cleo Borac,Silviu Borac
Publisher: N.A
ISBN: 9780692245668
Category:
Page: 114
View: 1032
2nd Edition - 2014 About "Competitive Mathematics for Gifted Students" This series provides practice materials and short theory reminders for students who aim to excel at problem solving. Material is introduced in a structured manner: each new concept is followed by a problem set that explores the content in detail. Each book ends with a problem set that reviews both concepts presented in the current volume and related topics from previous volumes. The series forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. Full solutions explain both reasoning and execution. Often, several solutions are contrasted. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Ready to participate in a math competition such as MOEMS, Math Kangaroo in USA, or Noetic Math? This series will open the doors to consistent performance. About Level 2 This level of the series is designed for students who know the multiplication tables, integer division with remainder and basic operations with decimals. Our level 1 books explain concepts that may need review before attempting level 2. Level 2 books are suitable for preparing Math Kangaroo 3-4 and MOEMS-E. Many of the concepts presented, however, reach much farther into the AMC-8 level. Level 2 consists of: Word Problems (volume 5), Operations (volume 6), Arithmetic (volume 7), and Combinatorics (volume 8). About Volume 7 - Arithmetic This volume provides material for the practicing problems with combinations of digits, cryptarithms, repdigits, palindromes, digit sum and digit product, sequences, sums of consecutive numbers, divisibility rules and remainders. Divisibility rules are not proven at this level, only applied (proofs in level 3 books). For some students, it may be necessary to work on our level 1 books before attempting level 2.