So You Think You Know III
The secret qualities of numbers revealing the keys to understanding ancient cryptic works. Numbers related to biology, chemistry and secrets of Fibonacci and Polynacci Single Digit Cycles. Golden Angles and the Great Pyramid are new discoveries together with a detailed study of long division Single Digit Properties and Magic Squares. An ancient method of calculating planetary distances is detailed.
Evolutionary Optimization Algorithms
The text covers evolutionary optimizing algorithms with the help of MATLAB and Python programming in a comprehensive manner. It will be an ideal reference text for readers in diverse engineering fields including electrical, electronics and communication, computer science and mechanical engineering.
Polyadic Transcendental Number Theory
The existence of transcendental numbers was first proved in 1844, by Joseph Liouville. Advances were made by Charles Hermite, proving the transcendence of the number e, and Ferdinand von Lindemann, proving the transcendence of the number π. The consequence of these discoveries was the negative solution to the problem of squaring the circle, which has stood for many years. In the 20th century, the theory of transcendental numbers developed further, with general methods of investigating the arithmetic nature of various classes of numbers. One of these methods is the Siegel-Shidlovskii method, previously used for the so-called E- and G-functions.Polyadic Transcendental Number Theory outlines the extension of the Siegel-Shidlovskii method to a new class of F-series (also called Euler-type series). Analogues of Shidlovskii's famous theorems on E-functions are obtained. Arithmetic properties of infinite-dimensional vectors are studied, and therefore elements of direct products of rings of integer p-adic numbers are considered. Hermite-Pad矇 approximations are used to investigate the values of hypergeometric series with algebraic irrational parameters. Moreover, the book describes how to use Hermite-Pad矇 approximations to obtain results on the values of hypergeometric series with certain transcendental (polyadic Liouville) parameters. Based on recent results, this book contains indications of promising areas in a new field of research. The methods described will allow readers to obtain many new results.
An Introduction To Chaotic Dynamical Systems
This widely used graduate text introduces modern topics in dynamical systems. The author includes new material on complex dynamics leading to key revisions. Striking color photos illustrating both Julia and Mandelbrot sets are included. This book assumes no prior acquaintance with advanced mathematical topics.
Vedic Tricks Made Mathematics Easy
Unveiling the Power of Vedic Mathematics: Essential InsightsEfficiency in Calculation: Vedic Mathematics provides highly efficient techniques for mental calculations, enabling individuals to perform complex computations quickly. This efficiency is particularly valuable in situations where rapid calculation is crucial.Versatility Across Mathematical Operations: The techniques in Vedic Mathematics are versatile and applicable across various mathematical operations, including addition, subtraction, multiplication, division, algebraic equations, and even advanced mathematical concepts.Promote Skills of Mental Calculations: Vedic Mathematics strongly emphasizes mental calculations, fostering the development of strong mental calculation skills. It not only enhances cognitive abilities but also makes mathematical tasks more accessible without the reliance on external tools.Applicability to Competitive Exams: Many of the Vedic Mathematics techniques are designed to streamline calculations in competitive exams where time is a critical factor. As a result, students find these methods beneficial for solving problems quickly and accurately in exam settings.Mental Calculation: Vedic Mathematics emphasizes mental calculation, promoting the development of mental agility and mathematical intuition.Universality and Speed: The techniques are not limited to specific types of problems; they can be applied universally, making them adaptable to various mathematical scenarios. The methods are designed to be straightforward and can often lead to faster calculations compared to conventional methods.Educational Applications: Vedic Mathematics is often used as an educational tool to make learning mathematics more engaging, accessible, and enjoyable for students.Connection to Profound Wisdom: Vedic Mathematics is sometimes considered a part of the broader Vedic tradition, with enthusiasts believing it embodies a profound approach to mathematics.
Human-Like Decision Making and Control for Autonomous Driving
This book details research into human-like driving technology, utilising game theory to better suit a human and machine hybrid driving environment. Covering feature identification and modelling of human driving behaviours, the book explains how to design algorithms for decision making and control of autonomous vehicles in complex scenarios.
Techniques for Designing and Analyzing Algorithms
This text presents the main techniques of algorithm design, namely, divide-and-conquer algorithms, greedy algorithms, dynamic programming algorithms, and backtracking. Graph algorithms are studied in detail, and a careful treatment of the theory of NP-completeness is presented.
Math Mammoth Grade 8 Answer Keys, Canadian Version
This book includes answers for Math Mammoth Grade 8-A and 8-B student worktexts (Canadian version), for all of the chapter tests, and for the cumulative reviews. The other parts of the curriculum may be purchased separately.
Math Mammoth Grade 8-B Worktext, Canadian Version
Math Mammoth Grade 8-B Worktext, Canadian version is the student book for the second half of grade 8, and part of the Math Mammoth Grade 8 complete curriculum. The curriculum is essentially the same as the U.S. version of Math Mammoth Grade 8, only customized for the Canadian audience in these aspects: - The curriculum uses the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.- The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.- Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.- Page (paper) size is Letter.The US version of the curriculum is aligned to the Common Core Standards, which means this curriculum may not be properly aligned to the eighth grade standards in your province. However, you can probably find material for any missing topics in neighbouring grades.The book starts with chapter 5, graphing linear equations. Students study slope, and graph and write linear equations in slope-intercept and standard forms. They also learn about parallel and perpendicular lines.In chapter 6, students delve into square roots, cube roots, and irrational numbers and solve equations involving square and cube roots. The rest of the chapter is spent studying the Pythagorean Theorem and its applications.Next, in chapter 7, we focus on systems of linear equations. Students learn the three basic techniques for solving these and also solve a variety of problems that are solved with a pair of linear equations. The last chapter covers statistical topics: scatter plots and two-way tables.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so students can understand the math, not just learn "HOW" to do it.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.It requires very little teacher preparation.: )The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext.Each chapter introduction also includes a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 8-A Worktext, Canadian Version
Math Mammoth Grade 8-A Worktext, Canadian version is the student book for the first half of grade 8, and part of the Math Mammoth Grade 8 complete curriculum. The curriculum is essentially the same as the U.S. version of Math Mammoth Grade 8, only customized for the Canadian audience in these aspects: - The curriculum uses the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.- The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.- Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.- Page (paper) size is Letter.The US version of the curriculum is aligned to the Common Core Standards, which means this curriculum may not be properly aligned to the eighth grade standards in your province. However, you can probably find material for any missing topics in neighbouring grades.This book starts with a study of exponent laws, using both numerical and algebraic expressions. The first chapter also covers scientific notation (both with large and small numbers), significant digits, and calculations with numbers given in scientific notations.In chapter 2, students learn about geometric transformations (translations, reflections, rotations, dilations), common angle relationships, and volume of prisms, cylinders, spheres, and cones. Next, in chapter 3, our focus is on linear equations.Students both review and learn more about solving linear equations, including equations whose solutions require the usage of the distributive property and equations where the variable is on both sides.Chapter 4 presents an introduction to functions. Students construct functions to model linear relationships, learn to use the rate of change and initial value of the function, and they describe functions qualitatively based on their graphs.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so students can understand the math, not just learn "HOW" to do it.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.It requires very little teacher preparation.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 8 Tests and Cumulative Reviews, Canadian Version
Math Mammoth Grade 8 Tests & Cumulative Reviews (Canadian version) contains the chapter tests, end-of-year test and cumulative reviews for Math Mammoth Grade 8 complete curriculum (Canadian version).
Discovering Dynamical Systems Through Experiment and Inquiry
The book differs from most texts on the topic by blending the use of computer simulations with inquiry-based learning (IBL). Students can discover examples and counterexamples through manipulations built into the software though a link to the website.
Handbook of the Tutte Polynomial and Related Topics
The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials.Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial's many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial.Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
Calling Carlos
English: James gives details of what he does during the day. The main thing he does is, he calls his friend, Carlos. At bedtime, since he was unable to contact Carlos, he thinks about the many things they both did that day. Before going to sleep, James decides to reset his alarm clock for 7:00 a.m., and he can't wait until tomorrow to call Carlos, again! This book helps children learn how to tell time to the hour and to the half hour with the use of analogue and digital clock illustrations on every page. The digital clocks include "AM" or "PM" to help with this concept. The story is bilingual (English and Spanish), so it can help with teaching about time in both languages. The back pages include learning activities. Espanol: James da detalles de lo que hizo durante el d穩a. Lo que hace principalmente es, llamar a su amigo, Carlos. A la hora de dormir, como no pudo comunicarse con Carlos, piensa en las muchas cosas que los dos hicieron ese d穩a. Antes de dormirse, James decide volver a poner su despertador para las 7:00 a.m., y no puede esperar hasta ma簽ana para llamar a Carlos, 癒otra vez! Este libro ayuda para que los ni簽os y ni簽as aprendan a leer el reloj a la hora y a la media hora con el uso de ilustraciones de un reloj anal籀gico y otro digital en cada p獺gina. El reloj digital incluye "AM" o "PM" para ayudar con ese concepto. El libro es biling羹e (ingl矇s y espa簽ol), as穩 que puede ayudar con la ense簽anza del reloj en los dos lenguajes. Las p獺ginas de atr獺s incluyen actividades de aprendizaje.
Math Mammoth Grade 3 Answer Keys
Math Mammoth Grade 3 Answer Keys (2024 edition) contains answers to Math Mammoth Grade 3-A and 3-B student worktexts, to chapter tests, to the end-of-year test, and to the cumulative review lessons. This is the full-color version.
Math Mammoth Grade 3-B Worktext
Math Mammoth Grade 3-B Worktext (2024 edition) is the student book for the latter half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers four-digit numbers, division, measurement, geometry, and fractions. Please note: this is a student worktext and does not contain the answers. The answer keys for grade 3 are sold as a separate book. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. The curriculum meets and exceeds the Common Core standards.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.For multiplication tables and division facts, you can use our online practice program (free).
Math Mammoth Grade 3 Tests and Cumulative Reviews
Math Mammoth Grade 3 Tests and Cumulative Reviews (2024 edition) includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 3 curriculum. Please note: The book does not include the answer key. The answer keys for grade 3 are sold as a separate book.
Math Mammoth Grade 3-A Worktext
Math Mammoth Grade 3-A Worktext (2024 edition) is the student book for the first half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers addition, subtraction, rounding, word problems, the concept of multiplication, multiplication tables, time, and money. Please note: This is a student worktext and does not contain the answers. The answer keys for grade 3 are sold as a separate book. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching.The curriculum meets and exceeds the Common Core standards. FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 6-A Worktext, International Version
Math Mammoth Grade 6-A worktext (International version, 2022 edition) is the student worktext for the first half of grade 6, and part of the Math Mammoth Grade 6 complete curriculum. This book covers a revision of the four operations with whole numbers, beginning algebra concepts, decimal arithmetic, ratios, and percent.The worktext contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.The first chapter revises the four operations with whole numbers (including long division), place value and rounding. Students are also introduced to exponents. Chapter 2 delves into algebra topics, such as expressions and equations, inequalities and using two variables. Chapter 3 has to do with decimals, revising all of decimal arithmetic. Chapter 4 is about ratios, rates, unit rates, equivalent ratios and problem solving using bar models. In chapter 5, the goal is to develop a basic understanding of percent, to see percentages as decimals and to learn to calculate discounts. A companion to this book, Math Mammoth Grade 6-B worktext covers the second half of 6th grade math (available separately). Also available are the answer keys and a book containing cumulative revisions and chapter tests.
Math Mammoth Grade 6-B Worktext, International Version
Math Mammoth Grade 6-B worktext (International Version; 2022 edition) is the second part of a complete math curriculum for sixth grade, and part of the Math Mammoth Grade 6 complete curriculum. This book covers a revision of the four operations with whole numbers, beginning algebra concepts, decimal arithmetic, ratios, and percent.In this book, the main areas of focus are: prime factorization, GCF, and LCM;a revision of fraction arithmetic, plus division of fractions;the concept of integers, coordinate grid, addition & subtraction of integers;geometry: revision of quadrilaterals & drawing problems; area of triangles & polygons; volume of rectangular prisms with fractional edge lengths; surface area; statistics: concept of distribution, measures of centre, measures of variation, boxplots, histograms.A companion to this book, Math Mammoth Grade 6-A worktext covers the first half of 6th grade math (available separately). Also available are the answer keys and a book containing cumulative revisions and chapter tests.
Math Mammoth Grade 6 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 6 Tests and Cumulative Revisions (international version) contains the chapter tests, end-of-year test, and cumulative revision worksheets for Math Mammoth Grade 6 curriculum (international version). It does not contain answers; the answer key book may be purchased separately. This is the 2022 edition.
Math Mammoth Grade 6 Answer Keys, International Version
This book includes answers for the Math Mammoth Grade 6-A and 6-B student worktexts (international version), for all the chapter tests, the end-of-year test, and for the cumulative revisions. This is the 2022 edition.
Math Mammoth Grade 5 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 5 Tests and Cumulative Revisions (International Version) contains the chapter tests, end-of-year test, and cumulative revision lessons for Math Mammoth Grade 5 Complete Curriculum (International Version). Answers are not included; the answer key book may be purchased as a separate book.
Math Mammoth Grade 5-B Worktext, International Version
Math Mammoth Grade 5-B Worktext (International Version) is the student book for the second half of grade 5 mathematics, and part of the Math Mammoth Grade 5 complete curriculum. This book covers decimal multiplication and division, fraction addition and subtraction, fraction multiplication and division, and geometry.This book starts with chapter 6, which continues our study of decimals. The focus is on multiplying decimals by decimals, dividing decimals by decimals, and conversions between measuring units. Chapter 7 covers the addition and subtraction of fractions - another focus topic of 5th grade besides decimals. In chapter 8, we study the multiplication and division of fractions from various angles. Chapter 9 takes us to geometry, starting with a review of angles and polygons. Then, students learn to classify triangles and quadrilaterals, and study the concept of volume in the context of right rectangular prisms (boxes).Being a worktext, the book contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'), and is for the most part self-teaching.Features: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, not just learn "HOW" to do it.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental maths and number sense.It requires very little teacher preparation.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations and further practice.Please note this is a student book and does not contain the answers. The answer key book is available separately.The other parts of Math Mammoth Grade 5 curriculum are: grade 5-A student worktext, grade 5 answer keys, and grade 5 tests and cumulative revisions.
Math Mammoth Grade 5 Answer Keys, International Version
This book includes answers for Math Mammoth Grade 5-A and 5-B student worktexts (International Version), for all of the chapter tests, and for the cumulative revisions.
Math Mammoth Grade 5-A Worktext, International Version
Math Mammoth Grade 5-A Worktext (International Version) is the student book for the first half of grade 5 mathematics, and part of the Math Mammoth Grade 5 complete curriculum. This book covers the four operations, large numbers and the calculator, problem solving, the first part of decimal arithmetic, and graphing.Being a worktext means the book contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'), and is for the most part self-teaching.Features: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental maths and number sense.It requires very little teacher preparation ("open and go").The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations and further practice.Please note this student book does not contain the answers. The answer key book is available separately.The other parts of Math Mammoth International Version Grade 5 curriculum are: grade 5-B student worktext, grade 5 answer keys, and grade 5 tests and cumulative revisions.
Math Mammoth Square Roots & the Pythagorean Theorem
Math Mammoth Square Roots & The Pythagorean Theorem is a relatively short worktext focusing on irrational numbers, square roots, and the Pythagorean Theorem and its applications.First, students learn about taking a square root as the opposite operation to squaring a number. They learn about irrational numbers, and how to find approximations to square roots both with a calculator and with a guess-and-check method. Students also practice placing irrational numbers on the number line, using mental math to find their approximate location.Next, the book has a review lesson on how to convert fractions to decimals. The following lesson has to do with writing decimals as fractions, and teaches a method for converting repeating decimals to fractions.Then it is time to learn to solve simple equations that involve taking a square or cube root, over the course of two lessons. After learning to solve such equations, students are now fully ready to study the Pythagorean Theorem and apply it.The Pythagorean Theorem is introduced in the lesson by that name. Students learn to verify that a triangle is a right triangle by checking whether it fulfills the Pythagorean Theorem. They apply their knowledge about square roots and solving equations to solve for an unknown side in a right triangle when two of the sides are given.Next, students solve a variety of geometric and real-life problems that require the Pythagorean Theorem. This theorem is extremely important in many practical situations. Students should show their work for these word problems to include the equation that results from applying the Pythagorean Theorem to the problem and its solution.There are literally hundreds of proofs for the Pythagorean Theorem. In this book, we present one easy proof based on geometry (not algebra). As an exercise, students are asked to supply the steps of reasoning to another geometric proof of the theorem. Students also study a proof for the converse of the theorem, which says that if the sides of a triangle fulfill the equation a2 + b2 = c2 then the triangle is a right triangle.Our last topic is distance between points in the coordinate grid, as this is another simple application of the Pythagorean Theorem.
Math Mammoth Grade 2 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 2 Tests and Cumulative Revisions (International Version) contains the chapter tests, end-of-year test, and cumulative revision worksheets for Math Mammoth grade 2 complete curriculum. It does not contain answers; the answer key book may be purchased separately.
Math Mammoth Grade 2-A Worktext, International Version
Math Mammoth Grade 2-A Worktext (International Version) is the student worktext for the first half of grade 2, and part of the Math Mammoth Grade 2 complete curriculum. This book, 2-A, covers some revision, even and odd numbers, doubling, reading the clock, addition and subtraction facts within 0 - 18, adding two-digit numbers, geometry and fractions. The rest of the topics for 2nd grade are covered in the student book 2-B. Please note: this is a student worktext and does not contain the answers. The answer key book is available separately.Being a worktext, the book contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.Some main features of Math Mammoth complete curriculum (Light Blue series) are: focuses on conceptual understanding;uses lots of visual models and pattern exercises;mastery-oriented, focusing at length on a topic;emphasizes mental maths and number senserequires little preparation from the teacher.This curriculum is essentially the same as the US version of Math Mammoth Grade 2, only customised for the international audience in these aspects: The currency used in the money chapters in grades 1-3 is the Australian dollar.The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms to British international standards (British English).Page (paper) size is A4.Please note this is a student worktext and does not contain the answers. The answer key book is available separately.The other parts of Math Mammoth Grade 2 curriculum (International Version) are: grade 2-B student worktext, grade 2 answer keys, and grade 2 tests and cumulative revisions.
Math Mammoth Grade 4 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 4 Tests and Cumulative Revisions (International Version) contains the chapter tests, end-of-year test, and cumulative revision lessons for Math Mammoth grade 4 complete curriculum. Note: this book does not contain answers. The answer key book for grade 4 may be purchased as a separate book.
Math Mammoth Grade 2 Answer Keys, International Version
This book includes the answers for the Math Mammoth International Version Grade 2-A and 2-B student worktexts, for all of the chapter tests, and for the cumulative revisions for grade 2. The other parts of the curriculum may be purchased separately.
Math Mammoth Grade 4 Answer Keys, International Version
This book includes the answers for the Math Mammoth Grade 4-A and 4-B (International Version) student worktexts, for all of the chapter tests, and for the cumulative revisions. The A and B worktexts, and a book containing the cumulative revisions, chapter tests and the end-of-the-year test may be purchased as separate books.
Math Mammoth Grade 4-B Worktext, International Version
Math Mammoth Grade 4-B Worktext (International Version) is the student worktext for the second half of grade 4, and part of the Math Mammoth Grade 4 complete curriculum. This book covers division, geometry, fractions and decimals.The worktext contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.Please note this is a student worktext and does not contain the answers. The answer key book is available separately.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental maths and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations and further practice.For multiplication tables and division facts, you can use our online practice program (free).The other parts of Math Mammoth International Version Grade 4 curriculum are: grade 4-A student worktext, grade 4 answer keys, and grade 4 tests and cumulative revisions.
Math Mammoth Grade 2-B Worktext, International Version
Math Mammoth Grade 2-B International Version is the student worktext (in full color) for the second half of grade 2, and part of the Math Mammoth Grade 2 complete curriculum. This book covers three-digit numbers, measuring, regrouping in addition and subtraction, money (using Australian money) and the introduction to multiplication. The rest of the topics for 2nd grade are covered in the student book 2-A. Please note: this is a student worktext and does not contain the answers. The answer key book is available separately.Being a worktext, the book contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.Some main features of Math Mammoth complete curriculum (Light Blue series) are: focuses on conceptual understanding;uses lots of visual models and pattern exercises;mastery-oriented, focusing at length on a topic;emphasizes mental maths and number senserequires little preparation from the teacher.This curriculum is essentially the same as the US version of Math Mammoth Grade 2, only customised for the international audience in these aspects: The currency used in the money chapters in grades 1-3 is the Australian dollar.The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms to British international standards (British English).Page (paper) size is A4.The other parts of Math Mammoth International Version Grade 2 curriculum are: grade 2-A student worktext, grade 2 answer keys, and grade 2 tests and cumulative revisions.
Math Mammoth Grade 4-A Worktext, International Version
Math Mammoth Grade 4-A Worktext (International Version) is the student worktext for the first half of grade 4 mathematics, and part of the Math Mammoth Grade 4 complete curriculum. This book covers addition, subtraction, patterns, graphs, large numbers and place value, multi-digit multiplication, time, and measuring.The worktext contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.Please note this is a student worktext and does not contain the answers.Features: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental maths and number sense.It requires very little teacher preparation, which is a big help to most parents.: )The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations and further practice.For multiplication tables and division facts, you can use our online practice program (free).The other parts of Math Mammoth Grade 4 (International Version) are: grade 4-B student worktext, grade 4 answer keys, and grade 4 tests and cumulative revisions.
Math Mammoth Grade 1 Answer Keys, International Version
This book includes the answers for the Math Mammoth Grade 1-A and 1-B student worktexts (International Version), for all of the chapter tests, and for the cumulative revisions for grade 1. The other parts of the curriculum may be purchased as separate books.
Math Mammoth Grade 1-B Worktext, International Version
Math Mammoth Grade 1-B Worktext (International Version) is the student worktext for the second half of grade 1 mathematics studies. In this part B, the main areas of study are: addition and subtraction facts within 10;clock to the half hour;geometric shapes and measuring length;adding and subtracting within 100; andcounting coins (Australian currency).The worktext is in full color, and contains both the necessary instruction and the problems & exercises (the 'text' and the 'work'), and is for the most part self-teaching. It does not contain the answers.Features of the curriculum: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, not just learn "HOW" to do it. Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired. The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much. There is a strong emphasis on mental maths and number sense. Requires very little teacher preparation, which is a big benefit to most teachers/parents.: ) The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material. After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice. For addition and subtraction facts, you can use our online practice program (free). A companion to this book, Math Mammoth Grade 1-A worktext, covers the first half of 1st grade maths (available separately). Also available are the answer keys and a book containing cumulative revisions and end-of-chapter tests.
Math Mammoth Grade 1 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 1 Tests and Cumulative Revisions (International Version) contains the chapter tests, the end-of-year test, and cumulative revision worksheets for Math Mammoth Grade 1 curriculum. This book does not contain answers; the answer key book may be purchased separately.
Math Mammoth Grade 1-A Worktext, International Version
Math Mammoth Grade 1-A Worktext (International Version) is the student worktext for the first half of grade 1 mathematics studies. In this part A, the main areas of study are: The concepts of addition and subtraction;strategies for addition and subtraction facts; anddeveloping understanding of whole number relationships and place value till 100.The worktext is in full color, and contains both the necessary instruction and the problems & exercises (the 'text' and the 'work'), and is for the most part self-teaching. It does not contain the answers.Features of the curriculum: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, not just learn "HOW" to do it. Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired. The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much. There is a strong emphasis on mental maths and number sense. Requires very little teacher preparation, which is a big benefit to most teachers/parents.: ) The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material. After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice. For addition and subtraction facts, you can use our online practice program (free). A companion to this book, Math Mammoth Grade 1-B worktext, covers the second half of 1st grade maths (available separately). Also available are the answer keys and a book containing cumulative revisions and end-of-chapter tests..
Math Mammoth The Four Operations (with a Touch of Algebra)
Math Mammoth The Four Operations (with a Touch of Algebra) is a mathematics worktext meant primarily for fifth and sixth grades. Being a worktext means that this book is a textbook and workbook together: the lessons include both the explanations of the concepts, as well as practice exercises.The main topics of this book are mental math strategies, simple equations and expressions, the order of operations, partial products, using all four operations in solving problems, and number patterns in the coordinate grid.Students encounter the exact definition of an equation and an expression. They practice the order of operations with problems that also reinforce the idea of the equal sign ("=") as denoting equality of the right and left sides of an equation. These kinds of exercises are needed because students may think that an equal sign signifies the act of finding the answer to a problem (such as 134 + 23 = ?), which is not so.Students solve simple equations with the help of a bar model. They also use the pan balance model to solve simple one and two-step equations and even some three-step equations.We review the thought of partial products (multiplying and dividing in parts), including how those partial products are seen in the multiplication algorithm, and how to use mental math to divide numbers in parts.Although the book is named "The Four Operations," the idea is not to practice each of the four operations separately, but rather to see how they are used together in solving problems and in simple equations. We are trying to develop the student's algebraic thinking, including the abilities to: translate problems into mathematical operations, comprehend the many operations needed to yield an answer to a problem, "undo" operations, and so on. Many of the ideas in this book are preparing students for algebra.The answers are appended.
Math Mammoth Factors & Factoring
Math Mammoth Factors & Factoring is a worktext that covers typical number theory topics for upper elementary school: divisibility rules, finding factors of a given number, prime numbers, prime factorization, the greatest common factor, and the least common multiple. These topics are usually covered in grades 4-6.The book begins with 4th grade topics, starting out with the concept of divisibility and the common divisibility rules. The lesson Prime Numbers brings out the concept of a prime number as one that is only divisible by 1 and by itself. Armed with the knowledge about divisibility, students now learn how to find factors of a given two-digit number in the lesson Finding Factors.The following lesson, Primes and Finding Factors, is a review lesson about factors, primes, and divisibility rules, originally intended for beginning of 5th grade. You can use it as a review of the first four lessons of this book, or for students that have some knowledge of these topics already.The next two lessons delve into prime factorization using a factor tree. The first lesson on the topic only uses two-digit numbers. In the latter, students are introduced the sieve of Eratosthenes and they factorize three-digit and larger numbers.The last topics in the book are the greatest common factor (GCF), the least common multiple (LCM), and factoring sums, intended mainly for 6th grade. Factoring sums means writing a sum such as 42 + 18 as 6(7 + 3). We first find a common factor of 42 and 18 (which is 6), and use that to factorize the sum. The lesson only deals with numeric examples, but it is actually preparing students for algebra, where the same process is done with variables; for example x2 + 2x is factored as x(x + 2).The book ends in a review lesson. Answers are appended.
Math Mammoth Division 2
Math Mammoth Division 2 is a continuation from the Math Mammoth Division 1. It focuses on the topics of long division, remainder, problem solving, average, divisibility, and factors. The book is most suitable for fourth grade.We start out by reviewing basic division facts by single-digit numbers (such as 24 繩 4 or 56 繩 7). After that, we study terminology of division and dividing numbers by whole tens and hundreds (such as 400 繩 20). Next students practice the order of operations-this time with division as one of the operations.Then we study the concept of remainder, preparing students for the upcoming lessons on long division. At first, the concept of remainder is presented visually. Soon, students solve simple division problems with a remainder, written with the long division symbol (or long division "corner", as I like to call it).Next comes a set of lessons intended to teach long division in several small steps. We start with divisions where each of the digits in the dividend (thousands, hundreds, tens, and ones) can be divided evenly by the divisor (for example, 3096 繩 3). As the next step, there is a remainder in the ones. Then, the divisions have a remainder in the tens. Finally, there is a remainder in the hundreds and in the thousands, and this completes the step-by-step learning process for long division. The lessons also include lots of word problems to solve.After long division, we study the concept of average, which is a nice application of division, and problems that involve finding a fractional part of a quantity using division. For example, we can find 3/4 of a number by first finding 1/4 (dividing by 4) and then multiplying the result by 3. Students get help from visual bar models to solve the problems.The last section deals with elementary number theory. We study basic divisibility rules (though not all of them), prime numbers, and finding all factors of a given two-digit number.
Math Mammoth Multiplication 2
Math Mammoth Multiplication 2 is a worktext focusing on multi-digit multiplication and related topics. It best suits fourth grade mathematics.The first lessons briefly review the concept of multiplication and the multiplication tables. Next, students encounter equations in disguise - presented with shapes on both sides of a pan balance - in the lesson Scales Puzzles. This lesson is intended to be fun and motivational.Then, the focus shifts to multi-digit multiplication (also called multiplication algorithm or multiplying in columns). We start out by learning to multiply numbers by multiples of ten and hundred (for example, 20 ? 4 or 500 ? 6). After this is mastered, students learn the very important concept of multiplying in parts, or partial products. This means that, for example, we multiply 4 ? 63 in two parts: first we multiply 4 ? 60 = 240 and 4 ? 3 = 12, and lastly the results are added: 240 + 12 = 252.This principle underlies all other multiplication algorithms, so it is important to master. We don't want children to "blindly" memorize the multiplication algorithm without understanding what is going on with it. The partial products algorithm (multiplying in parts) also ties in with an area model, and it is very important that students see the connection between this visual model and the procedure.The book contains two lessons about multiplying in columns the "easy way". This "easy way" is a simplified form of the traditional multiplication algorithm, based on partial products. You may skip these two lessons at your discretion. The method taught in those lessons is most useful for students who may have trouble with the traditional form of the algorithm. This method is also helpful in cementing the student's understanding of the partial products method.The traditional, or standard, form of multiplication algorithm is taught next, and is hopefully fairly easy, with the partial products as a foundation.Students also study estimation, the order of operations, and multiplying with money. There are numerous word problems in all of the lessons. Students are encouraged to write number sentences for the word problems-essentially learning to show their work and their thinking process.The lesson So Many of the Same Thing has to do with proportional reasoning. The idea is really simple, and prepares students for learning ratios and proportions in middle school.The last major topic in the book is multiplying two-digit numbers by two-digit numbers. Again, we first study partial products and tie that in with an area model. The lesson Multiplying in Parts: Another Way is optional. Lastly, the book teaches the standard algorithm for two-digit by two-digit multiplication. Students will practice multiplication with more digits in the book Mammoth Multiplication & Division 3.
Math Mammoth Place Value 2
Math Mammoth Place Value 2 is a short worktext dealing with place value and three-digit numbers.The first lessons present three-digit numbers using a visual model of the base-ten blocks (hundred-flats, ten-pillars, and one-cubes) and number lines. To reinforce the important concept of place value, children practice separating three-digit numbers into their different "parts" (hundreds, tens, and ones), and making numbers from these parts.Next, we study skip-counting by tens, by twos, and fives. Then students compare and order three-digit numbers, including comparing simple number expressions.After this, we study rounding three-digit numbers to the nearest ten and to the nearest hundred. Lastly, the book includes a lesson on reading bar graphs and pictographs, which provide a nice real-life application for using three-digit numbers.
Math Mammoth Place Value 1
Math Mammoth Place Value 1 focuses on place value and two-digit numbers and is primarily meant for first grade level math.When children count, they basically just learn numbers as some kind of continuum that goes on without end. With simple counting, your child might not catch on to the inherent structure of the number system. Our number system is based on the idea that if you have lots and lots of objects, the efficient way to count and denote them is with groups of tens, hundreds, and thousands - not individually.The crucial point in understanding the concept of place value is therefore that a certain position represents a certain size group. The digit in each position tells us how many groups of that size there are. For example, in the number 2,381, an adult already knows that the 8 represents eight tens, and not just "8" and that the 3 represents three hundreds, and not just "3". The place of the digit tells us the size of the group, and the digit itself tells how many of that group.The initial lessons of the book that introduce tens and ones use a 100-bead abacus extensively. This 100-bead abacus or school abacus simply contains ten beads on ten rods, for a total of 100 beads. It is not the special abacus used by the Chinese or the Japanese. Each bead simply represents one. The 100-bead abacus lets children both "see" the numbers and use their touch while making them.You will need to purchase this school abacus separately, such as on Amazon, or make your own.The abacus is used in the first lessons, but it is not the only model used in the book. We also use base-ten blocks as a visual representation of two-digit numbers. If you own a set of base-ten blocks (manipulatives), you can use them along with the visual exercises, if desired.Moreover, we also use number lines and the 100-chart. Number lines help to visualize how numbers continue indefinitely and also relate to the concept of measuring. The 100-chart helps the child to be familiar with the numbers below 100 and find patterns in the number system.While most of the lessons in the book focus on place value, students also practice adding and subtracting multiples of ten, and rounding numbers to the nearest ten. The two lessons near the end of the book about tally marks and graphs are real-life applications of two-digit numbers. The last lesson about regrouping can be challenging, thus is optional.
Math Mammoth Add & Subtract 2-B
Math Mammoth Add & Subtract 2-B is a continuation to the book Math Mammoth Add & Subtract 2-A. The goal of this book is to study addition and subtraction within 0-100, both mentally and in columns, especially concentrating on regrouping in addition (carrying) and in subtraction (borrowing).Mental math is important because it builds number sense. This book includes many lessons that practice mental math. For example, the child practices adding and subtracting two-digit numbers when one of the numbers is a whole ten (such as 30 + 14 or 66 - 20).The students also learn to solve sums such as 36 + 8 or 45 + 9 with mental math (there is a regrouping), comparing them to the sums 6 + 8 and 5 + 9. Since 6 + 8 fills the first ten and is four more than the next ten, the sum 36 + 8 fills the next whole ten (40), and is four more than that, or 44.At the same time, students also learn to add two-digit numbers with regrouping. This is explained in detail with the help of visual models (base-ten blocks). You are welcome to use actual physical manipulatives, if you prefer. The main concept to understand is that 10 ones are regrouped to form a new ten, and this new ten is written using a little "1" in the tens column.After addition, the lessons focus on column subtraction, initially without regrouping and then with regrouping.The lesson Regrouping practices breaking down a ten into 10 ones. It is crucial that the child understands what happens here. Otherwise, they might end up only memorizing the procedure, and will probably at some point misremember how it was done. If you notice that the child does not understand the concept of regrouping, provide more practice with concrete manipulatives or visual exercises before proceeding.After learning regrouping, students practice mental subtraction in two separate lessons. One of them expounds on several methods for mental subtracting. The other is about Euclid's game-a fun game that also practices subtraction of two-digit numbers.
Math Mammoth Add & Subtract 2-A
Math Mammoth Add & Subtract 2-A deals with two main themes: strategies for adding and subtracting within 0-20; such as adding just one more, a trick with nine and eight, and subtracting using addition;memorizing the basic addition and subtraction facts of single-digit numbers with an answer between 10 and 18.While focusing on addition and subtraction techniques, the lessons also include many word problems.The goal is to memorize the facts, or at least become so fluent with them that an outsider cannot tell if the child remembers the answer or uses some mental math strategy to get the answer.Some children will accomplish this quicker and need less practice, whereas others will take longer. Thus, don't assign all the exercises in the book by default. Use your judgment, and try to match the amount of exercises to your child's need. The ones that don't get assigned can be used later for review. You can also use games to reinforce the facts, and in place of some of the exercises in the book (a list of games is provided in the book).Learning addition and subtraction facts is quite important for later study. For example, regrouping in addition and subtraction (carrying/borrowing) requires the ability to recall the basic facts efficiently and fluently.We will start the book with a few mental math strategies (Add Using "Just One More" and A Trick with Nine and Eight). The lesson Adding within 20 reviews those strategies and gives more practice. These initial lessons don't yet involve actual memorization techniques.The lesson Subtract to Ten explains another basic strategy, and has to do with subtracting in parts. For example, to do 13 - 5, one can subtract 5 in two parts: first do 13 - 3, which equals 10, and then subtract the rest, or 2 more. Memorizing the subtraction facts will be more efficient, but I want children to understand this strategy, because it is useful in many other situations also.Then we review how to complete the next whole ten, which is an important concept. An example of this concept is the question: What number do you add to 23 to get 30? As an equation, we write: 23 + __ = 30.In the next lesson, we study sums that go over ten, doing these sums in two parts. For example, in the sum 9 + 7, the child first completes 10 by adding 9 + 1. Then, the child adds the rest, or 6, to 10. Learning this prepares the child for addition facts where the sum is more than 10.The next lessons, Adding with 9, Adding with 8, Adding with 7, and Adding with 6, provide lots of practice for learning and memorizing the basic addition facts. There are 20 such facts: 9 + 2 till 9 + 9: 8 facts8 + 3 till 8 + 8: 6 facts7 + 4 till 7 + 7: 4 facts6 + 5 till 6 + 6: 2 factsThe last part of the book includes various lessons titled Number Rainbows and Fact Families with.... These give lots of practice and reinforcement for the basic addition and subtraction facts, emphasizing the connection between addition and subtraction as a strategy for subtraction facts.The follow-up to this book, Add & Subtract 2-B, practices adding and subtracting two-digit numbers mentally and in columns (regrouping).
