Math Mammoth Subtraction 1
Math Mammoth Subtraction 1 is a worktext that covers the concept of subtraction, the relationship between addition and subtraction, and the various meanings of subtraction.In the first lesson, Subtraction Is Taking Away, the child learns the basic meaning of subtraction as taking away objects, and learns to write subtractions from an illustration where some objects are crossed out.In the next lesson, the child counts down to subtract, which ties in subtraction with the number line. This is a transitional strategy to solve subtraction problems, because later students will learn more efficient ways to subtract, but it is important conceptually.The following lesson, Subtraction and Addition in the Same Picture, begins the study of the relationship between addition and subtraction. This concept will span several lessons. This first lesson presents two sets of objects, such as blue and white balls, and the student writes both an addition sentence and a subtraction sentence from this illustration.The lesson When Can You Subtract? concentrates on the idea that some subtractions, such as 4 - 5, are meaningless when you think of taking away. The child also makes subtraction patterns in this lesson.Then we continue studying the connection between addition and subtraction in the lesson Two Subtractions from One Addition. As an example, the child writes both 8 - 3 = 5 and 8 - 5 = 3 from the addition 3 + 5 = 8. This idea ties in with fact families, a concept that is coming up soon.In the lesson Two Parts - One Total, we study word problems that do not involve the idea of taking away but have two parts making up a total. For example, if there are 10 flowers of which some are white and some are red, and seven of them are white, how many are red?Then we study fact families, which means writing two additions and two subtractions using the same three numbers.In the lesson How Many More? students find how many more or how many fewer objects one person has than the other by drawing the objects. This lesson can easily be done with manipulatives if desired.In the very next lesson, "How Many More" Problems and Differences, we continue the theme, this time writing a missing addend addition for problems that ask "how many more." For example, Veronica has 4 marbles and Ann has 6. We write the missing addend sentence 4 + ___ = 6 to find how many more Ann has. In the next lesson the child then learns to write subtraction sentences for such problems.
Math Mammoth Addition 1
Math Mammoth Addition 1 is a worktext (includes both teaching and exercises), dealing with the concept of addition and addition facts within 0-10 (in few occasions numbers between 10 and 20 are used). The book is most suitable for first grade.The book starts out with very easy addition problems within 0-5, using pictures. If the student does not yet know the symbols + and =, you can introduce them first orally. In other words, use blocks or rocks and make addition problems where you use both kinds of wordings: "Three blocks and four blocks makes seven blocks. Three blocks PLUS four blocks EQUALS seven blocks." Play like that until the child can use the words PLUS and EQUALS in his/her own speech. This will make it easier for him/her to use the written symbols.Soon the lessons start including "missing addend" problems. We first use pictures, and gradually get to the abstract 1 + __ = 5 with symbols only. Keep in mind that children may confuse this problem with1 + 5 = __. You can word these problems like this: "1 and how many more makes 5?" You can MODEL them by drawing: First draw 1 ball. Tell the child that we need to have a total of 5 balls. He is to draw more until there are five balls. In the missing addend problem, however many balls the child has to draw is the number that goes on the empty line. So, first there is one ball, then we need to add (draw) some more to make 5. But how many more were drawn?After that, the book contains many lessons called Sums with... whose goal is to help the child memorize addition facts.My approach to memorization is many-fold: Structured drill, such as you see in the lessons Sums with 5, Sums with 6, and so on. This is not random drill, because you will start it by showing the pattern or the structure in the facts. This will help the student to tie the addition facts in with a context and help him understand the facts more on a conceptual level, instead of merely memorizing them at random. In sums with 5, the child learns the number combinations that add up to 5: 0 & 5, 1 & 4, and 2 & 3. This understanding is the basis for the drills.Using addition facts in games, in math problems, everyday life, or anywhere else. Games are especially useful because they help children like mathematics.Random drilling may also be used as a tool among others.Memory helps such as silly mnemonics or writing math facts on a poster and hanging it on the wall. These are not needful for all children.However, keep in mind that children will need LOTS of opportunities to add numbers to actually memorize the facts, so the memorization may not totally occur as your child works through this book. These same addition facts are further studied and used in the Math Mammoth Subtraction 1 book, and in all later math work since they are constantly used. At the latest, your child should memorize addition facts during second grade.
Math Mammoth Fractions 2
Math Mammoth Fractions 2 continues the study of fraction topics after Math Mammoth Fractions 1. (I sincerely recommend that the student study the Fractions 1 book prior to studying this book, if he has not already done so.)This book is meant for fifth grade, and deals in-depth with the following topics: simplifying; including simplifying before multiplyingmultiplication of fractions (and of mixed numbers)division of fractionsWe start out by simplifying fractions. Since this process is the opposite of making equivalent fractions, studied in Math Mammoth Fractions 1, it should be relatively simple for students to understand. We also use the same visual model, just backwards: This time the pie pieces are joined together instead of split apart.Next comes multiplying a fraction by a whole number. Since this can be solved by repeated addition, it is not a difficult concept at all.Multiplying a fraction by a fraction is first explained as taking a certain part of a fraction, in order to teach the concept. After that, students are shown the usual shortcut for the multiplication of fractions.Then, we find the area of a rectangle with fractional side lengths, and show that the area is the same as it would be found by multiplying the side lengths. Students multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.Simplifying before multiplying is a process that is not absolutely necessary for fifth graders. I have included it here because it prepares students for the same process in future algebra studies and because it makes fraction multiplication easier.Students also multiply mixed numbers, and study how multiplication can be seen as resizing or scaling. This means, for example, that the multiplication (2/3) ? 18 km can be thought of as finding two-thirds of 18 km.Next, we study the division of fractions. The first lesson on the topic shows how fractions can be seen as divisions; in other words, for example, 5/3 is the same as 5 繩 3. This of course gives us a means of dividing whole numbers and getting fractional answers (for example, 20 繩 6 = 3 2/6).The next lesson on the topic explores the thought of solving division problems by multiplying, and then introduces reciprocal numbers and the common shortcut for fraction division.The following two lessons focus on two ways to think about division: equal sharing, and fitting the divisor (measurement division), and how they apply to fraction division. Here is an example of equal sharing: If two people equally share 4/5 of a pizza, how much will each person get? This is represented by the division (4/5) 繩 2 = 2/5.
The 2018-2024 Canadian Twin Prime Conjecture Solo Expedition
... one of - if not the most famous proof in all of mathematics - admired for its elegance - simplicity and profundity is Euclid's Proof of Infinite Primes - mathematical rigor currently enjoys an unprecedented historical resurgence over its long history - yet to this author - it seems the strength of the deep-learned analysis and logical arguments used in ancient Greek proof somehow remains missing in contemporary mathematics - to address this - the author does not follow conventional research protocol and abandons research into all prior knowledge on the elusive proof of the long-standing Twin Prime Conjecture - rather - a rare summit attempt is made from first principals alone - equipped with little more than the definition of a twin prime - this Canadian mathematician begins a six year mathematical solo research expedition into unravelling the chaos that is the twin primes - always in search of patterns - the nature of the of twin primes has led several mathematicians to conclude that the exhibited random pattern is chaotic - no discernible pattern exists - under such conditions we cannot predict anything about how twin primes behave nor attempt to count them over increasingly large - infinite domains - lacking a proof akin to Euclid's - that outcome places twin primes outside the harmonious mathematics of the ancient Greeks - a world that we mathematicians have always sought to retain - such incongruity and disharmony is jarring and harsh for any mathematician to accept - after undergoing my transformation into a mathematical alpinist - the expedition strategy was to focus not on the (twin) primes but rather their theoretical complement - the odd composites - it was conjectured by the author that a deeper understanding of these simplistic mathematical entities would indirectly reveal how twin primes are constructed - to summit one of the highest unclimbed mathematical peaks - required new innovative techniques - bold daring thoughts and inexhaustible patience and persistence - if you continue to climb and gain altitude you must - eventually - reach the summit - one painful step at a time - lastly - having reached the summit - by far the most daunting task was to collate and present the argument in such a manner that others would not only understand it but be convinced of the result in the same manner that those who read Euclid's proof are - with elegance - simplicity and profundity ...... this long-awaited Proof of the Twin Prime Conjecture rescues the harmonious nature of mathematics out of chaos ... it was an exhilarating unforgettable intellectual mathematical alpine expedition ... more than once I felt at the brink of physical and mental exhaustion and had to take a brief walk away simply to recover from the task - too often any discussion of the hard intellectual struggles are omitted from the discourse and too often the final result alone is presented as if it was the initial effort and attempt - when the truth involved so much more ...
Math Mammoth Introduction to Fractions
Math Mammoth Introduction to Fractions contains lessons for fraction arithmetic for grades 1-4. This material does not include division or multiplication of fractions, nor adding unlike fractions, which are topics for 5th and 6th grades. Also, most of the material here is for 3rd and 4th grades, and only a few lessons are meant for grades 1-2.The topics covered are on a simple level, constantly illustrated with visual models, and with small denominators. The presentation avoids spelling out specific rules for manipulating fractions, but instead relies on the usage of pictures on a very concrete level. Children easily confuse the various rules for fraction arithmetic, because there are so many. There is a place for the rules, as shortcuts for ideas that are already understood, but we do not start with them. The goal is to let the big ideas sink in conceptually first, followed by some shortcuts.The topics covered areone half and one fourthconcept of a fractionconcept of a mixed numbercomparing fractionsequivalent fractionsadding and subtracting like fractionsadding and subtracting mixed numbers with like fractional partsadding one fraction that has tenths and another that has hundredths (such as 3/10 + 7/100)multiplying a fraction by a whole numberThe lessons are organized by topic, not by increasing difficulty. For reference, 1st grade students study only the concept of one half and one fourth. In 2nd grade, they study the concept of a fraction and optionally the easiest (first) lesson on comparing fractions. In 3rd grade, students study the concept of a fraction, fractions on a number line, comparing fractions, and equivalent fractions. Then in 4th, they study mixed numbers, comparing fractions, equivalent fractions, adding and subtracting fractions and mixed numbers, and multiplying fractions by whole numbers.The answers are appended.
Math Mammoth Grade 8 Review Workbook
Math Mammoth Review Workbook, Grade 8 is intended to give students a thorough review of eighth grade math, following the topics listed in the Common Core Standards.The book has both topical as well as mixed (spiral) review worksheets, and includes both topical tests and a comprehensive end-of-year test. The tests can also be used as review worksheets, instead of tests.Please note: The content for this workbook is taken from Math Mammoth Grade 8 Complete Curriculum (Light Blue Series), so this book is redundant if you already own Math Mammoth grade 8.You can use this workbook for various purposes: for summer math practice, to keep a student from forgetting math skills during other break times, or to prepare students who are going into algebra 1.The topics reviewed in this workbook are: exponentsscientific notationgeometric transformationsvolumeangle relationshipslinear equationsintroduction to functionsgraphing linear equationssystems of linear equationssquare roots and the Pythagorean Theorembivariate dataPlease note this book does not contain lessons or instruction for the topics. It is not intended for initial teaching. It also will not work if the student needs to completely re-study these topics (the student has not learned the topics at all). For that purpose, please consider Math Mammoth Grade 8 Complete Curriculum, which has all the necessary instruction and lessons.
Math Mammoth Fractions 1
Math Mammoth Fractions 1 is the first book of two that cover all aspects of fraction arithmetic. This book covers the concepts of fraction and mixed number, equivalent fractions, adding and subtracting like and unlike fractions, adding and subtracting mixed numbers, comparing fractions, and measuring in inches. The book Math Mammoth Fractions 2 covers the rest of fraction arithmetic: simplifying fractions and multiplication and division of fractions.Studying fractions involves lots of rules, and many students learn them only mechanically, not really understanding the underlying concepts and principles. Students then end up making lots of mistakes because they confuse the different rules, and either apply the wrong one or apply the right rule but don't remember it quite right. All this can make students even fear fractions.To avoid that, we use the visual model of a pie divided into slices all the way through the book. It is a natural model because a circle can be divided into any number of circle sectors (slices). When students work with this model from lesson to lesson, they will eventually start seeing these pies in their mind. This, in turn, gives them the ability to do many of the easier fraction calculations mentally. It also enables students to really UNDERSTAND these concepts, and not just learn mechanical rules.You are welcome to use manipulatives along with the book; however the visual pie model is probably sufficient for most students in the fifth grade level. I have also included (in the appendix) printable cut-outs for fractions from halves to twelfths.This workbook is most suitable for 5th grade. However, it is not tied to any grade level and does not mention anything about grade levels (except in the introduction), and so it can be used in various settings. It is also very good for remedial teaching or for students with learning challenges because of its heavy usage of visual models.The answers are appended.
Diophantine M-Tuples and Elliptic Curves
This book provides an overview of the main results and problems concerning Diophantine m-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators. The book presents fragments of the history of Diophantine m-tuples, emphasising the connections between Diophantine m-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine m-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine m-tuples are used to construct elliptic curves with interesting Mordell-Weil groups, including curves of record rank with agiven torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems. This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. However, it can be of interest to other mathematicians interested in number theory and arithmetic geometry. The prerequisites are on the level of a standard first course in elementary number theory. Background in elliptic curves, Diophantine equations and Diophantine approximations is provided.
Sacred Geometry
Uncover the Hidden Wisdom of Sacred Geometry: Your Gateway to Divine Alignment and TransformationIn a world where challenges often appear insurmountable, where climate change serves as an urgent reminder of a deeper crisis, there exists a beacon of hope-a profound wisdom concealed within the timeless realm of Sacred Geometry.Sacred Geometry: The Universal Language of Divine Alignment beckons both newcomers and seasoned seekers on a vivid voyage into the heart of reality's concealed enigmas. This book is your key to unlocking the secrets vital for our survival and spiritual evolution.Embark on a journey where you will: 1. Unveil Universal Wisdom: Shift your energy and awareness by immersing yourself in the profound truths concealed within the very fabric of time and space, governed by the geometric dance of the Sun, Moon, and Earth.2. Explore Your Inner Architecture: Acquire fresh insights into the intricate structure of your existence and discover how divine alignment holds the power to transform life's challenges into opportunities for growth.3. Ascend to Higher Dimensions: Sacred geometry serves as the ancient key that unlocks gateways to elevated realms of understanding and consciousness.4. Tools for Inner Peace: Learn the art of constructing and utilizing sacred geometry tools to attain emotional equilibrium, conquer stress, and craft a life of abundance and well-being.5. Blueprint for Survival: Delve deep within the recesses of your heart center to open a portal to the wisdom of your soul. Transcend the illusion of separation and unlock your true potential to not merely survive but thrive.With over four decades of dedicated expertise, Gail and Gregory Hoag have pioneered groundbreaking technologies that have transformed the lives of tens of thousands across the globe with their teaching and tools. They have harnessed the power of divine archetypes to amplify higher dimensional energies and elevate the human experience, catalyzing personal and spiritual growth towards the path of higher consciousness, well-being, and profound connection.
Math Mammoth Grade 5 Review Workbook
Math Mammoth Grade 5 Review Workbook is intended to give students a thorough review of fifth grade math. It has both topical as well as mixed (spiral) review worksheets, and includes both topical tests and a comprehensive end-of-the-year test. The tests can also be used as review worksheets, instead of tests.You can use this workbook for various purposes: for summer math practice, to keep a child from forgetting math skills during other break times, to prepare students who are going into sixth grade, or to give fifth grade students extra practice during the school year.The topics reviewed in this workbook are: the four operationslarge numbers and the calculatorproblem solvingdecimalsgraphing and statisticsfractions: add and subtractfractions: multiply and dividegeometryThe content for these is taken from Math Mammoth Grade 5 Complete Curriculum, so it works especially well to prepare students for grade 6 in Math Mammoth. However, the content follows a typical study for grade 5, so this workbook can be used no matter which math curriculum you follow.Please note this book does not contain lessons or instruction for the topics. It is not intended for initial teaching. It also will not work if the student needs to completely re-study these topics (the student has not learned the topics at all). For that purpose, please consider Math Mammoth Grade 5 Complete Curriculum, which has all the necessary instruction and lesson.
What doesn’t belong?
This workbook has 40 printable pages to improve analysis and reasoning skills. Students analyze dinosaurs, dragons, robots, monsters, zombies, birds, bugs, mammals, reptiles, numbers, shapes, polygons, smilies, kids, adults, school stuff, hats, cars, and more. The goal is to find the thing (or things) that do not belong: One monster does NOT belong: It has no arms or legs.Another zombie does NOT belong: It just wants to hug you.Several dinosaurs do NOT belong: They think that they are too good to walk.One robot does NOT belong: It is too smart for the others.One ant does NOT belong: It keeps tripping over untied shoelaces. Another dragon does NOT belong: It loves everyone, herbivores and carnivores alike.One shape does NOT belong: It tends to run away from the others.Several numbers do NOT belong: They are odd.And more...Use these pages as a sponge activity or at a math center for early finishers, for homework or extra credit, at the beginning of the year or right before the summer. Critical thinking has never been more important for second grade, third grade, and fourth grade. Take a Look Inside to see what is in this workbook.
Math Mammoth Grade 8 Answer Keys
Math Mammoth Grade 8 Answer Keys includes answer keys to: Math Mammoth Grade 8-A worktext;Math Mammoth Grade 8-B worktext;End-of-chapter tests;End-of-year test;Cumulative reviews.
Synergies in Analysis, Discrete Mathematics, Soft Computing and Modelling
Math Mammoth Grade 8-A Worktext
Math Mammoth Grade 8-A Worktext is the first student book for eighth grade mathematics, and part of the Math Mammoth Grade 8 complete curriculum.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. Features Math 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-B Worktext
Math Mammoth Grade 8-B Worktext is the second student book for eighth grade mathematics, and part of the Math Mammoth Grade 8 complete curriculum. 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.Features Math 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 Tests and Cumulative Reviews
Math Mammoth Grade 8 Tests & Cumulative Reviews contains the end-of-chapter tests, the comprehensive end-of-year test, and optional cumulative review lessons for Math Mammoth grade 8 complete curriculum.
Computational Physiology
This open access volume compiles student reports from the 2023 Simula Summer School in Computational Physiology. The reports provide an overview of some tools available to model physiology in excitable tissues across scales and scientific questions. In 2023, Simula held the nineth annual Summer School in Computational Physiology in collaboration with the University of Oslo (UiO) and the University of California, San Diego (UCSD). Each year, the course focuses on modeling excitable tissues, with a special interest in cardiac physiology and neuroscience. Group research projects conducted by graduate students from around the world result in reports addressing problems of physiological importance. Reports may not necessarily represent new scientific results; rather, they can reproduce or supplement earlier studies.Reports from seven of the summer projects are included as separate chapters. The topics represented include multiscale mechanics, electrophysiology, pharmacology, and machine learning. This is an open access book.
Math Foundations
This bilingual book, in English and Chinese, is for people who have already learned math in one language and have the need to understand or teach in the other language. Students from China studying abroad, Chinese parents who need to teach their English speaking children, and people who wish to work in China, will all benefit from this book.
Approximation and Online Algorithms
This book constitutes the refereed proceedings of the 21st International Workshop on Approximation and Online Algorithms, WAOA 2023, held in Amsterdam, The Netherlands, during September 7-8, 2023The 16 full papers included in this book are carefully reviewed and selected from 43 submissions. The topics of WAOA 2023 were algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, FPT-approximation algorithms, geometric problems, graph algorithms, inapproximability results, mechanism design, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, resource augmentation, and scheduling problems
Magic Multiplication
65 x 39 = 2535108 x 312 = 3369627 x 84 = 2268Can you work out these calculations in your head? Many of us would say "No way!" For anyone who reads this book and learns the tricks it contains, it won't be difficult anymore.This book aims to stimulate enthusiasm for math through rapid calculation, thereby creating a solid mathematical foundation for further learning. The goal is to express profound mathematical ideas in simple language, conveying the magic and mystery of calculation. As long as you can multiply two-digit numbers, do addition and subtraction, and understand simple negative numbers, you can handle the basics of this book.
Applied Numerical Analysis with Matlab(r)/Simulink(r)
This textbook provides a compact but comprehensive treatment that guides students through applied numerical analysis, using MATLAB(R)/Simulink(R). Ideal as a hands-on source for courses in Numerical Analysis, this text focuses on solving problems using market-standard software, corresponding to all key concepts covered in the classroom. The author uses his extensive classroom experience to guide students toward deeper understanding of key concepts, while they gain facility with software they will need to master for later studies and practical use in their engineering careers.
Women in Numbers Europe IV
This volume contains research and expository content based on a wide variety of topics within modern number theory and arithmetic geometry. Research in this volume arises from or is connected with the Women in Numbers Europe (WiNE) IV conference held in summer 2022 in Utrecht, The Netherlands. The contents of this volume are of interest to professional mathematicians, graduate students, and researchers working in number theory, arithmetic geometry, and related areas.
Math Mammoth Grade 6-A Worktext, Canadian Version
Math Mammoth Grade 6-A worktext (Canadian version) is the first student book for sixth grade, and part of the Math Mammoth Grade 6 complete curriculum. In this book, students encounter the beginnings of algebra, learning about algebraic expressions, one-variable equations and inequalities, integers, and ratios. We also review and deepen the students' understanding of decimals, and study ratios and percent as new topics for 6th grade. Please note: The answer key is not included. All answer keys for grade 6 are sold in a separate book. The year starts out with a review of the four operations with whole numbers (including long division), place value, and rounding. Students are also introduced to exponents and do some problem solving.Chapter 2 starts the study of algebra topics, delving first into expressions and equations. Students practice writing expressions in many different ways, and use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. We also study briefly inequalities and using two variables.Chapter 3 has to do with decimals. This is a long chapter, as we review all of decimal arithmetic, just using more decimal digits than in 5th grade. Students also convert measuring units in this chapter.Ratios is a new topic (chapter 4). Students are already familiar with finding fractional parts from earlier grades, and now it is time to advance that knowledge into the study of ratios, which arise naturally from dividing a quantity into many equal parts. We study such topics as rates, unit rates, equivalent ratios, and problem solving using bar models.Percent (chapter 5) is an important topic to understand thoroughly, because of its many applications in real life. The goal of this chapter is to develop a basic understanding of percent, to see percentages as decimals, and to learn to calculate discounts.This curriculum is essentially the same as the U.S. version of Math Mammoth, only customized for the Canadian audience in these aspects: The curriculum uses the metric measurement units. Since Canadians do use imperial units, such as inches and pounds, in some contexts, the curriculum does mention them, but not often.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 sixth grade standards in any Canadian province. However, you can probably find material for any missing topics in the neighbouring grade levels of Math Mammoth materials.Available separately, Math Mammoth Grade 6-B worktext covers the second half of 6th grade math. Also available are the answer key book (which includes all answer keys for grade 6) and a book containing cumulative reviews and chapter tests.
Math Mammoth Grade 6-B Worktext, Canadian Version
Math Mammoth Grade 6-B worktext (Canadian version) is the second student book for sixth grade, and part of the Math Mammoth Grade 6 complete curriculum. This book contains chapters 6-10 of the curriculum.In chapter 6, we first review prime factorization, and then study the greatest common factor and the least common multiple.Chapter 7 first presents a thorough review of fraction operations from 5th grade (addition, subtraction, and multiplication). The topic of focus in the chapter is fraction division. Students also do some problem solving with fractions.In chapter 8, students are introduced to integers. They plot points in all four quadrants of the coordinate plane and learn to add and subtract with negative numbers. Multiplication and division of integers are studied in 7th grade.In geometry (chapter 9), the focus is on the area of polygons. This is studied in a logical progression: first, the area of right triangles, then the area of parallelograms, then, the area of triangles, and lastly the area of polygons. We also review some topics from earlier grades (quadrilaterals, perimeter, basic drawing). Other major topics in this chapter are calculating surface area of some solids using nets, and volume of rectangular prisms with fractional edge lengths.Lastly, in chapter 10, students study statistics. The focus idea is that of a statistical distribution. Students learn about measures of center and measures of variability, and how to summarize distributions using those. They learn how to make dot plots, histograms, boxplots, and stem-and-leaf plots.This curriculum is essentially the same as the U.S. version of Math Mammoth, only customized for the Canadian audience in these aspects: The curriculum uses the metric measurement units. Since Canadians do use imperial units, such as inches and pounds, in some contexts, the curriculum does mention them, but not often.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 sixth grade standards in any Canadian province. However, you can probably find material for any missing topics in the neighbouring grade levels of Math Mammoth materials.Available separately, Math Mammoth Grade 6-A worktext covers the first half of 6th grade math. Also available are the answer keys and a book containing cumulative reviews and chapter tests.
Math Mammoth Grade 6 Answer Keys, Canadian Version
This book includes answers for the Math Mammoth Grade 6-A and 6-B student worktexts (Canadian version), for all the chapter tests and end-of-year test, and for the cumulative reviews for grade 6. The other parts of the 6th grade curriculum (the 6-A and 6-B worktexts and the cumulative reviews & tests book) may be purchased separately.
Math Mammoth Grade 6 Tests and Cumulative Reviews, Canadian Version
Math Mammoth Grade 6 Tests & Cumulative Reviews (Canadian version) contains the end-of-chapter tests, the end-of-year test, and cumulative reviews lessons to match Math Mammoth Grade 6 curriculum (Canadian version).
Lecture Notes on Geometry of Numbers
This book serves as an illuminating introduction to the intricacies of the geometry of numbers. It commences by exploring basic concepts of convex sets and lattices in Euclidean space and goes on to delve into Minkowski's fundamental theorem for convex bodies and its applications. It discusses critical determinants and successive minima before explaining the core results of packings and coverings. The text goes on to delve into the significance of renowned conjectures such as Minkowski's conjecture regarding the product of linear forms, Watson's conjecture, and the conjecture of Bambah, Dumir, and Hans-Gill concerning non-homogeneous minima of indefinite quadratic forms. Dedicated to Prof. R.P. Bambah on his 98th birthday, a living legend of number theory in India, this comprehensive book addresses both homogeneous and non-homogeneous problems, while sprinkling in historical insights and highlighting unresolved questions in the field. It is ideally suited for beginnersembarking on self-study as well as for use as a text for a one- or two-semester introductory course.
Theory of Groups of Finite Order
Theory of Groups of Finite Order, is a classical and a rare book, that has been considered important throughout the human history, and so that this work is never forgotten we at Alpha Editions have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and redesigned. These books are not made of scanned copies of their original work, and hence their text is clear and readable. This remarkable volume falls within the genres of Science Mathematics
Math Mammoth Grade 3 Answer Keys, Canadian Version
This book includes answers for Math Mammoth Grade 3-A and 3-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 at Lulu.
Math Mammoth Grade 3 Tests and Cumulative Reviews, Canadian Version
Math Mammoth Grade 3 Tests and Cumulative Reviews (Canadian Version) contains the chapter tests, end-of-year test, and cumulative revision worksheets for Math Mammoth grade 3 curriculum. It does not contain answers; the answer key book may be purchased separately.
Math Mammoth Grade 3-B Worktext, Canadian Version
Math Mammoth Grade 3-B Worktext (Canadian version) is the student book for the second half of third grade math. In this part B, the main areas of study are: place value (4-digit numbers)the concept of division and basic division facts; geometry (area and perimeter); measurement; fractions. The curriculum is essentially the same as the U.S. version of Math Mammoth Grade 3, only customized for the Canadian audience in these aspects: The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.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.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).A companion to this book, Math Mammoth Grade 3-A worktext, covers the first half of 3rd grade math (available separately).
Math Mammoth Grade 3-A Worktext, Canadian Version
Math Mammoth Grade 3-A worktext (Light Blue Series) is the student book for the first half of third grade math. In this part A, the main areas of study are: addition and subtraction within 1,000 (including mental math); the concept of multiplication; the multiplication tables; telling time and working with time intervals; counting coins and solving problems related to money.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).This curriculum is essentially the same as the U.S. version of Math Mammoth Grade 3, only customized for the Canadian audience in these aspects: The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.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.The currency used in the chapter on money is the Canadian dollar.Page (paper) size is Letter.
A Practical Arithmetic
A Practical Arithmetic is an unchanged, high-quality reprint of the original edition of 1873. Hansebooks is editor of the literature on different topic areas such as research and science, travel and expeditions, cooking and nutrition, medicine, and other genres. As a publisher we focus on the preservation of historical literature. Many works of historical writers and scientists are available today as antiques only. Hansebooks newly publishes these books and contributes to the preservation of literature which has become rare and historical knowledge for the future.
Complete Arithmetic, Part II
An essential guide to arithmetic for students and teachers alike. This book covers topics such as fractions, decimals, and advanced algebra, making it an ideal resource for anyone looking to develop their mathematical skills.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Cockers Arithmetick, Perused by J. Hawkins
First published in 1678, Edward Cocker's Arithmetick is a classic text that has been used for centuries to teach the principles of mathematics. This edition, perused by J Hawkins, includes helpful explanations and examples that make even the most complex concepts easy to grasp. Whether you're a student, a teacher, or just someone who loves numbers, this book is sure to become a favorite.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Hamilton's Essentials of Arithmetic; Volume 2
Hamilton's Essentials of Arithmetic is an indispensable guide to the fundamental principles of mathematics. Written by Samuel Hamilton, an experienced teacher and mathematician, this book covers all the essential topics in arithmetic, from basic operations and fractions to percentages, algebra and geometry. With clear explanations and worked examples, as well as a wide range of practice exercises and quizzes, Hamilton's Essentials of Arithmetic is an ideal textbook for students of all ages and abilities.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Practical Arithmetic
First published in the mid-19th century, this classic textbook teaches arithmetic through a series of practical and relevant problems, such as measuring land, calculating interest, and making change. With clear explanations and plenty of practice exercises, this book is perfect for anyone looking to improve their numeracy skills.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Masters' Ready Reckoner
This practical book is a comprehensive guide to everyday arithmetic. It includes information on measurements, weights and measures, and other important calculations. It is an excellent resource for students, professionals, and anyone else who needs to perform quick calculations on a regular basis.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Introduction To The Theory
This classic introduction to the theory of numbers provides a clear and accessible guide to the fundamental concepts and techniques of number theory. Ramsey's elegant exposition covers everything from prime numbers and diophantine equations to modular forms and zeta functions, making this an essential text for anyone interested in this fascinating field. With exercises and solutions included at the end of each chapter, this book is ideal for self-study or as a text for an undergraduate course in number theory.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Introduction to the National Arithmetic on the Inductive System
This classic mathematics textbook covers arithmetic using the inductive system, written by Benjamin Greenleaf who was a prominent American educator and mathematician. Through accessible language and carefully crafted examples, Greenleaf introduces important concepts in arithmetic, making this book an essential resource for students and teachers alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Intellectual Arithmetic, Upon the Inductive Method
This book provides a comprehensive and detailed study of arithmetic, with a focus on the inductive method of reasoning. The author provides insightful commentary and analysis in a highly readable style. A must-read for educators and mathematicians.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Introduction To The Theory
This classic introduction to the theory of numbers provides a clear and accessible guide to the fundamental concepts and techniques of number theory. Ramsey's elegant exposition covers everything from prime numbers and diophantine equations to modular forms and zeta functions, making this an essential text for anyone interested in this fascinating field. With exercises and solutions included at the end of each chapter, this book is ideal for self-study or as a text for an undergraduate course in number theory.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
