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 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 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 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.
Real Time Reduced Order Computational Mechanics
The book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity.This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme "Mathematical Analysis, Modelling and Applications", especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling. In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet.
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 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 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-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 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 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 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 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-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-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 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 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.
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 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.
Euler’s number with two million digits
The number e, called sometimes Euler's number, is a mathematical constant that is the base of natural logarithm.The number e can be calculated as is the limit of (1 + 1/n)n as n approaches infinityHere we present that number printed, in his first two million digits, in a single volume.
The Golden Ratio with two million digits
Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Often symbolized as Phi (φ), is also expressed as one plus the square root of five, divided by two.The Golden Ratio has profoundly influenced both art and architecture, serving as a guiding principle for achieving balance and aesthetic beauty.Here we present that number printed, in his first two million digits, in a single volume.
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.
Addition & Place Value
This workbook has 47 printable pages to help your students write the expanded form and word name of a sum. Each page has from 9 to 20 problems, from single to nine-digit addition problems. Students compute the sum and then write the answer as the word name or in expanded form. Hundreds. Thousands. Millions.Common Core Standards: 2.OA.B.2 2.NBT.A.3 and B.7 and 3.NBT.A.2 and 4.NBT.A.2 and B.4And, if you are interested in more Place Value activities, then take a look at these workbooks: Place Value: Thousands and MillionsAddition & Place ValueSubtraction & Place ValueMultiplication & Place Value
Subtraction & Place Value
This workbook has 47 printable pages to help your students write the expanded form and word name of a difference. Each page has from 9 to 20 problems. Problems range from single to nine-digit subtraction problems. Students compute the difference and then write the answer as the word name or in expanded form. Hundreds. Thousands. Millions.Common Core Standards: 2.OA.B.2 2.NBT.A.3 and B.7 and 3.NBT.A.2 and 4.NBT.A.2 and B.4And, if you are interested in more Place Value activities, then take a look at these workbooks: Place Value: Thousands and MillionsAddition & Place ValueSubtraction & Place ValueMultiplication & Place Value
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 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.
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-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-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. 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 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.
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.
