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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.

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 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 & 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.

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).

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.

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-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.

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) 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 at Lulu.

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 (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.

This book includes answers for the Math Mammoth Grade 4-A and 4-B student worktexts (Canadian version), for all the chapter tests, for the end-of-year test, and for the cumulative review lessons in Math Mammoth Grade 4 curriculum (Canadian version).

Math Mammoth Grade 4 Tests and Cumulative Revisions (Canadian version) contains the end-of-chapter tests, end-of-year test, and cumulative review lessons for Math Mammoth grade 4 curriculum. Note: this book does not contain answers. The answer key book for grade 4 may be purchased separately.

Math Mammoth Grade 4-B worktext (Canadian version) is the student worktext for the latter half of the 4th grade math, and part of Math Mammoth complete curriculum for fourth grade. The book starts out with the topic of division. The focus is on learning long division and using division in word problems.In the geometry chapter, students first revise area and perimeter, and then concentrate on the topic of angles. Students measure and draw angles, solve simple angle problems and classify triangles according to their angles. They also study parallel and perpendicular lines.Fractions and decimals are presented last in the school year. These two chapters practise only some of the basic operations with fractions and decimals. The focus is still on conceptual understanding and on building a good foundation towards 5th grade math, where fractions and decimals will be in focus. FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children 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.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.

Math Mammoth Grade 4-A worktext (Canadian version) is the student worktext for the first half of the 4th grade math, and part of Math Mammoth complete curriculum for fourth grade. This book starts out with a review of addition and subtraction, patterns, and graphs. We illustrate word problems with bar diagrams and study finding missing addends, which teaches algebraic thinking. Children also learn addition and subtraction terminology, the order of operations, and statistical graphs.Next come large numbers-up to millions, and the place value concept. At first the student reviews thousands and some mental math with them. Next are presented numbers up to one million, calculations with them, the concept of place value and comparing. In the end of the chapter we find out more about millions and an introduction to multiples of 10, 100, and 1000. The third chapter is all about multiplication. After briefly reviewing the concept and the times tables, the focus is on learning multi-digit multiplication (multiplication algorithm). The children also learn why it works when they multiply in parts. We also study the order of operations again, touch on proportional reasoning, and do more money and change related word problems.The last chapter in the 4-A worktext is about time, temperature, length, weight, and volume. Students will learn to solve more complex problems using various measuring units and to convert between measuring units. FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children 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.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.

Math Mammoth Grade 5 Tests and Cumulative Reviews (Canadian Version ) contains the chapter tests, end-of-year test, and cumulative review worksheets for Math Mammoth grade 5 curriculum. It does not contain answers; the answer key book may be purchased separately.

Math Mammoth Foundational Word Problems is a workbook intended for students in 3rd grade and above that need more practice with word problems. I especially aim to help students in 4th-7th grades who have trouble with word problems and who need to "go back to the beginning", so to speak, to learn to solve them.The problems are generally based on a knowledge of third grade math, such as regrouping in addition and subtraction, the multiplication tables, concept of division, and calculating change. The problems do not require long multiplication, long division, or calculations with fractions or decimals (with the exception of money amounts).The worksheets have examples and some instruction about common strategies for word problems. Students are often encouraged to write down the calculations they do. They are also encouraged to make a drawing or a sketch of the situation in the problem, to help them understand the situation and to see what math operation is involved.Overall, most of the problems require two or more steps; however, some problem sets focus on differentiating what math operation should be used, and those only require a single step.Several problem sets are designed to help students to master problems that involve equal-size groups. These questions either ask for the total (and are thus solved by multiplying), or they ask for the size of the group or for the quantity of the groups (one can write a missing number multiplication sentence, such as 3 × ___ = 18 or use division).The book also includes word problems with fractions, with large numbers, with money, geometry word problems, and challenges in the form of puzzle corners.You can download sample pages from this link: https://www.mathmammoth.com/word_problems/Foundational_Word_Problems_samples.pdf

Math Mammoth Grade 6-B Worktext is the second student book in Math Mammoth grade 6 curriculum, meant for the latter half of 6th grade. This is the 2022 edition.The main areas of study in Math Mammoth Grade 6-B worktext are:prime factorization, GCF, and LCMfraction arithmetic with a focus on division of fractionsthe concept of integers, coordinate grid, addition & subtraction of integersgeometry: review of quadrilaterals & drawing problems; area of triangles & polygons; volume of rectangular prisms with fractional edge lengths; surface areastatistics: concept of distribution, measures of center, measures of variation, boxplots, stem-and-leaf plots, histogramsChapter 6 first reviews prime factorization and then teaches students two new concepts: the greatest common factor and the least common multiple. We also apply those concepts factor to simplify fractions and to find common denominators for adding fractions.In Chapter 7, students first review addition, subtraction, and multiplication of fractions from fifth grade. Then we focus on a new topic: the division of fractions. The chapter also includes ample practice in solving problems with fractions.Chapter 8 introduces students to integers (signed numbers). They plot points in all four quadrants of the coordinate plane, reflect and translate simple figures, and learn to add and subtract with negative numbers. (Multiplication and division of integers will be studied in 7th grade.)The next chapter, Geometry, focuses on calculating the area of polygons. After a brief review of terminology for triangles and quadrilaterals and drawing fundamentals, this new topic is presented simply in a logical progression: first, the area of a right triangle; next, the area of a parallelogram; then, the area of any triangle; and finally, the area of a polygon. After that, students learn how to use nets of simple solids to calculate their surface area. Lastly, we turn to the concept of volume. Students have already learned to find the volumes of rectangular prisms in 5th grade. Now they calculate the volumes of rectangular prisms with fractional edge lengths.The final chapter is about statistics. Beginning with the concept of a statistical distribution, students learn about measures of center and measures of variability. They also learn how to make dot plots, histograms, boxplots, and stem-and-leaf plots as ways to summarize and analyze distributions.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children 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.Very little teacher preparation is required.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.This is the full-color version of the worktext. Please note that it does not include the answers; they are sold as a separate book.

Math Mammoth Grade 6-A Worktext is the student book for the first half of grade 6 mathematics. This student worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. This is the 2022 edition.The main areas of study in Math Mammoth Grade 6-A are:review of the basic operations with whole numbersbeginning algebra topics: expressions, equations, and inequalitiesreview of all decimal arithmeticintroduction to ratios and percentprime factorization, GCF, and LCMa review of fraction arithmetic from 5th grade, plus a focus on division of fractionsthe concept of integers, coordinate grid, addition & subtraction of integersgeometry: review of quadrilaterals & drawing problems; area of triangles & polygons; volume of rectangular prisms with fractional edge lengths; surface areastatistics: concept of distribution, measures of center, measures of variation, boxplots, stem-and-leaf plots, histogramsThis book 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.In chapter 3 we review all of decimal arithmetic, just using more decimal digits than in 5th grade. Students also practice conversions of measurement units.Ratios (chapter 4) is a new topic for sixth grade. Students are already familiar with finding fractional parts of quantities 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.In chapter 5, the goal is to develop a basic understanding of percent, to see percentages as decimals, and to learn to calculate discounts.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children 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.Very little teacher preparation is required.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.The curriculum meets and exceeds the Common Core standards. This is the full-color version; in other words, the inside pages are in full color. Please note this is a student worktext and does not contain answers.

Math Mammoth Grade 2-A worktext is the student book for the second half of grade 2 mathematics. It covers some revision of 1st grade math, reading the clock, addition and subtraction facts within 18, adding two-digit numbers, geometry topics, and fractions.This student worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. This is the full-color version; in other words, the inside pages are in full color. Please note this is a student worktext and does not contain answers.Features of the curriculum:Math 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 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).This Canadian version of the 2-A worktext is essentially the same as the U.S. version, but is customised for Canadian audiences in these aspects:The spelling conforms to British international standards (British English).Page (paper) size is Letter.

Math Mammoth Grade 2 Answer Keys (International version; Canada) contains answer keys to Math Mammoth Grade 2-A and 2-B student worktexts, chapter tests, the end-of-year test, and the cumulative revision lessons. This is the full-color version; in other words, the inside pages are in full color.

Math Mammoth Grade 2 Tests and Cumulative Reviews includes consumable student copies of chapter tests, the end-of-year test, and additional cumulative review lessons to match Math Mammoth Grade 2 curriculum. This is the full-color version.