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Mathematics Workbook 6B Grade

ArchiMath Publishing LLC

Authors: Zvezdelina Stankova, Zdravka Paskaleva, Maya Alashka, Raina Alashka
Pages: 158 

ISBN: 978-954-779-208-1

Available: Paperback & PDF

In the 6B workbooks, students continue to build on the foundation set in 6A; this set has a heavy emphasis on algebra and arithmetic skills needed to progress to more advanced topics in the later books.


The 6B Workbook will strengthen the basic knowledge and skills needed to master the 6B material. To each topic in the 6B Textbook correspond problems in the 6B Workbook that every student should be able to solve. Some problems have a solution and some have the beginning of a solution. After working on such problems, students should be able to complete on their own the remaining problems.

The 6B Worksheets highlight the basic knowledge in 6B Textbook; have a teaching component; help students learn to organize and correctly write solutions to problems; and save time for the teacher in searching for more problems. The 6B Worksheets can be used for independent work by the student; to assign homework; to conduct tests; and for practical work with applications.

Chapter 6. Common Fractions

  1. Proper and Improper Fractions
  2. Mixed Numbers
  3. Basic Property of Fractions: Expanding
  4. Basic Property of Fractions: Reducing
  5. Comparing Fractions
  6. Converting Fractions

 to a Common Denominator

  1. Representing Common Fractions

 on a Number Ray

  1. Converting between Decimals

 and Common Fractions

  1. Finite and Infinite Repeating Decimals
  2. Adding Fractions with

 Same Denominators

  1. Adding Fractions

 with Different Denominators

  1. Subtracting Fractions

 with Equal Denominators

  1. Subtracting Fractions

 with Different Denominators

  1. Adding and Subtracting

 Common Fractions and Decimals

  1. Adding and Subtracting Fractions.

 Finding an Unknown Number

  1. Evaluating Numerical Expressions
  2. Multiplying Common Fractions
  3. Multiplying Fractions. Properties
  4. Dividing Common Fractions
  5. Dividing Fractions. Exercises
  6. Operations with Common Fractions

 and Decimals

  1. Operations with Fractions.

 Finding an Unknown Number

  1. Operations with Fractions.

 Evaluating Numerical Expressions

  1. Summary of “Common Fractions,”
  2. Summary of “Common Fractions,”

 Preparation and Test Techniques (Review)

  1. Sample Test and Exams


Chapter 7. Applications of Fractions

  1. Part of a Number
  2. Part of a Number. Basic Exercises
  3. Word Problems Solved by

 Introducing Parts of the Number 1

  1. Percent. Definition
  2. Percent. Basic Exercises
  3. Percent. Basic Exercises (Continuation)
  4. Percent. Applications
  5. Applications of Common Fractions.

 Area of a Triangle and a Trapezoid

  1. Areas of Geometric Figures
  2. Processing Information Given in a Table
  3. Processing Information Given in a Table

 (Practical Exercises)

  1. Circular Diagram. Histogram
  2. Summary of “Applications of Fractions”
  3. Sample Test and Exams

Chapter 8. Exponentiation

  1. The Operation of Exponentiation.

 Powers with Natural Exponents

  1. Numerical Expressions Containing Powers.


  1. Finding the Unknown Component When

 Operating with Powers. Exercises

  1. Multiplying Powers with Same Bases
  2. Dividing Powers with Equal Bases
  3. Finding Numerical Value of Expressions

 Containing Powers. Exercises

  1. The Power of a Product
  2. The Power of a Quotient
  3. The Power of a Power
  4. Operations with Powers. Exercises
  5. Scientific Notation of a Natural Number.


  1. Summary of “Exponentiation”
  2. Sample Test

Chapter 9.

Rational Numbers

 Part I: Modulus, Addition, and Subtraction

  1. Positive and Negative Numbers

 The Set of Rational Numbers

  1. Representing Rational Numbers

 on the Number Axis

  1. Opposite Numbers. Absolute Value

 (Modulus) of a Rational Number

  1. Modulus of Rational Numbers. Exercises
  2. Comparing Rational Numbers
  3. Adding Rational Numbers

 with Same Signs

  1. Adding Rational Numbers

 with Opposite Signs

  1. Properties of Addition
  2. Subtracting Rational Numbers
  3. Adding and Subtracting Rational Numbers.


  1. Algebraic Sum
  2. Algebraic Sum. Exercises
  3. Finding the Unknown Summand
  4. Summary of “Rational Numbers,”
  5. Sample Test

 for Constructing

  1. Multiplying Rational Numbers
  2. Properties of Multiplication
  3. Adding, Subtracting, and Multiplying

 Rational Numbers. Exercises

  1. Dividing Rational Numbers. Properties
  2. Dividing Rational Numbers. Exercises
  3. Multiplying and Dividing Rational Numbers.


  1. Finding the Unknown Factor
  2. Operations with Rational Numbers.


  1. Finding Powers of Rational Numbers
  2. Powers with Zero and Integer Exponent
  3. Powers with Integer Exponents.
  4. Summary of “Rational Numbers,”
  5. Sample Test for Constructing Diagrams


Chapter 10. Circles and Polygons

  1. Circle. Length of a Circle
  2. Circle. Length of a Circle. Exercises
  3. Length of a Circle. Practical Exercises
  4. Disc. Area of a Disc
  5. Constructing a Circular Diagram
  6. Polygon. Regular Polygon
  7. Area of a Polygon
  8. Summary of “Circles and Polygons”
  9. Test

Chapter 11. Graphing and Data

  1. Cartesian Coordinate System
  2. Coordinates of a Point.
  3. Reflecting Points across a Line.
  4. Representing Data in Tables and Graphs
  5. Understanding Data in Tables and Graphs
  6. Arithmetic Mean. Applications
  7. Summary of “Applications. Statistics”
  8. Sample Test

Chapter 12. Yearly Review

  1. Operations with Fractions (Review)
  2. Part of a Number. Percent (Review)
  3. Geometric Figures (Review)
  4. Rectangular Parallelepipeds (Review)
  5. Number Theory: Divisibility (Review)
  6. General Problems on Chapters 1-7
  7. Tests 1-2 and Exams 1-2 on Chapters 1-7
  8. Tests 3-4 on Chapters 1-7
  9. Exponentiation (Review). Test
  10. Rational Numbers (Review). Test
  11. Exit Level: Test 1, Test 2
  12. General Tests on 6th Grade Material


A1. Properties of Rational Numbers

 Properties of Powers

 A2. Geometric Figures and Solids

 A3. Statistical Data

 for Constructing Diagrams