Skip to content

Mathematics Textbook 6A Grade

ArchiMath Publishing LLC

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

Pages: 216 

ISBN: 978-954-779-197-8

Available: Paperback & PDF

 The 6 grade textbooks are the first in the series. In 6A, a core goal is to develop basic numeracy — as students study the algebraic operations and their properties, they encounter the natural numbers and decimals. They begin work with variables, setting up a solid base for the work that is to come in later books.


In geometry, students begin by carefully defining geometric objects and build to discussions on area and perimeter of plane figures, plus volumes of simple solids. Students get a taste of number theory in their work with prime factorization and divisibility rules.

This introduction to the series invites students to become confident mathematics enthusiasts by introducing basic facts, explaining the not-so-basic operations that we use in our number system, and modeling excellent solutions.

Our Mathematics Textbooks and Workbook series focuses on building a truly solid foundation of mathematical knowledge and skill, with deep explorations into algebra, geometry, and general logic and problem solving. In addition to the core content, these textbooks place a strong emphasis on communicating mathematics clearly, doing computations efficiently, and using common sense to check if answers and results make sense.

  1. Natural Numbers. Operations
  2. Expressions and Efficient Calculations with Natural Numbers
  3. Word Problems and Expressions Again
  4. Variables and Basic Equations
  5. How Mathematicians Write Solutions
  6. Sample Pre-Tests and Exams
  7. How to Study for and How to Take Test


8. Fractional Numbers
9. Fractional Numbers. Common Fractions
10. Units of Measure. Intro to Metric System
11. Decimals. Introduction
12. Reading and Writing Decimals
13. Properties of Decimals
14. Multiplying and Dividing a Decimal
by 10, 100, 1000

  1. Comparing Decimals
  2. Representing Decimals on a Number Ray
  3. Adding Decimals
  4. Adding Decimals. Properties of Addition
  5. Subtracting Decimals
  6. Subtracting Decimals. Exercises
  7. More Equations (Review w/ Extension)
  8. Dependence of a Sum and a Difference

 on Their Components

  1. Adding and Subtracting Decimals
  2. Multiplying Decimals
  3. Multiplying Decimals.

 Properties of Multiplication

  1. Dividing a Decimal by Natural Number
  2. Dividing a Decimal by a Decimal
  3. Dependence of a Product and a Quotient

 on Their Components

  1. Operations with Decimals
  2. Calculating with a Calculator. (Project)
  3. Expressions, Units, and Words Again
  4. Length of a Segment Equal to the Sum or

 Difference of Segments

  1. Multiplying and Dividing the Length of

 a Segment by a Natural Number

  1. Basic Motion Equation. Average Speed
  2. Motion Problems
  3. Solving Word Problems. Exercises
  4. Review of the Topic

 “Fractional Numbers. Decimals”

  1. Sample Test and Exam

Chapter 3. Geometric Figures in the Plane

  1. Basic Geometric Figures (Review)
  2. Triangle. Types of Triangles (Review)
  3. Distance from a Point to a Line
  4. Altitudes in a Triangle
  5. Rectangle (Review)
  6. Area of a Rectangle (Review)
  7. Units for Length versus Units for Area

 (Review with Extensions)

  1. Converting Units for Area. Exercises
  2. Area of a Right Triangle
  3. Area of a Triangle
  4. Area of a Triangle. Exercises
  5. Quadrilateral and its Perimeter
  6. Area of a Quadrilateral
  7. Parallel Lines
  8. Parallelogram. Rhombus
  9. Perimeter of a Parallelogram
  10. Area of a Parallelogram
  11. Area of a Parallelogram. Exercises
  12. Trapezoid. Perimeter of a Trapezoid
  13. Trapezoid. Types of Trapezoids
  14. Area of a Trapezoid
  15. Area of a Trapezoid. Exercises
  16. Areas of Geometric Figures. Exercises
  17. Review of the Topic

 “Geometric Figures in the Plane”

  1. Sample Test and Exams


  1. Divisibility of a Sum
  2. Criterion for Divisibility by 2 and by 4
  3. Criterion for Divisibility by 5, 10, 25
  4. Criterion for Divisibility by 3 and by 9
  5. Criteria for Divisibility. Exercises
  6. Common Divisor and Greatest Common

 Divisor of Natural Numbers

  1. Representing Natural Numbers as

 as Product of Prime Factors

  1. Finding a Common Divisor (CD) and

 Greatest Common Divisor (GCD)

 by Factoring into Prime Factors

  1. Common Multiple and Least Common

 Multiple (LCM) of Natural Numbers

  1. Finding the Least Common Multiple

 (LCM) of Natural Numbers. Exercises

  1. Review of the Topic “Divisibility”
  2. Sample Test and Exams

79. Determining the Position of a Point in a Coordinate System
80. Rectangular Parallelepiped. Cube
81. Rectangular Parallelepiped. Exercises
82. Surface Area of a Rectangular Parallelepiped
83. Surface Area of a Rectangular
Parallelepiped. Exercises
84. Practical Work: Constructing a Model
of a Rectangular Parallelepiped
85. Volume of a Rectangular Parallelepiped
86. Units of Measure for Volume
87. Surface Area and Volume of a Rectangular
Parallelepiped. Exercises
88. Exercises with Practical Applications
89. Review of the Topic
“Rectangular Parallelepipeds”
90. Sample Test and Exams