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- Grade 5
- Grade 6
- Grade 7
- Grade 8

- History of arithmetic and geometry
- History of numbers

- History of ancient numeral systems
- Ancient measurement methods for length and weight

- The simplest geometric shapes: point, straight line, segment, semi-straight, polyline
- Cutting tasks
- Polyhedra: scans of polyhedra
- Circle, radius, diameter, chord, sector, segment

- Bodies of rotation
- Square and cube of a number
- Units of measurement of lengths, areas, and volumes
- Corners: measurement and types of angles

- Solving word problems through operations

- Using tables to solve word problems

- Numeral systems
- Classes and digits in the decimal system for natural numbers

- Addition, subtraction, multiplication, and division of natural numbers

- Tables of operations on numbers
- Quick counting techniques
- Division with the remainder
- Even and odd numbers
- Rules of divisibility for numbers divided by 3,4,8,9,6,7,11,13,1001

- Comparing numbers
- Solving equations using operation components
- Approximate value of a number
- Converting a number from one number system to another

- Fractions and shares
- Ordinary fractions
- Mixed numbers
- Addition and subtraction of ordinary fractions with the same denominator
- Addition and subtraction of mixed numbers
- The concept of a decimal fraction

- Comparison of decimals
- Addition and subtraction of decimals
- Multiplication of decimals
- Division of decimals
- Multiplication and division of decimals by 10, 100, 1000, etc
- Multiplication and division of decimals by 0.1, 0.01, 0.001, etc

- Numerical puzzles
- The arithmetic mean: practical application of the arithmetic mean in real life
- The average speed of movement
- Coloring pages, drawings, ornaments, patterns

- The concept of interest: solving percentage problems
- The use of a calculator in calculations
- Math games

- Solving the simplest logical problems

- Solving logical problems using tables

- Magic squares
- Simple and compound numbers
- The Sieve of Eratosthenes
- Least common multiple
- Greatest common divisor
- Euclid’s algorithm
- Parallel and perpendicular lines

- Random events: the probability of a random event
- Positive and negative numbers
- Line coordinates
- The modulus of the number
- Comparison of numbers

- The basic property of fractions
- Mutually prime numbers
- Comparison of fractions
- Reciprocal-inverse fractions
- Operations with ordinary fractions: addition, subtraction, multiplication, division
- Three main tasks on fractions
- Converting an ordinary fraction to decimal and vice versa

- Relationships and proportions
- Properties of proportions
- Percentage and percentage ratio
- Direct and inverse proportional dependencies
- Solving problems using proportions
- The division of the value in this respect
- Letter expressions: ratio

- Axial and central symmetries
- Coordinate plane

- Constructions on the coordinate plane: polylines, symmetries

- Patterns, coloring pages

- Sets of numbers: natural, integer, rational
- Addition and subtraction of rational numbers

- Table of operations with rational numbers

- Solving equations

- Solving problems using equations

Algebra

- Numbers and calculations. Numeric Puzzles
- Even and odd numbers
- Divisibility of natural numbers. Divisibility rules. Pigeonhole principle

- Constructible problems
- Game Challenges

- The concept of an equation as a model of a process
- Linear equation with one variable

- Using equations to solve text problems
- Interpretation of a real situation in the form of a linear equation

- Equivalent expressions. Identities
- Powers with natural exponent
- Natural exponent properties
- Monomials
- Polynomials
- Addition and subtraction of polynomials
- Multiplication of monomial by a polynomial
- Multiplication of polynomial by polynomial
- Division of polynomial by polynomial
- Factoring polynomials. Bracketing the common factor

- Factoring polynomials. Grouping method
- Product of sum and difference of two expressions
- Difference of two squares
- Square of a sum and square of a difference
- Convert polynomial to square of a sum or square of a difference
- Sum of a cube and difference of a cube
- Various methods of factoring a polynomial

- The relationship between the quantities
- Representations of functions

- Function graph
- Linear function, its graph and properties

- Equations with two variables
- Linear equation with two variables and its graph
- Systems of linear equations with two variables. Graphical method of solving a system of two linear equations with two variables
- Systems of linear equations: solving by substitution

- Systems of linear equations: solving by addition method
- Systems of linear equations: solving by analytical comparison
- Solving problems using systems of linear equations

Geometry

- Geometric figures
- Line

- Point, line, plane
- What does geometry study?

- Arrangement of points, lines, planes
- Angles, polygonal lines, polygons

- Circle
- Arrangement of a circle and straight line

- Congruence tests for triangles
- Isosceles triangle

- Triangle inequality
- Concept of property statement and its converse

- Proving lines are parallel
- Sum of angle measures in a triangle

- Sum of angle measures in polygon
- An exterior angle of a triangle

- Line segment construction
- Angle construction, angle bisector

- Construction of circumscribed and inscribed circles
- Perpendicular line construction

- Rational fractions
- The main property of a rational fraction

- Addition and subtraction of rational fractions with the same denominators
- Addition and subtraction of rational fractions with different denominators

- Multiplication and division of rational fractions. Raising a rational fraction to a power

- Identical transformations of rational expressions

- Equivalent equations
- Degree with negative integer exponent
- Integer exponent properties

- Function y = k / x and its graph
- Graphical method for solving equations in one variable.

- Function y = x2 and its graph
- Square roots. Arithmetic square root
- The set and its elements
- Subset. Operations on sets
- Number sets

- Arithmetic square root properties
- Identical transformations of expressions containing arithmetic square roots
- Function y = (root of x) and its graph

- Quadratic equations. Types of quadratic equations
- Solving incomplete quadratic equations

- Formula for the roots of a quadratic equation (2 formulas)
- Vieta’s Theorem

- Square trinomial. Factoring a square trinomial
- Equations with parameters (linear, square)

- Solving equations that reduce to quadratic equations
- Rational equations as mathematical models of real situations

- Numerical inequalitiess

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