Online Math Center

# Curriculum

## History of Math

• History of arithmetic and geometry
• History of numbers
• History of ancient numeral systems
• Ancient measurement methods for length and weight

## Fundamental Geometry

• The simplest geometric shapes: point, straight line, segment, semi-straight, polyline
• 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 World Problems

• Solving word problems through operations
• Using tables to solve word problems

## Natural Numbers

• Numeral systems
• Classes and digits in the decimal system for natural numbers
• Addition, subtraction, multiplication, and division of natural numbers

## Numeral Operations

• 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

• 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

## Math Games

• 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

## Logical Math

• Solving the simplest logical problems
• Solving logical problems using tables

## Algebraic Math

• 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

## Complex Fractions

• 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

## Geometry

• Axial and central symmetries
• Coordinate plane
• Constructions on the coordinate plane: polylines, symmetries

## Math Games

• Patterns, coloring pages

## Rational Numbers

• Sets of numbers: natural, integer, rational
• Addition and subtraction of rational numbers
• Table of operations with rational numbers

## Equations

• Solving equations
• Solving problems using equations

Algebra

## Math Games

• Numbers and calculations. Numeric Puzzles
• Even and odd numbers
• Divisibility of natural numbers. Divisibility rules. Pigeonhole principle
• Constructible problems
• Game Challenges

## Linear equation with one variable

• 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

## Polynomial expressions

• 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
• Cube of a sum and cube of a difference
• Various methods of factoring a polynomial

## Functions

• The relationship between the quantities
• Representations of functions
• Function graph
• Linear function, its graph and properties

## Systems of linear equations with two variables

• 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

## Basic concepts of geometry

• Geometric figures
• Line
• Point, line, plane
• What does geometry study?

## Basic properties of points, lines, planes

• Arrangement of points, lines, planes
• Angles, polygonal lines, polygons
• Circle
• Arrangement of a circle and straight line

## Triangles

• Congruence tests for triangles
• Isosceles triangle
• Triangle inequality
• Concept of property statement and its converse

## Parallel lines

• Proving lines are parallel
• Sum of angle measures in a triangle
• Sum of angle measures in polygon
• An exterior angle of a triangle

## Geometric constructions

• Line segment construction
• Angle construction, angle bisector
• Construction of circumscribed and inscribed circles
• Perpendicular line construction

## Rational expressions

• 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

## Math Assessment 1

• Multiplication and division of rational fractions. Raising a rational fraction to a power
• Identical transformations of rational expressions

## Math Assessment 2

• 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.

## Math Assessment 3 Square roots. Real numbers

• 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

## Math Assessment 4 Quadratic equations

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

## Math Assessment 5

• 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

## Math Assessment 6

• Numerical inequalitiess

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