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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
- 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 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
- Sum of a cube and difference of a cube
- 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
- Quadratic equations. Types of quadratic equations
- Solving incomplete 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