7th grade
Students expand their understanding of basic concepts in algebra and geometry. They work with algebraic expressions, linear equations, and systems of equations, and become familiar with elements of combinatorics. Basic geometry concepts, including triangles, are also introduced.
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lesson 1
Numerical expressions -
lesson 2
Algebraic expressions -
lesson 3
Properties of arithmetic operations -
lesson 4
Powers with natural exponents -
lesson 5
Properties of powers with natural exponents- 1 . Multiplying exponents with the same base
- 2 . Dividing exponents with the same base
- 3 . Raising an exponent to another exponent
- 4 . Raising a product to an exponent
- 5 . Raising a fraction to an exponent
- 6 . Writing numbers in exponent form
- 7 . Comparing numbers in exponent form
- 8 . Finding the number of trailing zeros in a product
- 9 . Finding the last digit of an expression's value
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lesson 6
Monomials -
lesson 7
Multiplying and dividing monomials -
lesson 8
Polynomials
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lesson 9
Adding and subtracting polynomials -
lesson 10
Multiplying and dividing polynomials- 1 . Multiplying a monomial by a polynomial
- 2 . Simplifying expressions: Multiplying a monomial by a polynomial
- 3 . Finding the power of a polynomial
- 4 . Multiplying polynomials
- 5 . Simplifying expressions: Multiplying polynomials
- 6 . Finding the numerical value of a polynomial
- 7 . Dividing a polynomial by a monomial
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lesson 11
Factoring polynomials -
lesson 12
Short multiplication formulas- 1 . Formula for the square of a sum
- 2 . Formula for the square of a difference
- 3 . Finding the square of numbers
- 4 . Simplifying expressions: Formulas for the square of a sum and difference
- 5 . Equations: Formulas for the square of a sum and difference
- 6 . Formula for the difference of squares
- 7 . Performing a product: Formula for the difference of squares
- 8 . Factoring: Formula for the difference of squares
- 9 . Simplifying expressions: Formula for the difference of squares
- 10 . Numerical expressions: Finding the difference of squares
- 11 . Equations: Formula for the difference of squares
- 12 . Formula for the cube of a sum
- 13 . Formula for the cube of a difference
- 14 . Representing in polynomial form: Formulas for the cube of a sum and difference
- 15 . Simplifying expressions: Formulas for the cube of a sum and difference
- 16 . Numerical expressions: Formulas for the cube of a sum and difference
- 17 . Formula for the sum of cubes
- 18 . Formula for the difference of cubes
- 19 . Performing a product: Formulas for the sum and difference of cubes
- 20 . Factoring: Formulas for the sum and difference of cubes
- 21 . Simplifying expressions: Formulas for the sum and difference of cubes
- 22 . Numerical expressions: Formulas for the sum and difference of cubes
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lesson 13
Algebraic fractions -
lesson 14
Linear equations -
lesson 15
Coordinate system -
lesson 16
Concept of a function
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lesson 17
Linear function- 1 . Creating tables
- 2 . Drawing the graph of a function
- 3 . Identifying the quadrants of a function's graph
- 4 . Writing the formula for a linear function based on its graph
- 5 . Finding the zeros of a function
- 6 . Finding the intersection points of a function with the coordinate axes
- 7 . Constructing a function through points
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lesson 18
System of linear equations -
lesson 19
Combinatorics- 1 . Basic principles of combinatorics: Addition principle
- 2 . Basic principles of combinatorics: Multiplication principle
- 3 . Understanding factorials
- 4 . Types of combinatorial problems: Permutations
- 5 . Types of combinatorial problems: Combinations
- 6 . Methods for solving combinatorial problems: Graphical method
- 7 . Methods for solving combinatorial problems: Tree diagram
- 8 . Methods for solving combinatorial problems: Tables
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lesson 20
Basic concepts of geometry -
lesson 21
Angles -
lesson 22
Lines- 1 . Perpendicular lines
- 2 . Parallel lines
- 3 . Oblique lines
- 4 . Angles formed by the intersection of two straight lines
- 5 . Angles formed by two straight lines and a transversal
- 6 . Conditions for the parallelism of two straight lines
- 7 . Angles formed by two parallel lines and a transversal
- 8 . Completing sentences
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lesson 23
Triangles- 1 . Types of triangles by their sides
- 2 . Types of triangles by their angles
- 3 . Median, altitude, and angle bisector of a triangle
- 4 . Congruence of triangles: SAS (Side-Angle-Side) criterion
- 5 . Congruence of triangles: SAS criterion: Problems
- 6 . Congruence of triangles: ASA (Angle-Side-Angle) criterion
- 7 . Congruence of triangles: ASA criterion: Problems
- 8 . Congruence of triangles: SSS (Side-Side-Side) criterion
- 9 . Congruence of triangles: SSS criterion: Problems
- 10 . Sum of interior angles of a triangle
- 11 . Exterior angle property of a triangle
- 12 . Angles in triangles: Problems
- 13 . Types of triangles: Isosceles triangle
- 14 . Types of triangles: Equilateral triangle
- 15 . Types of triangles: Right triangle
- 16 . Relationships between the sides and angles of a triangle
- 17 . Triangle inequalities
- 18 . Completing sentences
- 19 . Completing sentences