Ukraine 7th Grade Curriculum - Mathematics

This curriculum outlines the learning objectives and content for 7th-grade mathematics in Ukraine, covering Algebra and Geometry. It is based on the curriculum published by the Ministry of Education and Science of Ukraine.

Algebra

Course Objectives: The primary goal of the 7th-grade algebra course is to equip students with the skills to perform transformations of algebraic expressions, solve equations and inequalities, and apply these skills to mathematics and related subjects, as well as practical situations.

Content:

• Whole Expressions (30 hours):
• Expressions with variables.
• Whole rational expressions.
• Identities and identical expression transformations.
• Degrees with natural indicators and their properties.
• Monomials and polynomials.
• Operations on polynomials (addition, subtraction, multiplication).
• Formulas for squared binomials, difference of squares, sum and difference of cubes.
• Decomposition of polynomials into multipliers.
• Functions (10 hours):
• Functional dependence between quantities.
• Functions, their definitions, domains, value areas, and graphs.
• Methods of defining a function.
• Linear functions, their graphs, and properties.
• Direct proportionality.
• Linear Equations and Their Systems (18 hours):
• Linear equations with one and two variables.
• Systems of linear equations with one and two variables.
• Graphical method for solving systems of equations.
• Substitution and addition methods for solving systems of equations.
• Linear equations and their systems as mathematical models for text problems.

Geometry

Course Objectives: The focus of the 7th-grade geometry course is on geometric figures and their properties. The fundamental concepts are point, line, plane, belonging to, and lying between.

Content:

• Elementary Geometric Figures and Their Properties (8 hours):
• Basic geometric shapes and their properties (point, line, segment, ray, angle).
• Measurement of segments and angles.
• Angle bisector.
• Distance between points.
• Mutual Placement of Straight Lines on the Plane (12 hours):
• Adjacent and vertical angles and their properties.
• Parallel and perpendicular lines and their properties.
• Distance from a point to a line.
• Angles formed by intersecting lines.
• Properties of angles formed when parallel lines are intersected by a transversal.
• Triangles. Signs of Equality of Triangles (22 hours):
• Triangles and their elements (height, bisector, median).
• Congruence of geometric shapes.
• Congruence criteria for triangles.
• Types of triangles.
• Isosceles triangles, their properties, and characteristics.
• Triangle inequality.
• Sum of angles in a triangle.
• Exterior angles of a triangle and their properties.
• Properties of right-angled triangles.
• Circle and Circular Disk (8 hours):
• Circle, circular disk, and their elements.
• Tangent to a circle and its properties.
• Basic constructions: constructing a triangle given three sides, constructing an angle equal to a given angle, constructing an angle bisector, bisecting a segment, constructing a perpendicular line.
• Circumscribed and inscribed circles.

This structured curriculum provides a comprehensive overview of the topics covered in 7th-grade mathematics in Ukraine, enabling students to develop a strong foundation in algebra and geometry.