Serbia 8th Grade Curriculum - Mathematics

Mathematics (4 classes per week, 136 classes per year)

Goals and Tasks: The mathematics curriculum aims to equip students with fundamental mathematical knowledge and skills necessary for understanding phenomena and patterns in nature and society. It prepares them for practical problem-solving in various real-life situations, lays the groundwork for further mathematical education and self-learning, and contributes to the development of mental abilities, a scientific worldview, and well-rounded personal growth.

Curriculum Content:

• Similarity of Triangles: Thales' theorem, similarity of triangles, application of similarity to right-angled triangles.
• Point, Line, and Plane: Relationship between a point and a line, a point and a plane. Elements determining the position of a line and a plane. Relationships between lines; skew lines. Relationships between a line and a plane, normal to a plane, distance from a point to a plane. Relationships between two planes. Orthogonal projection onto a plane (of points, line segments, and lines). Polyhedron.
• Linear Equations and Inequalities with One Unknown: Linear equation. Equivalence of equations. Solving linear equations with one unknown. Linear inequality. Equivalence of inequalities. Solving simpler examples of linear inequalities with one unknown. Applications.
• Prism: Prism: concept, types, elements. Net of a prism. Surface area of a prism: surface area of a right quadrilateral prism, regular triangular prism, and regular hexagonal prism. Volume of a prism: volume of a right quadrilateral prism, regular triangular prism, and regular hexagonal prism; mass of a solid.
• Pyramid: Pyramid: concept, types, elements. Net of a pyramid. Surface area of a pyramid: calculating the surface area of a quadrilateral pyramid, regular triangular pyramid, and regular hexagonal pyramid. Volume of a pyramid: volume of a quadrilateral pyramid, regular triangular pyramid, and regular hexagonal pyramid.
• Linear Function: Linear function (y = ax + b). Graph of a linear function; zero of a function. Implicit form of a linear function. Drawing and interpreting graphs of linear functions.
• Graphical Representation of Data: Representing dependent variables in tables and in a coordinate system. Graphical representation of statistical data in the form of diagrams (bar graphs, pie charts,...). Calculating the mean and median. Comparing sample values with the mean.
• Systems of Linear Equations with Two Unknowns: Concept of a linear equation with two unknowns. Concept of a system of two linear equations with two unknowns. Equivalence of systems of linear equations. Solving systems using the substitution method and the method of opposite coefficients; graphical representation of solutions. Various examples of applying systems of linear equations to solve problems from life, geometry, physics, etc.
• Cylinder: Cylinder and its elements. Net of a cylinder. Surface area and volume of a right cylinder.
• Cone: Cone and its elements. Net of a cone. Surface area and volume of a right cone.
• Sphere: Concept of a sphere. Intersections of a sphere and a plane. Surface area and volume of a sphere.

Note: Four one-hour school written assignments are mandatory per year (with corrections taking 8 classes).

Implementation of the Curriculum:

The curriculum emphasizes a student-centered approach, focusing on developing problem-solving skills and understanding the practical applications of mathematical concepts. Teachers are encouraged to use a variety of teaching methods, including demonstrations, problem-solving sessions, and hands-on activities, to engage students and cater to different learning styles. The curriculum also promotes the use of real-world examples and interdisciplinary connections to make learning more relevant and meaningful for students. Regular review and integration of previously learned material are also emphasized to ensure a solid foundation and a cohesive understanding of mathematical concepts.