The Mathematics Curriculum in Primary and Lower Secondary Grades

The curriculum in all subjects for Bulgaria is centralized, and determined by the Ministry of Education. There is a single curriculum for primary and presecondary education, which are compulsory for all students. All students are required to study the same topics, at the same level of difficulty, with the same workload (study hours). From Grade 9, most subjects are taught at two levels. Level 1 covers knowledge basics, and is intended for students who are not expecting to go into a career related to the subject. Although it generally covers the same topics as Level 1, Level 2 is taught to greater depth, includes additional topics, and requires more study hours. From Grade 9, students are required to choose one of the two levels for each subject, where possible. Although it does not happen often, students are allowed to move from one level to another within a particular subject.

The National Education Content Standards for all subjects were approved by the Ministry of Education in 2000. These standards outline what students are expected to know and be able to do by the end of each level of schooling (primary, presecondary, and secondary). In 2001, instructional programs for every subject were developed for each grade level, stipulating topics of study as well as skill objectives.
The main topics of the primary school mathematics curriculum (Grades 1 to 4) are natural numbers and geometrical figures. The curriculum includes a basic introduction to reading, using, and interpreting data from tables, graphs, and diagrams. Primary school students do not study fractions or decimals, except for 1/2, 1/3, 1/4, and 1/10 (i.e., the concept of division by two, three, four, and 10).

Mathematics content standards, expected learning outcomes, and core topics for students at the end of Grade 4 are presented in Exhibit 1.

Exhibit 1: Mathematics Learning Outcomes at the End of Grade 4

Area of Content/Competency	Expected Learning Outcomes
Numbers	Read and write natural numbers and know the decimal numbering system; compare and order natural numbers Add and subtract natural numbers Multiply and divide by one-digit and two-digit numbers; understand the connection between components of arithmetic operations Know the order of operations and the function of parentheses; solve numeric equations with up to three operations Know the Roman numeral system Understand the concept of the fractions 1/2, 1/3, 1/4, and 1/10
Geometric Figures	Know geometric shapes (straight and curved lines, rays, line segments, angles, triangles, rectangles, squares, circumference) and their elements Distinguish types of shapes (angles and triangles) Draw line segments by given length and angles by given degree measurement Draw triangles, squares, and rectangles on a square grid
Measurement	Know units of measurement for length (millimeter, centimeter, meter, and kilometer), weight (gram, kilogram, ton), time (second, minute, hour, day, week, month, year, century), money (Bulgarian currency), and angles (degree), and how to convert units of measurement Know units of measurement for area (mm², cm², m², km², daa) Measure line segments and angles Convert uniform metric units Calculate perimeter of a triangle and a rectangle, and area of a rectangle
Modeling	Use numerical expressions to build mathematical models for situations represented by “n more,” “n less,” “n times more,” or “n times less” Model real world situations using mathematical equations (trade problems, and perimeter and area of polygons problems) Analyze the content and interpret the results of solved problems Make educated guesses using organized real world data

In accordance with the national mathematics curriculum, students in Grades 5 and 6 study rational numbers, focusing on fractions and decimals in Grade 5, and negative numbers in Grade 6. In geometry, students in Grades 5 and 6 study the main properties of certain three-dimensional figures, as well as formulas for surface and volume and the area of a triangle. The curriculum includes reading, using, and interpreting data from tables, graphs, and diagrams.

Grade 7 is a milestone in the study of mathematics in Bulgaria. Students begin the study of algebra with the introduction of algebraic expressions, linear equations, and inequalities. They are given a formal, axiomatic introduction to the study of geometry, and begin to study congruent triangles and the application of their properties.

The mathematics curriculum in Grade 8 (the final grade of presecondary education) covers the study of numbers, beginning with the introduction of irrational numbers and square roots; solving quadratic equations, using the set of real numbers; the basic idea of functions followed by the study of linear functions and y=ax² and solving simultaneous linear equations and inequalities. The geometry curriculum includes vectors and geometric transformations, as well as certain properties of angles connected with a circle.

Mathematics content standards, expected outcomes, and core topics for students in Grade 8 can be found on the website of the Ministry of Education.²