Serbia

The Mathematics Curriculum in Primary and Lower Secondary Grades^a

The goals of the mathematics curriculum for primary school are stated as follows: “Providing students with basic mathematical knowledge and the ability to apply that knowledge to solving problems in everyday life; laying a foundation for continuing students’ mathematical education and self-education; and developing students’ mental abilities and their ability to form a scientific view of the world, as well as the overall development of their personality.”¹³

In the curriculum, there are teaching objectives and operational tasks prescribed for each grade. It offers descriptions of knowledge and skills that students are expected to obtain by the end of each grade in primary school. Standards for achievement in mathematics are specified in four areas of knowledge—Numbers and Operations, Geometry, Fractions, and Measuring and Measurements—at three levels: basic, intermediate, and advanced.¹⁴

Standards for achievement in mathematics at the end of the second cycle of primary education also are specified at basic, intermediate, and advanced levels for each of the following areas: Numbers and Numerical Operations, Algebra and Functions, Geometry, and Measuring and Data Analysis.¹⁵

Exhibit 1 presents the competencies students are expected to attain in mathematics in Grades 1 to 8.

Exhibit 1: Mathematics Curriculum, Grades 1–8

Grade Level	Competencies
Grades 1–416,17,18	Understand natural numbers including zero Perform operations with natural numbers and understand numerical expressions including equations and inequalities Identify and measure geometric shapes Understand the metric system, measure objects in the environment, and understand the relationship between familiar units of measurement Solve word problems with increasing levels of complexity Use mathematical language, including basic symbols, expressions, and formulas
Grade 519	Create and display sets and their subsets graphically; perform operations related to sets; understand the meaning of “and,” “or,” “no,” “every,” and “some” in mathematical contexts; and recognize familiar geometric objects (e.g., lines, line segments, rays, planes, circles, and angles) Understand the properties of angles formed by parallel lines and a transversal, and angles formed in figures with parallel sides Draw lines parallel to a given line Understand the basic rules of divisibility and how to divide natural numbers Determine the least common multiple and greatest common factor Understand the concept of fractions, know how to write fractions in different ways, convert fractions from one mode to another, compare fractions, and present fractions on the number line Read, compose, and calculate simple numerical expressions Solve simple equations and inequalities with fractions Recognize mathematical content in narrative form and express it in mathematical language Understand axial symmetry and its properties Identify the center of a line segment Construct angle bisectors and lines perpendicular to another line through a given point
Grade 620	Understand negative numbers, the structure of the sets of integers and rational numbers, and the absolute value of numbers Perform basic arithmetic operations with integers and rational numbers Read simple expressions containing rational numbers and calculate their numerical value Solve simple equations and inequalities on the set of rational numbers Express percentages and use them in practice; classify triangles and rectangles and know their basic properties; understand congruence and its properties, and know how to apply it when constructing triangles and rectangles Calculate the area of triangles, parallelograms, and rectangles Apply rules for calculating the area of triangles and rectangles in a variety of practical tasks Use deductive reasoning (e.g., defining statements and using the words “and,” “or,” “if…then…,” and “if and only if…”) Understand the need for presenting evidence in proofs and know how to do so in simple cases
Grade 721	Understand the concepts of squaring and finding square roots of rational numbers Find the approximate value of the square root of a rational number Understand the concept of exponentiation and operations with natural number exponents Perform basic arithmetic operations with polynomials Understand the rectangular coordinate system and its application Understand direct and inverse proportionality and its practical application Understand the Pythagorean theorem and how to apply it to geometric figures that contain a right triangle Recognize the most important properties of polygons and circles Construct regular polygons with 3, 4, 6, 8, and 12 sides and draw other regular polygons Recognize central angles and draw them using a protractor; understand the most important properties of polygons and circles and apply them in problems Understand the concepts of scale and proportion Translate word problems into mathematical language and solve them Use elements of deductive reasoning in simple proofs
Grade 822	Solve linear equations (including inequalities) and systems of linear equations in one or two unknowns and interpret solutions graphically Represent word problems using mathematical language and solve them Identify functional dependencies and display them in different ways Understand the concept of functions and graphical representations of functions Understand linear functions and their properties Draw and interpret linear functions Interpret data presented in graphs and tables Construct a table and draw appropriate graphs and diagrams from the data Calculate the median of a data set Understand the relationships among points, lines, and planes in space Understand projections in a plane and the elements and properties of solid figures (e.g., prism, pyramid, cylinder, cone, and sphere) Calculate the surface area and volume of a solid figure Apply knowledge of solid figures in practice, linking the content of mathematics and other areas Apply elements of deductive reasoning in proofs