Slovak Republic

The Mathematics Curriculum in Primary and Lower Secondary Grades

The mathematics curriculum for Grades 1 to 4 is in accordance with the ŠVP for the domains of Mathematics and Information and Communications Technology (ICT), and contains topics in both subject areas. The educational content is structured into five thematic fields, a structure that applies generally to other educational levels as well: Numbers, Variables, and Algebraic Calculations with Numbers; Patterns, Relationships, Functions, Tables, and Diagrams; Geometry and Measurement; Combinatorics, Probability, and Statistics; and Logic, Reasoning, and Proofs.⁸ Exhibit 1 presents the mathematics topics and competencies that were in effect in Grades 1 to 4 for students assessed in TIMSS 2015.

Exhibit 1: Mathematics Content Areas and Competencies, Grades 1–4⁹

Content Area	Competencies
Numbers, Variables, and Algebraic Calculations with Numbers	Know whole numbers up to 10,000 and their properties; read and write whole numbers in the decimal system; mark and compare numbers on an axis; inequalities (introductory) Perform basic calculations mentally, on paper, and with a calculator (multiplying and dividing up to 100); understand and explain the relationship between multiplication and division and calculations with these operations; work with numbers and round numbers to 10s and 100s; estimate and make approximations; check results Understand fractions with 2 and 3 as denominators, without writing the fractions (introductory) Solve contextual word problems from real life
Patterns, Relationships, Functions, Tables, and Diagrams	Create simple patterns of objects, figures, and numbers; recognize and create increasing and decreasing number patterns; find the rule in a pattern and continue the pattern Collect, group, and sort data according to a given criterion Record number of events; create tables and bar diagrams and draw simple conclusions based on them Discover the relationships among and accordingly sort corresponding data in a table
Geometry and Measurement	Recognize points, lines, and line segments; draw lines and line segments Know units of measurement for length and apply and convert between them independently; measure the length of line segments; add, subtract, and multiply line segments; compare line segments based on length Draw squares and rectangles on grid paper, and determine vertices, sides, and pairs of adjacent sides Enlarge and reduce geometrical plane figures on grid paper Construct triangles based on given side lengths, and determine vertices and sides Calculate perimeter of squares, rectangles, and triangles by adding their sides (introductory) Draw circles given center and distance and recognize their properties Construct geometrical space figures using cubes according to a given plan, and design a construction plan for geometrical space figures using cubes
Solving Applied Problems and Problems Developing Specific Mathematical Thinking	Solve problems by determining whether given statements (from mathematics and real life) are true or false; complete sentences to formulate true or false statements Recognize certain and impossible phenomena in simple situations Calculate arithmetic average for smaller sets of data (introductory) Solve problems in combinatorics and probability (introductory)

The mathematics curriculum for Grades 5 to 9 is in accordance with the ŠVP for the domain Mathematics and ICT, and contains topics in the two subject areas Mathematics and InformationScience.¹⁰. Exhibit 2 presents the mathematics topics and competencies that were in effect in Grades 5 to 9 for students assessed in TIMSS 2015.

Exhibit 2: Mathematics Content Areas and Competencies, Grades 5–9¹¹

Content Area	Competencies
Numbers, Variables, and Algebraic Calculations with Numbers	Use whole, integer, and rational numbers to depict real situations Read, write, and compare whole, integer, and rational numbers; use, write, and read correlations of equality and inequality; locate numbers on an axis Perform basic algebraic calculations mentally and on paper Round numbers, estimate, and check results Know and use different ways to express relationships quantitatively (i.e., whole numbers and their parts—fractions, decimals, and percentages), solve conceptual and applied problems Solve ratios by means of modeling and calculating; work with scale in maps and plans Represent real situations mathematically using variables and determine their value; represent real situations mathematically using equations and systems of equations and solve the equations Formulate and solve problems applying knowledge of numbers and algebraic calculations
Patterns, Relationships, Functions, Tables, and Diagrams	Create tables representing simple linear relationships; complete missing data based on a discovered rule and display data Discover functional relationships among variables and display them in the rectangular coordinate system Represent linear functions using equations, tables, and graphs; know examples of nonlinear functions; create tables and graphs for simple functions Discover and solve problems from real life involving direct and inverse proportions Display data in diagrams and read data in diagrams
Geometry and Measurement	Recognize, name, and describe basic geometrical space figures; find corresponding shapes in real life; identify their components (i.e., diagonals and relationships among edges) Know, describe, name, draw, and construct basic plane figures; know their basic elements and properties, and the fundamental relationships among their elements and properties Apply the rules of congruence and similarity of triangles in writing proofs and performing calculations Recognize and construct figures reflected across axes and points; understand simple geometrical transformations; know the basic properties of pairs of symmetrical figures and apply them to simple constructions Measure and calculate the perimeter, area, surface area, and volume of geometrical figures Know how to measure angles and calculate with angles; apply properties of known pairs of angles (e.g., supplementary, alternate, complementary) to calculate inner and outer angles of plane figures Know measuring tools and units; use them independently to take practical measurements Analyze and solve geometrical problems by applying acquired mathematical techniques
Combinatorics, Probability, and Statistics	Acquire skills in sorting objects according to given criteria through games and practical exercises Extract from a given group of elements a subgroup consisting of a given number of elements according to a given rule, and calculate the number of possible selections Collect, record, interpret, and graphically display data Orientate oneself in a set of data Attribute to statements from close environment the correct truth value Understand real life situations in terms of statistics and probability; recognize certain and impossible phenomena in simple situations
Logic, Reasoning, and Proofs	Quantify general statements and carry out their negation Judge the explicitness of simple instructions, directives, and acts Determine the correct use of “and,“ “or,“ “either/or,“ and “if… then“ Determine whether mathematical statements are true or false Recognize definitions, hypotheses, and proofs in mathematical texts