Czech Republic

The Mathematics Curriculum in Primary and Lower Secondary Grades

Mathematics at the primary level follows the FEP BE and is divided into four thematic areas of mathematics and its application: Numbers and Arithmetic Operations, Data and Relations, Plane and Spatial Geometry, and Problem Solving. Exhibit 1 shows what students should be able to do in each content area by the end of the fifth grade. The Standards for Basic Education, which took effect September 1, 2012, were introduced to the FEP BE, specifying more detailed content standards and student achievement outcomes in mathematics in Grades 5 and 9.

Exhibit 1: Mathematics Content Areas and Capabilities by the End of Grade 5

Content Area	Capabilities
Numbers and Arithmetic Operations	Read, record, and compare natural numbers and read and compose statements of equality and inequality Use natural numbers to model real-life situations, count objects in a given set, and create sets with a given number of elements Use linear arrangement and represent numbers on a number line Perform oral and written arithmetic operations on natural numbers Round natural numbers, perform estimates, and verify the results of arithmetic operations on natural numbers Use the commutative and associative properties of addition and multiplication when performing both oral and written calculations Create and solve problems that require the application of arithmetic operations on natural numbers Model and determine fractions as parts of a whole, and represent fractions using numbers Compare simple fractions, and add and subtract fractions with the same denominator Read decimals and show them on number line Understand the symbol “–” in negative numbers, and show negative numbers on a number line
Data and Relations	Understand the concept of time and perform simple time-unit conversions Describe simple relationships between real-world variables Gather, display, and classify data Complete tables, charts, diagrams, and sequences of numbers
Plane and Spatial Geometry	Draw basic plane figures (square, rectangle, triangle, and circle) and perform simple constructions Measure and estimate the length of line segments, add and subtract graphic line segments, and determine the length of a broken line or the perimeter of a polygon Construct parallel and perpendicular lines Determine the area of a geometric figure by means of a quadratic grid and use basic units of area Identify and draw simple axisymmetric figures on a quadratic grid and determine the axis of symmetry by folding paper
Problem Solving	Solve simple practical word problems as well as nonroutine problems

Mathematics at the lower secondary level also is divided into four thematic areas: Numbers and Variables, Data and Relations, Plane and Spatial Geometry, and Problem Solving. Exhibit 2 shows what students should be able to do in each content area by the end of the ninth grade.

Exhibit 2: Mathematics Content Areas and Capabilities by the End of Grade 9

Content Area	Capabilities
Numbers and Variables	Perform arithmetic operations on whole, natural, and rational numbers Calculate square numbers and square roots Round numbers, make estimates to a specified level of precision, and use calculators effectively Express whole-part relationships using natural numbers, ratios, fractions, decimals, and percentages Solve problems involving ratios and work with the graphic scales of maps and plans Solve problems involving percentages (including percentages greater than 100) Represent simple real-life situations using variables, expressions, and equations, including simultaneous equations Add, multiply, and factor polynomials
Data and Relations	Gather, evaluate, and process data and compare data sets Determine direct or inverse proportionality Express functional relations with tables, equations, and graphs Describe simple real-life situations with relations
Plane and Spatial Geometry	Characterize and classify basic plane and spatial figures and identify their properties Determine the size of an angle by measurement or calculation Estimate and calculate the area and perimeter of basic plane figures and the volume and surface area of three-dimensional figures Perform constructions of figures in a plane Apply theorems of congruent and similar triangles in proofs and calculations Construct and characterize centrally symmetric and axisymmetric figures Solve application problems with geometry
Problem Solving	Apply combinatory logic when solving problems, and use spatial reasoning to solve problems