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Croatia

The Mathematics Curriculum in Primary and Lower Secondary Grades

In 2005, the MSES began to implement a school reform project known as the Croatian National Education Standard (Hrvatski nacionalni obrazovni standard),6 after which the Syllabus for Primary School (Nastavni plan i program za osnovnu školu)7 was designed and implemented in August 2006. The syllabus contains the educational work plan for subjects in Grades 1 to 8. It is not presented in the form of a curriculum, but as a catalog, with education goals enumerated separately for each subject, grade, and teaching unit.

According to the syllabus, students should be able to do the following by the end of fourth grade:

  • Number
    • Whole numbers—Add, subtract, and compare whole numbers up to 1 million; demonstrate knowledge of place values; find values on a number line; add and subtract using a number line; differentiate between natural and ordinal numbers; estimate and round two-digit numbers to the nearest 10th; recognize multiples and factors of numbers; learn the multiplication table up to 10 × 10; multiply a two-digit number by 100; divide multiples of 100 by 100; multiply a two-digit number by a number with more than two digits; divide a number of three or more digits by a two-digit number; perform operations with and without brackets; perform money calculations (in kuna and lipa); know units for measuring liquid (deciliter and liter) and convert between them; know units for measuring mass (gram, dekagram, and kilogram) and convert between them; and learn basic algebraic terms, and that letters represent numbers in algebraic equations
    • Fractions and decimals—Use words to express fractions (e.g., one-third of an apple, or 5 is half of 10) and divide with a remainder
    • Number sentences with whole numbers—Solve word problems and simple equations
    • Patterns and relationships—Find a missing term in a sequence
  • Geometric Shapes and Measures
    • Points, lines, and angles—Differentiate among and draw flat, curved, and broken lines; draw and label lengths, and mark terminal points of lines; draw horizontal and vertical lines; draw straight lines that intersect and determine their point of intersection; differentiate between points that belong to a line and points that do not; recognize and draw right, acute, and obtuse angles; use informal coordinate systems (square grids) to locate points on a plane; draw circles with a compass
    • Two- and three-dimensional shapes—Identify two-dimensional geometric shapes (circle, triangle, rectangle, and square); identify three-dimensional geometric shapes (sphere, cylinder, cube, parallelepiped, and pyramid); draw and identify triangles according to shape (scalene, isosceles, and equilateral); draw right triangles; measure the perimeter of triangles; measure the perimeter and area of rectangles and squares; know units of area (cm2, dm2, and m2); use a square grid to measure area; estimate area and volume; calculate the volume of cubes and parallelepipeds; and know units of volume (cm3 and dm3)
    • Data display—Read, interpret, organize, and represent data in simple tables, compare information from bar graphs, and draw conclusions from data

By the end of eighth grade, students should be able to do the following:

  • Number
    • Whole numbers—Compare, round, add, subtract, multiply, and divide whole numbers; find numbers on a number line; determine the absolute value of a whole number; write, read, compare, add, subtract, and multiply natural numbers larger than 1 million; divide by two-digit numbers; use the commutative, associative, and distributive properties of multiplication; know the properties of divisibility; determine common multiples; use pocket calculators; and find square roots using a calculator
    • Fractions and decimals—Find fractions, decimals, and rational numbers on a number line; compare, add, subtract, multiply, and divide fractions; write equivalent fractions; convert fractions to mixed numbers; understand decimal places; compare, round, add, subtract, multiply, and divide decimals; convert decimal numbers to decimal fractions and vice versa; and write rational numbers as fractions and decimal numbers and compare them
    • Integers—Differentiate between positive and negative integers; find integers on a number line; compare, add, subtract, multiply, and divide integers; and determine the absolute value of an integer
    • Ratio, proportion, and percent—Recognize proportional quantities and apply ratios and proportionality in simple everyday situations; present proportionality graphically; calculate percentages; and determine interest
  • Algebra—Solve simple mathematical formulas and expressions containing one variable; solve simple linear equations and simple two-variable systems of two linear equations, and use substitution to verify the accuracy of solutions; substitute numerical values for variables in formulas and calculate the value of remaining variables; present simple numerical relationships (e.g., linear, pure quadratic, and square root) using appropriate vocabulary, associated value tables, equations, and graphics; convert simple word problems into algebraic notation (e.g., numerical sentences, linear equations, and systems of two linear equations), plan and execute solutions, and understand their significance; solve equations graphically and algebraically; graph linear functions; calculate with exponents; and perform calculations using scientific notation
  • Geometry—Measure and draw angles; construct angles using the properties of angle bisectors; identify, create, compare, and classify two-dimensional and three-dimensional geometric shapes, and recognize and describe their geometrical properties, including translation, axis symmetry, central symmetry, and rotation; recognize congruence, similarity, and symmetry in two-dimensional and three-dimensional forms; apply Thales’ theorem for right angles inscribed in circles; apply the Pythagorean theorem as it relates to the measurable features of squares, rectangles, equilateral triangles, isosceles triangles, rhombuses, and trapezoids; use the Cartesian coordinate system and read the coordinates of points in the system; determine perpendicular lines and planes; and apply formulas to determine length, area, surface area, perimeter, and volume
  • Data and Chance—Collect, classify, and interpret data using tables, frequency diagrams, bar graphs, and pie charts; determine the number of possible and favorable outcomes in simple situations; apply the terminology of probability; draw frequency and relative frequency histograms and find the arithmetic mean, median, quartiles, mode, range, and interquartile range of a series of numerical data; and calculate the probabilities of random events and explain them as relative frequencies