Hungary

The Mathematics Curriculum in Primary and Lower Secondary Grades

According to Act CXC of 2011 on National Public Education,⁴ the new national curriculum came into effect on September 1, 2013, implementing a spiral approach, for Grades 1, 5, and 9. TIMSS 2015 students were taught under the old national curriculum. Exhibits 2 and 3 present the main content objectives in the curricular framework⁵ for fourth and eighth grade mathematics pertaining to TIMSS 2015.

Exhibit 2:  Mathematics Content Objectives for Grade 4

Content Areas	Content Objectives
Arithmetic and Algebra	Natural numbers up to 10,000—Approximate and exact location on the number line; ordering numbers; estimating quantities with whole numbers; place value; rounding to the nearest 10, 100, and 1,000; order of magnitude; relationships between numbers (e.g., multiples and factors); sum, difference, product, and quotient Fractions—Representing equal parts of a whole; representing fractions with a small denominator and with the numerator 1 and their multiples; ordering fractions; finding equivalent fractions Understanding negative numbers as signed quantities or deficits Interpreting and executing mathematical operations Calculating with natural numbers Properties of operations (e.g., commutability, associativity, and dependence of sum, difference, product, and quotient on the magnitude of numbers); relationships among operations; estimating the outcome of operations; order of operations; use of brackets Understanding and describing algorithms and algorithmic thinking Solving number sentences for unknowns
Word Problems and Problem Solving	Interpreting word problems and real-world problems Creating mathematical models to describe problems, solving the problems, and interpreting the results
Sequences, Relations, and Functions	Collecting, organizing, and interpreting data; recognizing, describing, and generalizing relationships Ordering data into sequences, extending patterns, and finding missing terms Finding rules and writing rules in words Constructing and reading graphs; finding and generalizing mathematical relationships; formulating rules (e.g., by number sentences with missing numbers) Finding the relationships among data in a table Checking relationships using substitution
Geometry and Measurement	Properties of two- and three-dimensional geometrical shapes; angles; classifying two- and three-dimensional shapes by given properties; parallel and perpendicular lines; using compasses and rulers  Transformations—Visual concepts of congruence and similarity; copying two-dimensional shapes; performing translations, reflections, and rotations using copy paper Recognizing and extending geometrical patterns Orienting objects on lines and planes and in space by following instructions; orientation using a simple map Measurable properties and measurement—Knowing and using units of length (height, width, perimeter), mass, volume, time (year, month, week, hour, minute); converting between units of measurement Estimating or determining area, length, and volume of given shapes Measuring and calculating to determine perimeter and area
Statistics, Probability, and Combinatorics	Collecting, organizing, and displaying data in bar charts, tables, and graphs; reading data from bar charts, tables, and graphs; interpreting and using mean and average Determining frequency of events by performing experiments Generating and identifying objects that meet given conditions; finding all the events that meet given conditions Finding pairs and triplets from a few elements; arranging elements in tree diagrams and tables Understanding the meaning of and differentiating between certain, possible, and impossible events Conducting probability games, experiments, and observations

Exhibit 3:  Mathematics Content Objectives for Grade 8

Content Areas	Content Objectives
Arithmetic and Algebra	Natural numbers in the range of millions, whole numbers, fractions, decimals, and negative numbers; absolute value; reciprocals Rational numbers; relationships among natural, whole, and rational numbers The decimal number system and the binary number system Approximating, estimating, and checking solutions Operations with rational numbers, properties of operations, and order of operations Finding and using multiples and factors, identifying prime numbers, and prime factorization; positive integer exponentiation; divisibility rules; greatest common divisor and least common multiple The concept of percent (amount, base, rate) and solving problems involving percent Simplifying and comparing algebraic expressions; simple operations with algebraic expressions, and substitution into algebraic expressions Linear equations and inequalities
Sequences, Relations, and Functions	The number line, representations of intervals, and reading from diagrams Using tables or graphs of ordered pairs with linear relationships to find missing coordinates Representation of relationships between sets of numbers The Cartesian plane and representations of points in the Cartesian plane Functions and representations of functions in the Cartesian plane; linear functions; examples of nonlinear functions Solving linear equations graphically Arithmetic and geometric sequences
Geometry and Measurement	Parallelism, perpendicularity, and convexity Line reflection, point reflection, translation, and enlargement Symmetrical shapes Vectors and vector addition Elementary properties of quadrilaterals and triangles; special quadrilaterals and triangles Area and perimeter of rectangles, squares, trapezoids, deltoids, triangles, and circles Congruent triangles and altitude of triangles Relationships between angles forming a straight line and angles in geometric figures Net, volume, and surface area of cubes, prisms, and cylinders Geometric constructions (e.g., parallel lines, perpendicular lines, copying angles, perpendicular bisectors of a line segment, angle bisectors, and triangles) The Pythagorean theorem
Statistics and Probability	Concept of probability; probability games and experiments; differentiating between certain and impossible events; estimating probability Frequency, relative frequency, and properties of frequency; mode and extreme values of data Collecting, organizing, and representing data  Constructing bar charts, pie charts, and graphs; interpreting, reading, displaying, and analyzing simple graphs Calculating averages Analyzing, interpreting, and displaying data sets (mean, median, and mode)