Practice math topics
Each topic page explains one mathematical foundation in plain language and puts it in context: from which grade it appears, where it matters in everyday life, and which topics build on it.
Maths by grade
Practice examples by topic and grade
Grades follow the North Rhine-Westphalia curriculum; other German states may introduce topics at different times.
- Written addition and subtraction · From grade 5
- Small multiplication table · From grade 3
- Distributive law · From grade 4
- Estimation · From grade 3
- Written multiplication · From grade 5
- Written division · From grade 5
- Arithmetic laws · From grade 3
- Rounding · From grade 5
- Number line · From grade 5
- Large numbers · From grade 5
- Factors and multiples · From grade 5
- Prime numbers and prime factorisation · From grade 6
- Divisibility rules · From grade 6
- Fractions: meaning and representation · From grade 5
- Simplifying and expanding fractions · From grade 5
- Fractions: addition and subtraction · From grade 6
- Fractions: multiplication and division · From grade 6
- Decimals · From grade 6
- Integers · From grade 6
- Rational numbers · From grade 7
- Percentages · From grade 6
- Percentage and interest calculations · From grade 7
- Powers and roots · From grade 9
- Square roots · From grade 9
- Area of rectangles · From grade 5
- Area of triangles, parallelograms and trapezoids · From grade 7
- Scale · From grade 4
- Circumference and area of a circle · From grade 6
- Angle sums in triangles and quadrilaterals · From grade 7
- Surface area and volume of cuboids and cubes · From grade 5
- Surface area and volume of solids · From grade 9
- Cartesian coordinate system · From grade 5
- Pythagorean theorem · From grade 8
- Leg and altitude theorems · From grade 8
- Thales' theorem · From grade 7
- Intercept theorems · From grade 8
- Similarity and central dilation · From grade 8
- Trigonometry · From grade 9
- Law of sines · From grade 10
- Law of cosines · From grade 10
- Terms and variables · From grade 7
- Algebraic manipulation · From grade 8
- Vectors in space · From grade 11
- Lines and planes in space · From grade 13
- Linear equations · From grade 7
- Quadratic equations · From grade 9
- Equations with algebraic fractions · From grade 8
- Systems of linear equations · From grade 8
- Rule of three · From grade 6
- Proportional relationships · From grade 6
- Linear functions · From grade 7
- Quadratic functions · From grade 9
- Extremum problems and optimisation · From grade 12
- Exponential functions · From grade 10
- Sine function · From grade 10
- Frequencies · From grade 6
- Statistical measures · From grade 6
- Laplace probability · From grade 7
- Tree diagrams and multi-stage random experiments · From grade 7
- Conditional probability · From grade 10
- Binomial distribution · From grade 13
- Normal distribution · From grade 13
- Random variables: expectation and standard deviation · From grade 13
- Combinatorial counting · From grade 9
- Limits and continuity · From grade 11
- Differential calculus: derivatives · From grade 11
- Curve analysis · From grade 12
- Integration · From grade 12
- Fundamental theorem of calculus · From grade 12
- Natural exponential function · From grade 12
- Converting units · From grade 5
- Units of length · From grade 5
- Units of weight · From grade 5
- Telling time · From grade 5
Numbers and arithmetic
- Written addition and subtractionFrom grade 5
- Small multiplication tableFrom grade 3
- Distributive lawFrom grade 4
- EstimationFrom grade 3
- Written multiplicationFrom grade 5
- Written divisionFrom grade 5
- Arithmetic lawsFrom grade 3
- RoundingFrom grade 5
- Number lineFrom grade 5
- Large numbersFrom grade 5
- Factors and multiplesFrom grade 5
- Prime numbers and prime factorisationFrom grade 6
- Divisibility rulesFrom grade 6
- Fractions: meaning and representationFrom grade 5
- Simplifying and expanding fractionsFrom grade 5
- Fractions: addition and subtractionFrom grade 6
- Fractions: multiplication and divisionFrom grade 6
- DecimalsFrom grade 6
- IntegersFrom grade 6
- Rational numbersFrom grade 7
- PercentagesFrom grade 6
- Percentage and interest calculationsFrom grade 7
- Powers and rootsFrom grade 9
- Square rootsFrom grade 9
Geometry
- Area of rectanglesFrom grade 5
- Area of triangles, parallelograms and trapezoidsFrom grade 7
- ScaleFrom grade 4
- Circumference and area of a circleFrom grade 6
- Angle sums in triangles and quadrilateralsFrom grade 7
- Surface area and volume of cuboids and cubesFrom grade 5
- Surface area and volume of solidsFrom grade 9
- Cartesian coordinate systemFrom grade 5
- Pythagorean theoremFrom grade 8
- Leg and altitude theoremsFrom grade 8
- Thales' theoremFrom grade 7
- Intercept theoremsFrom grade 8
- Similarity and central dilationFrom grade 8
- TrigonometryFrom grade 9
- Law of sinesFrom grade 10
- Law of cosinesFrom grade 10
Algebra
Functions
Calculus
Probability and statistics
- FrequenciesFrom grade 6
- Statistical measuresFrom grade 6
- Laplace probabilityFrom grade 7
- Tree diagrams and multi-stage random experimentsFrom grade 7
- Conditional probabilityFrom grade 10
- Binomial distributionFrom grade 13
- Normal distributionFrom grade 13
- Random variables: expectation and standard deviationFrom grade 13
- Combinatorial countingFrom grade 9