Learning map Mathematics

How to read the map

Grade ↓ · Strand →	Arithmetic 7 of 34 building blocks practised	Algebra 1 of 19 building blocks practised	Functions 0 of 15 building blocks practised	Geometry 0 of 36 building blocks practised	Probability and statistics 8 of 23 building blocks practised
Grade 5/6	Natural numbers and place value (gap, no app yet) Comparing and ordering numbers (gap, no app yet) Rounding (gap, no app yet) Written calculation methods (gap, no app yet) Order of operations and laws of arithmetic (gap, no app yet) Estimating results (gap, no app yet) Powers and powers of ten (gap, no app yet) Factors, multiples and divisibility (gap, no app yet) Prime factors, HCF and LCM (gap, no app yet) Understanding fractions (gap, no app yet) Simplifying and expanding fractions (gap, no app yet) Fractions of a quantity (gap, no app yet) Adding and subtracting fractions (gap, no app yet) Multiplying and dividing fractions (gap, no app yet) Decimals and recurring decimals (gap, no app yet) Calculating with decimals (gap, no app yet) Negative numbers and absolute value (gap, no app yet) Percentages: basic terms (an app practises it) Estimating quantities (gap, no app yet) Converting units (gap, no app yet) Length, mass, money and time (gap, no app yet)	Simple equations (gap, no app yet) Number sequences and patterns (gap, no app yet)	Rule of three (gap, no app yet) Scale (gap, no app yet)	Basic plane shapes (gap, no app yet) Parallel and perpendicular lines (gap, no app yet) Measuring and drawing angles (gap, no app yet) Coordinate system (gap, no app yet) Symmetry (gap, no app yet) Special quadrilaterals (gap, no app yet) Drawing and constructing (gap, no app yet) Reflections, translations, rotations (gap, no app yet) Cuboids and cubes (gap, no app yet) Nets and oblique drawings: cuboids, cubes (gap, no app yet) Units of area and volume (gap, no app yet) Area and perimeter: rectangles, squares (gap, no app yet) Composite shapes (gap, no app yet) Volume and surface area: cuboids, cubes (gap, no app yet)	Representing data (gap, no app yet) Conducting surveys (gap, no app yet) Absolute and relative frequency (gap, no app yet) Arithmetic mean (gap, no app yet) Counting principle (gap, no app yet)
Grade 7/8	Calculating with negative numbers (gap, no app yet) Finding the percentage value (an app practises it) Finding the percentage rate (an app practises it) Finding the base value (an app practises it) Percentage increase and decrease (an app practises it) Percentage comparison (an app practises it) Percentage word problems (an app practises it) Percentage points and successive changes (gap, no app yet) Simple interest (gap, no app yet) Compound interest (gap, no app yet)	Expressions with variables (gap, no app yet) Simplifying expressions (gap, no app yet) Brackets and binomial formulas (an app practises it) Linear equations (gap, no app yet) Setting up equations (gap, no app yet) Rearranging formulas (gap, no app yet) Linear inequalities (gap, no app yet) Algebraic fractions (gap, no app yet) Equations with fractions (gap, no app yet) Simultaneous equations: graphical (gap, no app yet) Simultaneous equations: algebraic (gap, no app yet)	Relations between quantities (gap, no app yet) Direct proportion (gap, no app yet) Inverse proportion (gap, no app yet) Concept of a function (gap, no app yet) Representing functions (gap, no app yet) Linear functions (gap, no app yet) Equations of lines (gap, no app yet)	Hierarchy of quadrilaterals (gap, no app yet) Angle theorems (gap, no app yet) Constructing triangles (gap, no app yet) Congruence (gap, no app yet) Special lines in triangles (gap, no app yet) Chords, secants and tangents (gap, no app yet) Thales' theorem (gap, no app yet) Area and perimeter: triangles, quadrilaterals (gap, no app yet) Prisms and cylinders (gap, no app yet) Nets and oblique drawings: prisms, cylinders (gap, no app yet) Volume and surface area: prisms (gap, no app yet)	Random experiments (gap, no app yet) Relative frequency as an estimate (gap, no app yet) Concept of probability (gap, no app yet) Laplace formula (an app practises it) Complementary event (an app practises it) Multistage random experiments (an app practises it) Multiplication rule for paths (an app practises it) Drawing with and without replacement (an app practises it) Addition rule for paths (an app practises it) Writing probabilities (an app practises it) Events in tree diagrams (an app practises it) Simulations (gap, no app yet) Median, range and quartiles (gap, no app yet) Box plot (gap, no app yet) Reading charts critically (gap, no app yet)
Grade 9/10	Square roots (gap, no app yet) Real numbers (gap, no app yet) Laws of roots (gap, no app yet)	Laws of exponents (gap, no app yet) Negative exponents (gap, no app yet) Nth roots (gap, no app yet) Simple quadratic equations (gap, no app yet) Quadratic equations (gap, no app yet) Logarithms (gap, no app yet)	Quadratic functions (gap, no app yet) Applying quadratic functions (gap, no app yet) Power and root functions (gap, no app yet) Exponential functions (gap, no app yet) Radians (gap, no app yet) Sine and cosine functions (gap, no app yet)	Circumference and area of circles (gap, no app yet) Similarity (gap, no app yet) Intercept theorems (gap, no app yet) Pythagorean theorem (gap, no app yet) Right-angled trigonometry (gap, no app yet) Sine rule and cosine rule (gap, no app yet) Pyramids, cones and spheres (gap, no app yet) Nets and oblique drawings: pyramids, cones (gap, no app yet) Volume and surface area: cylinders (gap, no app yet) Volume and surface area: pyramids, cones, spheres (gap, no app yet) Calculations in triangles and polygons (gap, no app yet)	Samples and surveys (gap, no app yet) Two-way table (gap, no app yet) Conditional probability (gap, no app yet)

Click a building block to see what it builds on, when it is taught and which app practises it.

Strands and building blocks come from: KMK-Bildungsstandards Mathematik, ESA und MSA (2022) · The map as data (JSON)

How to read the map

Strand · a column: A part of the subject that runs over several school years.
Building block · a box: One thing a child can learn: “I can …”.
Grade band · a row: Roughly when a building block is taught. Choose a curriculum to see its grades.
App · the colour: Blue means covered: an app practises the building block. Dashed means a gap: no app practises it yet.

You see the grade band: roughly in which two school years a building block is taught. Each German state sets this a little differently. Choose a curriculum, and the map sorts the building blocks by its grades.

Not captured yet: Baden-Württemberg, Bavaria, Berlin, Brandenburg, Bremen, Hamburg, Mecklenburg-Western Pomerania, Lower Saxony, North Rhine-Westphalia, Rhineland-Palatinate, Saarland, Saxony, Saxony-Anhalt, Schleswig-Holstein, Thuringia

All terms and how they belong together · Why this method?