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	Natural numbers and place value (gap, no app yet) Comparing and ordering numbers (gap, no app yet) Rounding (gap, no app yet)again in grade 6 Written calculation methods (gap, no app yet) Order of operations and laws of arithmetic (gap, no app yet)again in grade 6 Estimating results (gap, no app yet)again in grade 6, 7 Powers and powers of ten (gap, no app yet)again in grade 10 Estimating quantities (gap, no app yet) Converting units (gap, no app yet)again in grade 10 Length, mass, money and time (gap, no app yet)	Simple equations (gap, no app yet)again in grade 7	Relations between quantities (gap, no app yet)again in grade 7	Basic plane shapes (gap, no app yet) Parallel and perpendicular lines (gap, no app yet) Coordinate system (gap, no app yet)again in grade 7 Symmetry (gap, no app yet)again in grade 6, 8 Special quadrilaterals (gap, no app yet) Drawing and constructing (gap, no app yet) Cuboids and cubes (gap, no app yet)again in grade 6 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)again in grade 6 Volume and surface area: cuboids, cubes (gap, no app yet)again in grade 6	Representing data (gap, no app yet)again in grade 7, 8, 9 Absolute and relative frequency (gap, no app yet)again in grade 6 Random experiments (gap, no app yet)again in grade 7
Grade 5/6no grade yet		Number sequences and patterns (gap, no app yet)	Scale (gap, no app yet)
Grade 6	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)			Measuring and drawing angles (gap, no app yet) Reflections, translations, rotations (gap, no app yet)again in grade 7 Composite shapes (gap, no app yet)again in grade 7	Arithmetic mean (gap, no app yet)again in grade 9 Concept of probability (gap, no app yet)again in grade 7
Grade 7	Negative numbers and absolute value (gap, no app yet) Calculating with negative numbers (gap, no app yet) Percentages: basic terms (an app practises it) 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)again in grade 8 Percentage comparison (an app practises it) Percentage word problems (an app practises it) Simple interest (gap, no app yet)again in grade 8 Compound interest (gap, no app yet)again in grade 8		Rule of three (gap, no app yet) Direct proportion (gap, no app yet)again in grade 8 Inverse proportion (gap, no app yet)again in grade 8	Angle theorems (gap, no app yet) Constructing triangles (gap, no app yet) Congruence (gap, no app yet)again in grade 8 Special lines in triangles (gap, no app yet)again in grade 8 Area and perimeter: triangles, quadrilaterals (gap, no app yet)	Relative frequency as an estimate (gap, no app yet)again in grade 10 Laplace formula (an app practises it) Complementary event (an app practises it)again in grade 10 Multistage random experiments (an app practises it)again in grade 10 Multiplication rule for paths (an app practises it)again in grade 10 Drawing with and without replacement (an app practises it) Addition rule for paths (an app practises it)again in grade 10 Writing probabilities (an app practises it) Events in tree diagrams (an app practises it)again in grade 10 Box plot (gap, no app yet)again in grade 8 Two-way table (gap, no app yet)again in grade 8
Grade 7/8no grade yet		Algebraic fractions (gap, no app yet)
Grade 8	Percentage points and successive changes (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)	Concept of a function (gap, no app yet) Representing functions (gap, no app yet)again in grade 9, 10 Linear functions (gap, no app yet) Equations of lines (gap, no app yet)	Hierarchy of quadrilaterals (gap, no app yet) Chords, secants and tangents (gap, no app yet) Thales' theorem (gap, no app yet) Prisms and cylinders (gap, no app yet)again in grade 9 Nets and oblique drawings: prisms, cylinders (gap, no app yet)again in grade 9 Volume and surface area: prisms (gap, no app yet)	Simulations (gap, no app yet)
Grade 9	Square roots (gap, no app yet) Real numbers (gap, no app yet) Laws of roots (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) Simple quadratic equations (gap, no app yet) Quadratic equations (gap, no app yet)	Quadratic functions (gap, no app yet) Applying quadratic 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) Volume and surface area: cylinders (gap, no app yet) Calculations in triangles and polygons (gap, no app yet)again in grade 10	Conducting surveys (gap, no app yet) Median, range and quartiles (gap, no app yet) Reading charts critically (gap, no app yet) Samples and surveys (gap, no app yet)
Grade 9/10no grade yet					Conditional probability (gap, no app yet)
Grade 10		Laws of exponents (gap, no app yet) Negative exponents (gap, no app yet) Nth roots (gap, no app yet) Logarithms (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)	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: pyramids, cones, spheres (gap, no app yet)	Counting principle (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) · Kerncurriculum Mathematik Gymnasium Sekundarstufe I, Hessisches Kultusministerium (Jahrgänge und Einheiten nach dem Lehrplan Mathematik G9) · 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 curriculum Hesse, Grammar school (G9). It places 123 of 127 building blocks in a grade. A building block stands in the first grade in which it is taught. “Again in grade …” says when the curriculum takes it up again. Building blocks without a grade stay in the striped row of their grade band.

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?