Terminating and repeating decimals
Why does 1/4 end as a decimal but 1/3 never does? Long division gives it away as soon as a remainder repeats.
Mathematics – grade 6
The curriculum assigns these units to exactly this grade (Saxony, Gymnasium up to grade 12). The unit numbers are the curriculum’s; optional areas (“Wahlbereiche”) are labelled W1–W3 here.
Unit 1Working with fractions
Representing fractions and decimals, including recurring ones, calculating with them using the laws of arithmetic and solving word problems.
Multiplying and dividing fractions with area models
Two strips overlap in a rectangle: the shared area is the product of the fractions. Dividing by a fraction is shown visually as well.
Equivalent fractions and comparing
Compare two fractions as bars or circles. When you expand a fraction, the pieces get smaller but the amount stays the same.
Representing fractions
Pizza, cake or a line: share it out fairly first, then colour some pieces. That is exactly what a fraction means.
Expression trees: the structure of terms
An expression drawn as a tree: whatever hangs lowest is calculated first. The order of operations stops being a rule and becomes visible.
Unit 2Relationships in everyday life
Unique and non-unique relationships in tables, diagrams and arrow diagrams; direct and inverse proportionality with the rule of three.
Direct and inverse proportion
Twice as many apples cost twice as much. Picture, table and graph show together when a relation is proportional, with the rule of three.
Function or not? Relations and their graphs
Exactly one y for every x? The arrow diagram, table and graph tell you straight away whether a relation is a function.
Unit 3Triangles and quadrilaterals
Proving the angle sum theorem, congruence theorems for constructions, special lines in a triangle, perimeter and area of triangles and quadrilaterals, and classifying quadrilaterals.
Angle sum in triangles and polygons
Tear off three corners, put them side by side, and you get a straight line: 180°, for every triangle. A quadrilateral gives 360°.
Congruence and constructing triangles
Construct triangles from three given parts with ruler and compass, step by step as in your exercise book. Sometimes there are no, one or two solutions.
Circumcircle, incircle and special lines in a triangle
Construct the special lines in a triangle. Each set of three always meets in one point, for example at the centre of the circumcircle or the incircle.
Perpendicular bisector and angle bisector
A point equally far from A and B never lies there by chance: the perpendicular bisector appears before you draw it with compasses.
Parallelogram, triangle and trapezium by decomposing
Cut off a triangle and put it on the other side: the parallelogram becomes a rectangle. Triangles and trapeziums work the same way.
The family of quadrilaterals
Move one corner and the square becomes a kite. When does a quadrilateral get which name?
Unit 4Prisms
Drawing prisms in cavalier perspective and as nets, calculating surface area and volume of right prisms.
Nets and surface areas of solids
Fold nets of a cube, cuboid, prism, pyramid and cylinder into a solid in 3D and calculate the surface area.
Prism and cylinder: surface area and volume
Layer by layer a prism grows upwards, and the curved surface of a cylinder unrolls into a rectangle.
Unit 5Connections: proportions
Stating parts as fractions and percentages, showing them in pie charts and finding them for areas and solids.
Representing fractions
Pizza, cake or a line: share it out fairly first, then colour some pieces. That is exactly what a fraction means.
Percentage bar
Discounts, VAT, surveys: one single bar holds the base value, the percentage and the part, one above the other.
Reading charts critically
Show the same data as bar, line and pie charts and more, and discover how charts can mislead.
Unit W1Finding conjectures with dynamic geometry (optional)
Measuring with geometry software and conjecturing relationships.
No separate simulation is planned for this.
Unit W2Entertaining geometry (optional)
Optical illusions, “impossible figures” and tiling puzzles.
No separate simulation is planned for this.
Unit W3Prime numbers (optional)
Prime factorisation, the sieve of Eratosthenes and the infinitude of primes.
Prime factorisation and divisibility
Break numbers down into prime factors, check divisibility rules and find primes with a sieve. This also gives you the gcd and the lcm.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): Lehrplan, Gymnasium, Mathematics, grade 6