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.
Mathematics – grade 8
Grade 8 (nine-year Gymnasium): topic fields of the curriculum; the order is binding only where the subject requires it. Topic fields 6 to 8 apply only in the computer science branch. The numbers are those of the curriculum.
Unit 1Congruence and triangle constructions
Congruence theorems and triangle constructions, the triangle inequality, altitudes and medians with centroid.
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.
Unit 2Terms
Rearranging and factorising terms, binomial formulas and Pascal’s triangle, algebraic fractions and fractional equations, laws of powers.
Binomial formulas with squares
The three binomial formulas as areas: a square splits into smaller squares and rectangles.
Unit 3Polygons and prisms
The family of quadrilaterals, areas by dissection and completion, prisms with surface area and volume.
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.
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.
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.
Unit 4Linear functions
The concept of function, linear functions with slope and y-intercept, rate of change, parallel and perpendicular lines.
Linear function
Change the slope and the y-intercept of a line and read off the slope triangle and the zero.
Function plotter with custom terms
Up to three of your own functions at once, with a table of values, zeros and intersections. The tool for anything that can be a graph.
Unit 5Circle and cylinder
The number π, circumference and area of circles, arcs and segments, surface area and volume of cylinders.
Circumference, area of a circle and the number π
A wheel rolls once and travels a bit more than three times its diameter. Cut into pieces, the circle becomes a rectangle and the area formula follows.
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 6Calculating in other number systems (computer science branch only)
Binary and hexadecimal systems, converting and calculating, the geometric series formula.
No separate simulation is planned for this.
Unit 7Propositional logic (computer science branch only)
Statements and truth values, connectives such as conjunction, disjunction, NAND and NOR, truth tables.
No separate simulation is planned for this.
Unit 8Deepening the regular topic fields (computer science branch only)
Deepening topic fields 1 to 5, for example means, tilings and filling graphs.
No separate simulation is planned for this.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): Lehrplan, Gymnasium, Mathematics, grade 8