MathematicsHesse curriculum · Gymnasium
Mathematics by grade
The units of Kerncurriculum (Hesse, Gymnasium) with matching simulations. The summaries are our own – the original text is authoritative.
Grade 7/8
- 1.1 Numbers
- 1.2 Operations and their properties
- 2.1 Plane figures
- 2.2 Solids
- 2.3 Relationships between geometric objects
- 3.1 Working with quantities
- 3.2 Measuring processes
- 4.1 Assignments (mappings) and their representations
- 4.2 Functions and equations
- 5.1 Statistical surveys and their evaluation
- 5.2 Dealing with chance
Grade 9/10
Grade 11
Grade 12
- Q1.1 Introduction to integral calculus
- Q1.2 Applications of integral calculus
- Q1.3 Deepening differential and integral calculus
- Q1.4 Integration techniques
- Q1.5 Ordinary differential equations
- Q2.1 Deepening of calculus
- Q2.2 Orientation and movement in space
- Q2.3 Lines and planes in space
- Q2.4 Matrices for describing transition processes
- Q2.5 Matrices for representing linear geometric transformations
Grade 13
More simulations
These simulations are not assigned to a grade in the Hesse curriculum.
Parabola through three points
Drag three points and the matching parabola always passes through all of them. The equation is worked out step by step.
Monte Carlo method: estimating π by chance
Random points fall on a square with a circle inside. From the share inside the circle you can estimate π.
Monty Hall problem
Play yourself or simulate thousands of games: is it worth switching doors?
Taylor polynomials
Term by term a polynomial hugs a function such as sin x ever more closely. That is pretty much how a calculator does it.
Fourier series
Square, sawtooth and other waves are built from many sine waves. You can also listen to them.
Spheres, lines and planes
A plane cuts the sphere in a circle, touches it at a point or misses it entirely. Including the equation of the sphere and the tangent plane.
The summaries describe the curriculum in our own words. The original text is authoritative.