On the basis of practice-oriented questions, students are introduced to the basics of mathematical modeling by scientists in various modules. Mathematical contents, such as angle sentences or matrix calculations, are applied which the students may already know from class. In addition to content competences, process-related competences in particular are promoted in the workshops. This includes problem solving and modeling, but also communication and argumentation as well as the use of tools (e.g. e-learning units, MATLAB, GeoGebra). For this purpose, the pupils work interactively in small groups on the problem and acquire the knowledge and the solutions themselves in the action-oriented modules.

	Topic	At least grade	Previous knowledge	Possible contents
	Animated movies	11	concept of functions, interpolation	interpolation
	Computer tomography	11	Straight lines in R2, calculation of intersections	Inverse  problems, parameter representation of straight lines and planes, matrices
	Data compression	9 11	concept of functions vectors, matrices	functional equations, trigonometric functions matrices, vectors and their multiplication
	Evolution	8	relative frequency, arithmetic mean, median, proportionality	Handling of data, distance measurement, transition matrices and stochastic processes, clustering methods, metrics
	Fitness tracker	9	concept of functions	functional equations, trigonometric functions
	Google	10	systems of linear equations	probability concept, limit value, transition matrices
	GPS	10	system of equations	systems of equations, tangent equations in three-dimensional space, compensation calculation
	Climate change	10	concept of function, differential calculus, arithmetic mean	linear regression analysis, coefficient of determination, hypothesis tests
	Artificial Intelligence	10	vectors	vectors, scalar product, distance point straight/plane
	Shazam	9	concept of functions	functional equations, trigonometric functions
	Solar energie	8 10	angle pairs	geometry, trigonometry, angle relations in triangles integration, optimization
	Social networks	7	First experiences with Boxplots	relative frequency, arithmetic mean, median, span, quartile distance, box plots

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