The plan proposes a succession of tasks exploiting the potential a priori
offered by Casyopee for approaching and studying the notion of function, and
especially:

- the role played by functions for solving problems arising from geometrical
situations,

- the role played by parameters for studying family of functions and
accessing generalization.

Specific importance is given to the construction of tasks where students can
choose different variables for exploring functional dependencies and to the
connection between algebra and geometry. This connection is supported in
Casyopee by geometric expressions which allow to express magnitudes in a
symbolic language mixing geometry and algebra. Moreover, according to the
choices made for the independent variable, the resulting algebraic expression of
functional dependence automatically produced by Casyopee can be of very
different complexity. The scenario aims at exploiting these didactical
functionalities of Casyopee and the different associated feedbacks, coherently
with the theory of didactic situations.

The instrumentalisation process is initiated in each phase of the scenario
through a collective phase orchestrated by the teacher, which also serves as a
devolution phase for the type of task which is considered.

The scenario is built around three main types of tasks :

- finding targetted second grade functions by acting on parameters (five
different tasks according to the semiotic forms used for these functions),

- functional modelling of a geometrical situation for solving a problem of
relationships between areas,

-functional modelling of a geometrical situation for solving an optimization
problem.