A theorem in triangles: Median drawn to the hypotenuse of a right triangle

In this scenario the pupils are called to understand the theorem through:

its proof, (thus proving the theorem is one of the main goal states of the lesson),

the effective usage of the geogebra applets (which are especially designed by the teacher for this purpose) and

guided discovery and exploration of real life problems.

Typical starting point of the exploratory learning approach is to engage students while introducing the problem by asking a challenging question or by presenting to them a problematic situation that touches upon their experiences and interests. During this lesson, the students are expected to collaborate in order to

prove the theorem,

apply the theorem in order to solve mathematical problems and

create their own mathematical problems (using their real-life experience and the newly-acquired knowledge) that can be solved with this theorem.

In this scenario, it is assumed that students are familiarised with the use of computers in general and the use of the Geogebra software (dynamic geometry tool), in particular. Thus, a typical entry behaviour is that students know how to handle the functionalities of the software.