Overall
Integrating technology into teaching mathematics allows open tasks which initiate investigations and explorations about mathematics in a dynamic way using different approaches. The presented tasks are so-called optimization problems. In those tasks it is a matter of finding the best solution. This can be done in general, with different strategies: On one hand, the two technologies presented allow all these different approaches, so they are very suitable to work on optimization problems. On the other hand the various approaches enable to think about the diversity of mathematics in the lessons, to link knowledge and to use it in a flexible way.

But before you integrate the optimization problems in the classroom (classroom activities and materials for teaching) we would like to give you the opportunity to solve three tasks on your own. Before you start solving the given problems, get an overview and think about different possible solutions and strategies.
After that, solve the tasks using a geometrical way, an algebraic way, a numerical way and a graphical way and get to know the different technologies. While working on the problems you don't only get to know the different technologies but also the potential and advantages of the technologies and perhaps also the limitations and difficulties.
And what will happen if you do not know what to do next? There are various types of help available (technical guides).
You will find hints for the different approaches (geometrical, graphical, algebraic and numerical)
Water gutter
Water gutter
Chicken fence
Chicken fence
Box problem
Box problem
Examples