## Eva’s windmills

*“Eva’s windmills” is a redesign by the Spanish CoI of the Windmills c-book unit initially designed by the Greek CoI.*

This redesigned c-book unit is focused on providing students with new alternative ways of learning using some mathematical advanced notions, all they included in most of curricula of secondary education. The redesigned unit shows some possible functionalities of these mathematical tools (why these tools are necessary) and providing a transversal view of mathematics, showing the connection between different mathematical areas of knowledge (arithmetic, geometrical, functional, etc.) with certain phenomena outside mathematics. More concretely, the c-book unit focuses on the understanding and putting in use the notion of infinity.

The c-book unit is composed of four phases:

The first one, ‘The Pythagorean Tree’ presents the problem of constructing fractal structures and to associate students’ exploratory activities and their formulation of initial conjectures with the notion of infinity. A whole narrative about fractals connect the successive activities of phase 1 in which students have to use their arithmetic and geometric knowledge, leading to discuss what it is happening in the infinity.

In the second phase, ‘Solving equations’ a new approach and use of the notion infinity is introduced. In the activities here included, the main focus concerns the relation among the number of solutions of an equation with the variation of the coefficients defining which defines the function. Some of the activities included in this phase will require that students look further what it is simply shown and discuss what it is happening in the infinity to decide about the solutions.

The third phase, ‘Calculating limits’, is aimed to a more ‘traditional’ context ox studying limits, but the differentiating element of this phase are the use and complementarity of widgets, which are provided with the aim of understanding limits from different perspectives.

Finally, in the last Phase 4, ‘Games’, invites students, as its name suggests, to have fun challenging their knowledge about limits in a contest against the clock.

**Available in 6 languages**

English:

http://mc2dme.appspot.com:80/mcs/tablet/DWOplayer.html?locale=en#c:5691286564634624

Spanish:

http://mc2dme.appspot.com:80/mcs/tablet/DWOplayer.html?locale=en#c:5108602511556608

Greek:

http://mc2dme.appspot.com:80/mcs/tablet/DWOplayer.html?locale=en#c:5713902453129216

French:

http://mc2dme.appspot.com:80/mcs/tablet/DWOplayer.html?locale=en#c:5767725372669952

Dutch:

http://mc2dme.appspot.com:80/mcs/tablet/DWOplayer.html?locale=en#c:5680257289945088

German:

http://mc2dme.appspot.com:80/mcs/tablet/DWOplayer.html?locale=en#c:5763356048752640