This document summarizes a GeoGebra presentation created by German students about the 2014 FIFA World Cup hosted in Brazil. The presentation featured models of World Cup logos, Brazilian stadiums and landmarks using geometric shapes. It combined work from grade 10 students who could solve equations and grade 8 students familiar with geometric shapes in GeoGebra. The teacher provided notes explaining the different mathematical abilities of the two grade levels and that the football theme motivated the students near the end of the school year.

1. Fußball WM 2014 in Brasilien
Logos, Stadien, Sehenwürdigkeiten
aus dem WM –Land
modelliert mit GeoGebra

2. We hope you enjoy
our presentation!
Thanks to the Spanish team for the basic idea!

3. Logo 1 WM 2014 in Brasilien

4. Copacabana

5. Im Stadion

6. Maracama Stadion

7. Zuckerhut in Rio

8. Architektur in Brasilien

9. Nationalstadion in Brasilien

10. Logo 2 der WM in Brasilien

11. Logo 3 der WM 2014 in Brasilien

13. Zuckerhut

14. Ponte da Amizade

15. Nationalstadion Brasilien

16. Maracama Stadion
Ellipse mit 5 Punkten

17. Rio de Janeiro

18. Museumsbau in Brasilien

19. Zuckerhut und Copacobana

20. Logo 4 der WM in Brasilien

21. Das Theater in Rio

22. Notes from the teacher
 This is a combination of work of students grade 10 and grade 8.
 Students of grade 10 know derivatives, how to calculate equations of
parabola and know different methods of approximation. They might solve
– if they are „forced“ – a system of linear equations.
 Students of grade 8 can determine linear functions, are more familiar with
GeoGebra and know different types of cones (with-out any equation).
They got to know when to approximate by a polynom (from degree as low
as possible) with the command polygon[A,B, C, ….] or by a cone with 5
chosen points.
 As it was at the end of the school year – all tests done and football world
championship – it had been a task that both groups liked very much.
6/2014, Monika Schwarze, PGU Unna