  The Heraeus Summer School series "Astronomy from four perspectives", funded
by the WE Heraeus Foundation, draws together teachers and teacher students,
astronomers, physicists and astronomy students from Germany and Italy. For each
summer school, participants gather at one of the four participating nodes:
Heidelberg, Padua, Jena, and Florence. The main goal of the series is to bring
astronomy into schools, which is achieved by educating and training the
teachers and teacher students. In this e-print, we present the exercises,
tutorials, and high-school classroom materials developed during the fifth
summer school of the series, which took place at Haus der Astronomie in
Heidelberg August 26 -- September 2, 2017. "The tutorials" were prepared
beforehand for the participants of the Summer schools, and are suitable for use
in teacher training. "Classroom materials" were developed mainly during the
summer school itself, and are suitable for high-school level teaching. They
include question sheets for pupils, and some pointers on where to use the
material in the German high school curriculum. Both sets of materials address
the summer school's four main topics: Supernova cosmology, the virial theorem,
rotation curves of galaxies, and the temperature of the cosmic microwave
background (CMB).
