This is the definition in the Collins German dictionary, but you can omit the 'modern' as is the norm and simply say 'secondary school'

This seems like a good choice. See education glossary below.

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Note added at 2003-03-03 14:20:19 (GMT)
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in 2 x 4 feet sheets and can be found at most building supply stores.
5.3.1.1.1. Hauptschule
The Hauptschule provides its pupils with a basic general education. It normally covers grades 5. In Länder with 6 years of primary school or with an Orientierungsstufe independent of type of school, it commences with grade 7. With 10 years of compulsory education, the Hauptschule also includes grade 10.
The subjects taught at Hauptschulen include German, a foreign language (usually English), mathematics, physics/chemistry, biology, geography, history, Arbeitslehre (i.e. pre-vocational studies) and social studies, music, art, sport, religious education and, in some Länder, domestic science and economics and other work-related subjects. Mathematics and foreign language lessons are frequently taught in sets according to the pupils\' aptitude. The aim of this is to better accommodate pupils\' different abilities, to enable them to obtain the Hauptschulabschluss and to facilitate their transition to other types of secondary school.
Länder in which full-time school attendance is compulsory for nine years offer pupils an opportunity to attend the Hauptschule for a tenth year, if they wish, in order to obtain another leaving certificate (e.g. the extended Hauptschulabschluss). As a secondary school, the Hauptschule also affords particularly able pupils an opportunity to obtain a more advanced qualification under certain conditions such as the Mittlerer Schulabschluss, either in a 10th year or in a subsequent vocational education. See chapter 5.3.1.11. for more information about qualifications.

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This information comes from a glossary published in the ATA Chronicle, March 1999, p. 21.