Germany uses a 5- or 6-point grading scale (GPA) to evaluate academic performance for the youngest to the oldest students. Grades vary from 1 (excellent, sehr gut) to 5 (resp. 6) (insufficient, nicht genügend). In the final classes of German Gymnasium schools that prepare for university studies, a point system is used with 15 points being the best grade and 0 points the worst. The percentage causing the grade can vary from teacher to teacher. Grades by education Primary and lower secondary education In primary and lower secondary education (1st to 10th grade), German school children receive grades based on a 6-point grading scale ranging from 1 (excellent, sehr gut) to 6 (insufficient, ungenügend). Variations on the traditional six grade system allow for awarding grades suffixed with "+" and "−". To calculate averages of suffixed grades, they are assigned fractional values, where 1 is 1.0, 1− is 1.3, 2+ is 1.7, 2 is 2.0, 2− is 2.3 and so on. As schools are governed by the states, not by the federal government, there are slight differences. Often a more granular scale of "1−" (equal to 1.25), "1-2" (= 1.5), "2+" (= 1.75), etc. is used; sometimes even decimal grading (1.0, 1.1, 1.2 and so on) is applied. In end-of-year report cards, only unmodified integer grades may be used; in some regions they are written in text form. Many states currently also prescribe the use of behaviour-based notes (Kopfnoten), which grade things such as Orderliness or General Behaviour. Pedagogic grading Teachers who teach Grundschule (primary school) or Sonderschule (special education school) are allowed to use "pädagogische Noten" ("pedagogic grades"). Thus if a student tries very hard, but still does very poorly compared to the rest of the class, the teachers are allowed to give them good grades because they tried so hard. Upper secondary education In the final classes of Gymnasium schools (11th to 12th/13th grade) the grades are converted to numbers ("points"), where "1+" equals 15 points and "6" equals 0 points. Since 1+ exists in this system, theoretically a final Abitur grade of less than 0.6 is possible and such grades are used in an informal setting, although officially any student with less than 1.0 will be awarded a 1.0 Abitur. When the point system is used, a grade of 4 (5 points) is the lowest passing grade, and 4− (4 points) the highest failing grade. Tertiary education German