This paper argues that school grades cannot be interpreted solely as a reward for a given school performance, since they also reflect teachers' assessments of pupils. A teacher's evaluation of a pupil's performance, as reflected in the grade awarded, might influence the effort that the pupil invests in learning. Grades might therefore serve as sticky assessments, affecting pupils' later school performance. Getting discounted grades in year 6 for a given level of maths performance assessed using a PISA-like test has a positive effect on maths test scores in year 8 of elementary education, and also influences later outcomes in secondary education. The empirical analysis tries to minimise the possible bias caused by measurement error in year 6 test scores (unmeasured ability) and employs classroom fixed-effect instrumental variable (IV) regression and difference-in-difference models. The empirical analysis is based on a unique Hungarian individual-level panel data-set containing two observations about the same individual -- one in year 6 (12/13 years old) and the other two years later, in year 8 (14/15 years old) of elementary education. The data for three entire school cohorts is analysed -- approximately 140,000 individuals.