Background: Building on the Realistic Accuracy Model, this paper explores whether it is easier for teachers to assess the achievement of some students than others. Accordingly, we suggest that certain individual characteristics of students, such as extraversion, academic self-efficacy, and conscientiousness, may guide teachers' evaluations of student achievement, resulting in more appropriate judgements and a stronger alignment of assigned grades with students' actual achievement level (as measured using standardized tests). Aims: We examine whether extraversion, academic self-efficacy, and conscientiousness moderate the relations between teacher-assigned grades and students' standardized test scores in mathematics. Sample: This study uses a representative sample of N = 5,919 seventh-grade students in Germany (48.8% girls; mean age: M = 12.5, SD = 0.62) who participated in a national, large-scale assessment focusing on students' academic development. Methods: We specified structural equation models to examine the inter-relations of teacher-assigned grades with students' standardized test scores in mathematics, Big Five personality traits, and academic self-efficacy, while controlling for students' socioeconomic status, gender, and age. Results: The correlation between teacher-assigned grades and standardized test scores in mathematics was r = 0.40. Teacher-assigned grades more closely related to standardized test scores when students reported higher levels of conscientiousness ([beta] = 0.05, p = 0.002). Students' extraversion and academic self-efficacy did not moderate the relationship between teacher-assigned grades and standardized test scores. Conclusions: Our findings indicate that students' conscientiousness is a personality trait that seems to be important when it comes to how closely mathematics teachers align their grades to standardized test scores.