Mathematics growth trajectory plays a significant role to predict future outcomes and careers. We examined the existence of different growth trajectories in mathematics during the late elementary-school period (from Grades 4 to 6) and the relationship between the trajectory group classification and later mathematics achievement (Grade 8). Then, this study examined the moderating effects of mathematics teachers' teaching styles. Two thousand six hundred eighty students participated in a 5-year longitudinal study in South Korea. Growth mixture modeling provided four distinctive classes of growth trajectories in elementary mathematics achievement, and all classes significantly predicted later achievement in Grade 8. Furthermore, the student's perception of teaching styles revealed different associations with mathematics achievement depending on growth trajectory groups. While direct teaching is positively associated with the high and the average performing groups, dialogic teaching is positively associated with the low performing group. The findings highlighted the growth trajectory is a critical component in predicting later academic achievement and students need appropriate instructional supports.