We used the Early Childhood Longitudinal Study--Kindergarten Cohort (ECLS-K) data to examine how important mathematics readiness levels are to subsequent achievement growth and the efficacy of instruction and engagement in producing such growth. The ECLS-K selected a nationally representative sample of kindergartners in fall 1998 and is following these children through the end of eighth grade. We employed the standardized mathematics assessments that were administered to the students by ECLS-K staff. Separately for students who began kindergarten with low, medium-low, medium-high, and high mathematics skill, we examined achievement growth through third grade and the effects of teacher-reported time on mathematics instruction and student engagement (as perceived by the teacher) on such growth. We found that students who began with the lowest achievement also showed the least growth over this period. Students in the two highest skills groups had similar growth, and the highest levels of growth. Students in the lowest group received the most time on instruction but had the lowest engagement with instruction. Time on instruction increased achievement for all students equally, but the effect of engagement was strongest among the lowest-performing group. The lower engagement of the lowest-performing group explained more than half of their lower achievement growth in grades K-3. If inequality in mathematics achievement is to be reduced, teachers must make greater efforts to improve the beginning knowledge and academic engagement of this group. (Contains 8 tables.)