Early childhood education programs (ECE) invest in assessments of classroom quality to enable accountability and to enact efforts towards quality improvement. The "Early Childhood Environment Rating System -- Revised" (ECERS-R) and "Classroom Assessment Scoring System" (CLASS) are two widely used classroom quality assessments that have inconsistently been linked to longitudinal change in preschoolers' school-readiness skills. The current study examined how the ECERS-R and CLASS scores relate to changes in preschoolers' skills and whether associations are stronger in the second half of the school year than across the whole school year. We used data from classrooms in a San Francisco Bay Area preschool program primarily serving low-income families; 164 classrooms were observed using the CLASS (N = 2,327) and 131 classrooms were observed using ECERS-R (N = 1,792). School readiness was assessed using teacher reports of cognitive, physical, self-regulation, social-emotional, verbal language, and written language development measured in the fall, winter, and spring and a direct assessment of children's letter awareness and pre-literacy skills measured in the fall and spring. Results showed that measures of classroom quality did not relate to children's skills in spring controlling for fall skills, while the ECERS-R "Interactions" was the only quality domain associated with all teacher-reported skills in spring controlling for winter scores. We provide recommendations to incorporate professional development, coaching, and assessment to improve classroom interactions and support child skills throughout the preschool year. [This paper was published in "Early Childhood Research Quarterly" v59 2022.]