Mathematical skills significantly predict students' educational paths. Mathematical achievement varies depending on the student's socioeconomic status (SES). However, the extent of the SES gap for specific mathematical skills remains unclear. In this cross-sectional study, we examined age variations by SES in three mathematical skills, applied problem-solving, arithmetic fluency, and written calculations, among students aged 7-12 in a socioeconomically segregated educational context. The contributions of the home environment and schools on SES gaps were also explored. The analytical sample comprised 10,665 students (49.2% girls, M[subscript age] = 10.1, SD = 1.3 years, 13.4% from Indigenous ethnic groups) from the Chilean Early Childhood Longitudinal Survey (Encuesta Longitudinal de Primera Infancia). Linear models revealed SES gaps across the three mathematical tasks at the beginning of primary education. The widest gap was observed in written calculations, which was moderated by the home environment. The findings also showed an exponential increase with age in the SES gap for written calculations and arithmetic fluency. However, for applied problem-solving, the initial gap increased and remained constant. Furthermore, schools accounted for 19%-21% of the variance related to the change of the SES gap in all three mathematical skills. The findings shed some light on the role of the home environment and the schools in maintaining, increasing, or decreasing socioeconomic gaps in specific mathematical skills at different ages.