We aimed to investigate the effects of phonological awareness -- PA, rapid automatised naming -- RAN, visuospatial and verbal working memory -- WM and executive functions -- EF on the reading and arithmetic skills of children with low- to medium-performance levels. Participants were 472 Brazilian children from 3rd to 5th grades. Quantile Regression Analysis was employed. The PA, RAN and EF were shared main predictors of both reading and math. Verbal WM emerged as a unique main predictor for reading, while visuospatial WM and visuospatial short-term memory were the main predictors for arithmetic. Among children with very low reading proficiency, the effects of cognitive predictors were more pronounced, a trend not observed in arithmetic. The results suggest varying magnitudes of cognitive predictors for reading when considering different levels of performance/difficulties. We also corroborate unique and shared main predictors of reading and math that have implications for research, clinical and educational settings.