This study of children from two U. S. states examined associations among four cognitive and academic skills: executive function (EF), visuo-motor integration, mathematics assessed with applied problems, and letter-word knowledge. Before (T1) and after (T2) kindergarten, children (N=555) were assessed using the Head-Toes-Knees-Shoulders (HTKS) EF task, the Beery-Buktenica test of Visuo-motor Integration (Beery VMI), and Woodcock-Johnson subtests of Applied problems and Letter-word identification. Bidirectional analyses showed that all T1 skills predicted at least one other skill, with T1 HTKS and T1 Applied problems predicting all skills. In addition, improving from T1 to T2 in Applied problems was associated with improvements in all skills using random effects analyses, based on differences between children nested in kindergarten classrooms. This overall pattern of results was confirmed using fixed effects analyses, which examined only within-child variability. We conclude that multiple skills undergird early mathematics learning and vice versa.