Mathematics achievement is an important predictor of later life and career prospects. Therefore, it is highly relevant to identify early determinants of math achievement. Recently, non-cognitive aspects such as home learning environment (home numeracy) and math anxiety were observed to significantly predict mathematics achievement beyond domain- specific early numerical skills. However, these aspects have hardly been considered jointly in one study. Therefore, this longitudinal study evaluated the predictive power of early numeracy skills, home learning environment, and math anxiety assessed at the end of kindergarten for mathematics achievement at the beginning of second grade in a normative sample of 85 children. Correlations and regression analyses indicated that early numeracy skills, home environment, and math anxiety have a unique and essential influence on math school achievement. It is, however, important to note that predictions seemed selective for different components of math achievement such as written computation, sequences, and comparisons. Results indicated that home numeracy only predicted performance on sequences, whereas math anxiety seemed to affect written computation. Overall achievement as well as performance on the equation’s subtest were best predicted by early numeracy skills. Taken together, these results suggest that non-cognitive aspects of home numeracy and math anxiety significantly influence children’s future math achievement. Importantly, however, results also argue for selective influences that should be considered in future studies.