A large body of evidence supports the central influence of counting in the development of adequate arithmetic skills. Moreover a substantial amount of children with mathematical learning disabilities in elementary school can be correctly diagnosed in kindergarten by a combination of counting and magnitude estimation tasks. The present study expands previous findings, by adding language and logical thinking as predictors for arithmetic skills in kindergarten and grade 1.A sample of 63 children was tested in kindergarten on counting, logical thinking, estimation (number line estimation, number naming and number comparison), language and arithmetic skills. These children were tested again on arithmetic in grade 1. Results reveal that expressive language explains 24% of the variance in arithmetic skills among kindergarteners controlling for number naming and procedural counting knowledge as predictors. Moreover, language still predicts grade 1 arithmetic. In addition, our findings suggest that number naming and number comparison are better predictors than number line estimation of arithmetic skills in kindergarten.