Arithmetic abilities acquired in kindergarten are found to be strong predictors for later deficient arithmetic abilities. This longitudinal study (N = 684) was designed to examine if it was possible to predict the level of children's arithmetic abilities in first and second grade from their performance on preparatory arithmetic abilities in kindergarten. Furthermore, the role of intelligence in the assessment of developing mathematical reasoning and numerical facility was investigated. The results showed that good predictions of beginning arithmetic abilities can be made. Even in the long term, it was possible to make predictions of later arithmetic performances, especially for the domain of arithmetical reasoning. Logic thinking abilities such as seriation and classification and counting knowledge may be assessed in kindergarten as possible markers for at-risk development. Furthermore, it is important to take into account intelligence when looking for useful predictors of arithmetical reasoning. (Contains 4 tables.)