Block-building skills at age 3 are related to spatial skills at age 5 and spatial skills in grade school are linked to later success in science, technology, engineering, and mathematics (STEM) fields. Though studies have focused on block-building behaviors and design complexity, few have examined these variables in relation to future spatial and mathematical skills or have considered how children go about copying the model in detail. This study coded 3-year-olds' (N = 102) block-building behaviors and structural complexity on 3-D trials of the "Test of Spatial Assembly" (TOSA). It explored whether individual differences in children's building behaviors and the complexity of their designs related to accuracy in copying the model block structures or their spatial and mathematical skills at ages 4 and 5. Our findings reveal that block-building behaviors were associated with concurrent and later spatial skills while structural complexity was associated with concurrent and later spatial skills as well as concurrent mathematics skills. Future work might teach children to engage in the apparently successful block-building strategies examined in this research to evaluate a potential causal mechanism. [This is the online version of an article published in "Journal of Cognition and Development" (ISSN 1524-8372). For the final published version of this article, see EJ1259849.]