Previous studies have found that block play results in better spatial ability which may lead to greater mathematical skills. The current study examined a specific type of block play, structured block play in which a copy of a block configuration is constructed. Structured block play is a difficult cognitive task that requires an understanding of spatial relations, hand-eye coordination, and spatial working memory among others. This preliminary study was designed to determine whether training using structured block play would lead to improvements in skills linked to mathematical thinking. Two groups of children participated in the study. One group played a competitive structured block building game once a week for 8 weeks. A control group was also tested. All participants completed a kindergarten readiness assessment before and after the 8-week period. Children in the block play group showed significant improvements in the computation module of the assessment, showing improvements in the "makes a set of objects smaller or larger" skills. No such effect was observed for the control group. The results presented demonstrate that young children can, with assistance, engage in structured block play and that they have cognitive benefits from such block building activities.