This study of a preschool classroom of 4 year old children examines underlying skills of number sense such as counting and spatial skills and Spontaneous Focusing on Numerosity. It also investigates children's patterns of engaging in spontaneous mathematical activities in free-play activity centers in relation to behaviors associated with classroom achievement such as attention/persistence, self-regulation, perceived math ability, and motivation. A mixed method design with structured empirical measures and naturalistic observations was used. Several data sources were analyzed, including videotaped interviews, systematic observational data, and teacher ratings. Findings indicate that children who spontaneously focus on numerosity are advanced in their counting skills. Teacher rating of motivation and interest is also correlated with counting skills and spatial skills. Teacher rating of persistence is correlated with counting skills and child self-reports of persistence in math correlated with spatial skills. Variability existed in free play activity time, with social or dramatic play the only activity observed for all children. The major math activities chosen were those involving block construction and some computer games. It was noted that students less skilled in math tended to choose less cognitively challenging activities involving small motor tasks rather than more cognitively challenging activities. Using a Vygotskian socio-cultural lens, several suggestions are made about how verbal interactions with teachers and other adults may contribute to children's cognitive competence in math.