The article considers the relationship of physical and cognitive development of children as well as the processes of memory and attention. They determine the readiness of a child for school education. The analysis of existing theories made it possible to single out the conditions for their development. There was conducted a study to check the level of memory and attention development of 6-7-year-old children. Diagnostic results showed that the vast majority of children showed an average level of memorization, and a low level of attention development. The results of the diagnosis confirmed that the features of the mental development of the preschoolers do not allow a child to fix attention on subjects or actions for a long time, to maintain interest in the performed action. Physical development of children is at the average level. Unified patterns between the general level of mental development and the development of certain types of movements were revealed. Specially organized physical activity for children with a selection of exercises that require concentration of attention, memorizing patterns of movement, coordination will contribute to the development of memory and attention.