There are large parts of the infant and toddler school day that are taken up by adult-directed activities such as cleaning up, hand-washing, nap time, lessons, transitional activities, and circle time activities. All of these are important activities for children, but for ideas on how to give a child safe materials to entertain him- or herself for a while, here is a good list.
Don’t misunderstand the message – the primary purpose of providing these materials for children is for their own intellectual, physical, and social developmental needs. Children benefit from having time to explore on their own, uninterrupted by adults. It is the caregiver’s responsibility to provide appropriate materials, and get out of the way. Definitely supervise at all times! But, supervise at a distance, so that the child has an opportunity to explore independently.
This is not equivalent to the adult caregiver checking out in any way while the children play on their own. The adult is a mostly passive participant in the child’s active learning experience. Always present, always observing, so as to understand the child’s interests, communication habits, and progress from day to day, hour to hour.