The purpose of this booklet is to help teachers design and select appropriate mathematical problems for the early childhood years. Organizing the classroom for problem-solving sessions is its secondary focus. The material was gathered in early 1970s and first appeared in the National Council of Teachers of Mathematics' Thirty-Seventh Yearbook, "Mathematics Learning in Early Childhood." After noting the central role of problem solving in the curriculum, some characteristics of good problems are listed. Two sample problems are then discussed in detail. The majority of the booklet consists of selected problems for beginning stages and for later stages. Finally, attention is directed to suggestions for group work with problem solving. (MNS)