Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting sequences, explicitness of counting, and degree of rationality. The analysis yielded the multi-dimensional Counting Book Typology, which revealed nuanced ways counting books accurately portray numerical ideas as well as ways books could mislead young readers. The typology could aid researchers investigating how children learn with books to focus study design decisions on particular mathematics content features, which would clarify and strengthen resulting implications. Furthermore, this study revealed the need for more such conceptual tools to advance theorizing about learning math with children's books, which has been missing in research and practice.