This study examined young children’s cognitive engagement during classroom book reading with different types of books in Greek kindergarten schools. Twenty teachers read four books—two fiction (familiar/unfamiliar story format) and two information books (expository/narrative text). As expected, children’s and teachers’ cognitive engagement was highly correlated. Overall, most group discussion was of low cognitive demand, focusing on text recall and labeling. Information books and expository texts prompted more high cognitive demand discussion, while fiction books and narrative texts of information books prompted more low cognitive demand discussion. No differences on the cognitive level of discussion between the familiar and unfamiliar fiction books were found. The outcomes are discussed in terms of young children’s development of representational abilities.