Yes! The Common Core State Standards for English Language Arts and Literacy has published lists of recommended books by grade level. These lists do not include all good books (far from it!). Rather the lists suggest books of the right complexity and quality for children by grade level. The lists also suggest the wide range of subjects that a student should encounter in reading.
The Common Core Standards developers would prefer that you use these lists as guides to find appropriate reading material for you child. One of the criticisms of the Common Core Standards is that teachers will limit themselves to only the reading material listed.
For kindergarteners and first graders, the lists include stories, poetry, read-aloud stories, read-aloud poetry, informational texts and read-aloud informational texts. Some of the stories are classics such as Are You My Mother by P. D. Eastman and Green Eggs and Ham by Dr. Seuss. Others are newer stories.
When you read these or any books with your child, pause as you read and ask the child to tell you what is happening. If there are pictures, ask him what he learns from them. Ask him what he thinks will happen next. When you complete the book, ask him what it was about. Can he name the setting (time and place) and important characters? Pick out two or three new words and see if he remembers what they mean.
To find complete lists of recommended books for all grade levels, review the contents listing at the front of the Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects.
Below are the books recommended for kindergarten and first grade.