There are no specific titles assigned for first or second grades - the important thing is that they keep reading and that reading is enjoyable. They can do the reading themselves or you can read to them. Both of these activities build reading skills. Finding books that your children enjoy reading helps them develop a love of learning!
The only "assigned" titles are the ones selected as potential Caldecott, Newbery, or Geisel award winners, if you choose to participate in the St. Thomas School Library's Summer Reading Challenge. See the main Summer Reading Page for details!
The easiest way to determine if a book is at an appropriate independent reading level for your child is to use the “five finger” rule