There definitely are things that your child should probably know before he enters the second grade. While not all of these things may be required by the school, the fact of the matter is that when a child enters the second grade already significantly behind the rest of the class, there is a very little chance that he will be able to catch up before the end of the second grade year.
Before entering the second grade, your child should know how to read. This does not mean that your child will be able to read everything that is put in front of her. It also doesn’t mean that your child will be able to read every word, or even be able to sound out every word. It certainly doesn’t mean that your child will enjoy reading. It simply means that, before entering second grade, your child should be able to read a great many words, to understand very simple sentences, to recognize certain words that are especially frequent, and to know how to sound out many other words.
In terms of mathematics, there are also things that your child should know before entering second grade. He should be able to do at a minimum, single digit addition and subtraction. He should probably have a grasp on two-digit addition and subtraction, and many students will be able to do three digits. He should be able to count to 100 or higher, and should be able to count by 2s and by 5s and by 10s. He should understand the idea of a story problem, how it relates to math, as well as a number sentence. He should also understand concepts of greater than, less than, and equal to.
In other areas, the things that your child should know before entering second grade may vary from one school to the next, or from one teacher to the next. For example, one school district might have certain expectations in terms of civics or history, while another may have other sorts of requirements. If you are concerned that your child does not know the things that your child needs to know before entering second grade, you should talk with your child’s potential second grade teacher, or with her first grade teacher.