The expectations that a particular teacher has of your first grader will vary, of course, from one school to the next, as well as from one first grade teacher to the next. Still, there are certain skills and tasks that your first grader will be expected to be able to perform.
At the beginning of the first grade, your first grader will be expected to recognize and to write the letters of the alphabet, in both their lower and uppercase forms. She should be able to write her first name as well as her last name. She should be able to read some sight words, and probably color words. She should be able to retell a story in her own words. She should be able to follow spoken directions, and to focus on the teacher when she is teaching. Your first grader should be able to recognize numbers up to 100, and count to 100. She should be able to do simple addition and subtraction, count money, and tell time to the half hour.
During first grade, your first grader will be expected to expand his sight word vocabulary. He should be able to talk about elements in stories like plot and setting. He should be able to print. He should be able to write in complete sentences, and will probably be able to spell about 140 words. He should recognize shapes, and be able to add or subtract up to 20. He should be able to count money using coins.
By the end of first grade, your first grader will be expected to be reading. She will be expected to be able to tell her own stories. She should be able to use a ruler, a magnifying glass, and scales. She should have a solid grasp on all of the academic skills described above, plus she should be becoming more and more prepared for second grade.
Expectations can, of course, vary a great deal. To know what is expected from your first grader, you should talk with your childs teacher about specific expectations.