School and district language arts standards should play a role in choosing criteria for grading elementary essays. National standards include using written language to communicate effectively and using language structure and language conventions appropriately. For elementary essays, you'd look for those that stayed on topic and had appropriate punctuation and age-appropriate vocabulary. As the school year progresses, you'll want to increase your standards based on students' enhanced knowledge.
6 Trait Writing instruction and assessment is another way to teach and grade writing. Criteria comes in the form of the six traits: ideas, organization, word choice, sentence fluency, voice and conventions. Ideas are the main message of the essay, organization is how the essay is set up, word choice is the vocabulary used, sentence fluency is how the essay flows, voice is the essay's tone, and conventions are the appropriate use of spelling and punctuation. Some teachers also use the +1 trait, presentation. Education Northwest (http://educationnorthwest.org) provides criteria lists for each trait.
You may also want to assess elementary essays for more specific goals. You might ask students to include certain vocabulary words or particular punctuation marks within essays, depending on what they've been studying in class. While these tasks can be incorporated into the 6 Trait model (vocabulary words fitting into word choice, punctuation marks within conventions), you can also create your own unique grading guides.
Rubrics are numerical scoring guides that can be used to grade student work. Many school districts rely on them instead of traditional grades, using numbers to indicate whether students have exceeded, met, approached or failed to meet the standard in their school work and assessments. You can use an already existing 6 Trait rubric or a district rubric, or you can create your own rubric for a particular assignment. Another option is to create a grade guide by describing what an essay needs to have to earn an A, B and so on.