An article from brainy-child.com  identifies: " qualities and characteristics that are frequently found among gifted children, although no child will possess them all. One way that parents can tell if their children might be gifted is to focus on a range of behaviors that occur in the daily conversations, activities, and responses to learning opportunities." Quoting Smutny (2000), here is  a list of characteristics common in gifted four-, five-, and six-year olds (Smutny, 2000):

1. Express curiosity about many things
2. Ask thoughtful questions
3.
Have extensive vocabularies and use complex sentence structure
4. Are able to express themselves well
5.
Solve problems in unique ways
6.
Have good memories
7. Exhibit unusual talent in art, music, or creative dramatics
8.
Exhibit especially original imaginations
9. Use previously learned things in new contexts
10.
Are unusually able to order things in logical sequence
11.
Discuss and elaborate on ideas
12.
Are fast learners
13.
Desire to work independently and take initiative
14.
Exhibit wit and humor
15.
Have sustained attention spans and are willing to persist on challenging tasks
16.
Are very observant
17.
Show talent in making up stories and telling them
18.
Are interested in reading.

Your child might not show all of them all the time, but it takes more than  a casual observation to find that out. Perhaps you might want to see us.  And we might be able to help.