My little 8 year old brother is like this. He is very intelligent and gets outstanding grades, but sometimes has behavioral issues at home and school. He is normally very sweet and polite but has problems when he started being picked on at school. He gets angry and thinks he can behave the way he wants at school. When we sit him down and talk to him about why he can't do that; he still needs to behave well at school. He gained self confidence and self esteem and that took care of that. He also used to hang out with a rude group of boys who influenced his behavior negatively. We talked to the teacher to separate them and have him meet new friends who gave him a better school life and influenced him to make good behavior choices.

This is a common problem for gifted children in the classroom.  Kids who quickly complete assignments and are not challenged with more difficult or thought-provoking work become bored and disruptive.

You should schedule a meeting with his teacher to discuss the situation.  Find out what she thinks might be causing the behavior problem.  Ask the teacher how she differentiates lessons for the high-achievers in her class, such as your son.

Differentation is basically tailoring lessons and classwork to meet the different abilities and learning styles of kids in the classroom.  This is challenging to do, especially for new teachers.  It's also difficult if the classroom includes a broad range of kids from those who have learning challenges to those who are gifted.

Teachers who use projects as part of classroom activities can naturally differentiate instruction.  Teachers who primarily use worksheets for classroom activities can find it more difficult to differentiate.

If you find his teacher is generally not able or willing to provide your son more challenging classwork, arrange a meeting with the principal to discuss the situation.

You can find more advice on how to advocate for and help your gifted son in the Parent's section of Hoagie's Gifted Education:

http://www.hoagiesgifted.org/traditional_school.htm