What is he doing for the partnership?

Yes, a ten year old can be a member in an LLC, and can still be claimed as a dependent, however, Form 8615 is required for children under age 18 that had more than $1,800 of investment income, and the child will not be able to claim a dependency exemption on their own return.

I agree, he can be a partner and you can claim him as a dependent. His share of income/loss will be passive. So any losses may be suspended. Any income will be taxed at your rate (after the $1800). Some people use this as a way to move assets (either cash or the "future value" of the LLC) out of their estate.

I agree with the answers given by Brent and Boston CPA above and to further add. How did the 10 year old acquire the LLC interest? This may lead to a gift tax compliance issue.