Jessi,
I don't know how old the child is (which would possibly alter my response), but you might just give him/her the positive words and a little extra encouragement. I've worked in homeless shelters and transitional housing off and on for a long time and it's tough. Too often the kids needs get lost in the focus on stabilizing the parents.
If the child is a good reader, give them a book with an encouraging note in it...along the lines of "you're doing great!" Or maybe a special pencil that says good job if they achieve a (minor) milestone. Whatever you do though, don't single the child out....they may already feel "different" enough (you know, can't have friends over, etc.). Be sure that this child AND all the others know that you genuinely care about them (which I know you do).
(As an aside, I remember one little girl I worked with at a previous job was thrilled to have a "Special Recognition" certificate from her teacher for doing something...though I can't remember what it was. I do know that the certificate meant the world to her. She kept it in a "special envelope" until I surprised her one day with a frame for her. She was so proud that she had to hang it in her room at temporary home and wanted it above her bed so that everyone could see it when they came into her room.)
The biggest gift you can give this child is a great educational experience...make sure that they LOVE learning. That will be what changes things for this child as an adult and for their children.
Bear in mind that most homeless programs have a limited hotel stay (30 to 60 days) so the family may be moving again soon. Be sure to stay on top of things with the school social worker so that when the family moves again, transportation is again arranged for the family's new living situation.
Staying in the same school with the same teacher is absolutely critical to a homeless child. Unfortunately, I've seen situations where a child will attend as many as 7 different schools in one year (if the school doesn't work hard to keep a homeless kid in class) and too many different schools to count over their educational career. And then we wonder why some kids don't make it.....

!
I'm so glad you're a teacher!
Karen