Read to the third grader and encourage them to read on their own. Listening to others read can help them gain reading comprehension that is hard to gain on their own. Reading is the best and most efficient way to energize and enlighten a young mind. Also vary the reading material and try to find out which titles or subject generate the most interest from the third grader.
Help the third grader with math flash cards. Third grade is usually the first year that children are asked to start working out math problems in their head or on paper. While flash cards are a good tool, a parent can just simply asd their child random math questions. For example, ask the child to compute how much a grocery item sells for by the pound or ounce.
Take the third grader outdoors as much as possible. Also encourage them to ask scientific questions about how things work in nature. This will also help with peer bonding--as you both learn together. Often in third grade the science classes start to expand to more complicated theories and the child will be asked to make observations about nature.
Understand that most third graders are good at making friends with classmates but not so good at keeping friends. Help them understand the dynamics of a friendship. The may seem outside of the scholastic parameter but social dynamics is very important for a child to succeed and enjoy school.
Realize that at or around the third grade children start to assert their independence from the parents. This should not be taken as bad behavior, provided the assertion of independence is within reason. While this is healthy emotional growth in the third grader it can make helping the child with school harder. She will want to do more and more things on her own to show her competence. Be patient and understand this reaction for what it is.