Third-graders are accustomed to math and enthusiastic about learning, but they are still very young and have short attention spans. They're also being asked to learn new skills very quickly. Keep lessons short and allow the kids time to work on examples with worksheets to get familiar with the process. Mix up teaching styles. For instance, let the kids get physical. Instead of asking the result of two times four, tell a student to ask the right amount of fellow students, by name, to stand up. This not only brings a concept into real life, it provides physical activity and a sense of anticipation that will keep the whole class involved.
Keep kids active with a ballgame. Write a multiplication problem on the board, then toss a foam ball to one student. After she answers it correctly, write another problem on the board and have her toss the ball to another student. Continue until everyone has answered a question. Divide the class into teams and have them stand at the back of a room. Read a division problem and have one representative of each team race to the blackboard and write the answer, with the rest of the team yelling suggestions. Keep a tally and announce the winning team.
There are thousands of interactive math games available online and, given kids' affection for video games, they're a natural teaching aid. The Football Math -- Place Value Game makes kids complete a pass to a receiver, then correctly answer a place value question to continue. At each level, completing the passes and answering the questions gets more difficult, bringing out kids' natural competitive nature. Announce which game will be played the next day and kids will race home to practice. In the old days, that was called homework.
Form kids into small teams and have them solve multiplication and division worksheets against the clock. Organize the class into teams and play Multiplication Jeopardy. There are interactive templates online that allow you to load answers behind dollar amounts, but the game can be played by simply drawing a chart with the dollar amounts and crossing each off as the questions are answered. Have each team name a "speaker" who answers the questions, but give each team 30 seconds to confer on the answer. Have a scorekeeper compile the scores and announce a winner.