Social studies play a much larger role in third grade than they have in student's previous grades. Therefore, spend some time explaining the basics to your students. Before you can work on play-acting and other more "fun" kinds of activities, you should introduce the branches of government with a basic diagram. This can be a coloring sheet, or even a sheet on which the children have to fill in information about each branch as you lecture to the class. For best results, make your lecture interactive, asking the students questions about things they may already know: for example, the role of the president, which you may have introduced earlier in the year.
Once your students have a basic understanding of the branches of government, put the concept into more concrete terms by having them perform skits about it. With the list of duties you gave them in the diagram, divide your students into three groups, one for each branch of the government, and have them invent skits based on their branch's duties. After you have watched each skit, have the groups interact to show the different powers that the branches can exercise over one another (for example, with the passing of a bill). Carefully supervise each group, as third-graders have a tendency to take on a "know it all" attitude that can cause friction when working with others.
Present your students with a list of hypothetical situations, from tax increases to natural disasters. With the earlier list they made of the duties of each branch of government, have them identify ways in which each branch could respond to different situations. Consider giving a prize to the group that comes up with the most plausible solutions, but be sure to praise all students in specific, concrete ways: At this age, students will actively seek out praise and be unnecessarily hard on themselves if they think they have "failed."
One of the goals of third-grade social studies is to introduce children to a symbolic, or more abstract, way of viewing the world around them. Therefore, after having thoroughly explored the three branches of government, make a Venn Diagram, or three overlapping circles that look almost like Mickey Mouse, on the chalkboard. Have students identify which duties of each branch overlap with the duties of other branches, and enter those items into the overlapping areas of the circle. Classify other duties as belonging exclusively to one of the three branches.