This packet has students explore a variety of polar graphs. It is broken up into 6 sections--circles, cardiods, limacons, roses, lemniscates, and logarithmic spirals. Students are presented with a general form for the equation of each type of graph and then asked to plot points in order to sketch a graph of 1 or 2 specific equations. Students are then encouraged to graph several other equations of their type of graph on their graphing calculator in order to make some conjectures about how the parameters in the general equation impact the appearance of the polar graph.
In the past, I have always had students work in groups on just one type of graph, and then I have had them jigsaw in order to share their results and teach their type of graph to others. This has normally taken 2 class days to complete the entire process.