Methods: For the map projections each one used the country and geogrid shapefile in the World folder. In each separate each map, you changed the properties to change each Data Frame to the destined map projection. For example, the Geographic Projection Data Frame used WGS 1984. You do this for the next 4 maps. Make projections for Data Frames for Mercator Projection, Equidistant Conic, Sinusoidal, and Cylindrical Equal Area.
For the Wisconsin UTM map, you first used the states shapefile from the US folder. Go to the attributes and select the state of Wisconsin. From there, create a layer from the selected features. Export that data to create the new Wisconsin shapefile. Finally change the projection of Wisconsin to NAD 1983 UTM Zone 16N by changing the properties of the Data Frame.
In the next Data Frame add the states shapefile again from the US folder. Next add the stroads_miv5a shapefile. Even though the shapefiles projected "on the fly," you still need to put them in the same projection. Project the stroads_miv5a shapefile to the same projection as the states shapefile by using the tool Project from the ArcToolbox. This tool is under the Data Management, then the Projections and Transformations. Save the new projected stroads_miv5a.shp. Be sure to change the Data Frame properties to the projected system in the North American Lambert Conformal Conic.
Final Data Frame will be for Central Wisconsin. Start by adding the Cenral_WI_Cts.shp. Change the Data Frame geographic coordinate system to North America_1983. Add in the Lower_Chip_strms.shp then add the same projection as the first shapefile by using the project tool. Next add scale, North Arrow, and legend. Then export the map to Adobe Illustrator. From there use the Type feature to give the map a title, label each county by it's name, and add the authors name before completing the cmap.
Results: In the figure below, this shows the different projections for the world. The Map of Wisconsin is an example of a reprojection. The projection prior to this one did not work as well as the Wisconsin UTM. And the U.S. projection involved projecting the Michigan road ways in the same projection as the U.S. projection.
The Central Wisconsin counties involved getting the rivers and counties on the same projection and the most appropriate projection for the specified area. Then I added the legend, north arrow, and scale.
Michigan Department of Transportation. http://www.michigan.gov/mdot/
Price, Maribeth H.. Mastering ArcGIS (Seventh Edition).