The lab attempts to show how we can infer something about the 3-dimensional distribution of objects in space even if we cannot estimate distances, just based on the relative number of objects seen in different directions. It is important to emphasize this concept at the beginning of the lab, namely that we are trying to learn about the distribution of objects in space for objects to which we do not know the distance.
We start with the example of students in the classroom. Students are asked to make maps of the directions in which they see their fellow students. Again, you must emphasize that distances are irrelevant to the type of map we want to make here, only directions.
This initial exercise provides an opportunity to discuss how we can construct a map of objects in different directions, namely by using a ``globe'' or celestial sphere. You can discuss how we can represent such a sphere on a piece of paper by slicing it up and pasting the slices down. Show the ``sliced sphere'' and have everyone use the same convention for which slice represents the front of the classroom, the ``poles'' are up in the sky and down in the ground, etc.
Allow the students to start to make their maps. You will probably need to help various groups understand and visualize what is going on. Once the groups have completed their maps, have each group describe their map, and draw attention to similarities and differences between the maps for different groups (e.g., all groups should have objects only in the ``equatorial plane'' since students are all located in a plane, but groups in the middle of the classroom will have students at all ``longitudes'', whereas students at the edge of the classroom will have blank ``longitudes''.
Once this is done, students try to generalize their results to several ideal distributions: center of homogeneous distribution, edge of homogeneous distribution, center of planar distribution, edge of planar distribution.
At this point, you can try to discuss the choice of coordinate system, i.e. what would the maps look like if the ``poles'' were off to the side instead of up and down. This is probably a bit hard for students to grasp, so you might just wish to help them a bit, then show them what the map would look like. This is relevant for them to understand the distribution of Milky Way stars. Actually, a good way to demonstrate this would be to have some spheres already made up with planar distributions but at different orientations to the equator; then these spheres could be ``sliced'' showing the apparent location of the planar distribution on our style of maps. This would also provide an excellent opportunity to demonstrate to the students the sort of globes they will next be making.
After this, you move on to the distribution of astronomical objects on the celestial sphere. This provides an opportunity to discuss constellations (stars with similar directions, but not necessarily similar distances). Students plot on their celestial spheres locations of open and globular clusters, gaseous nebulae, and galaxies. The location of stars in the Milky Way is already done for the students.
After plotting is done, the students draw inferences about the distribution of each type of object in space. They should start with the Milky Way, then move on to other objects. They can both infer the spatial distributions, and then also compare these to the distribution of the Milky Way.
This can be a difficult lab. For some people, it is very difficult to visualize the maps, although for others it is easy. People are confused about the idea of positions on a globe; when they look around, they see people at different distances which they don't know how to accomodate. Also, it's hard to grasp why they aren't located on the map at all. A different approach might be good, perhaps with a large globe which we could cut up.