The idea of this lab is to demonstrate to the students the basic idea of measuring distances using parallax, and then to demonstrate that even though the principle is straightforward, to get good distances in practice requires accurate measurements. This lab also helps to show the concept of how measurement errors limit our ability to determine distances accurately.
You can start the lab with a brief review of what parallax is. Then tell them they are going to try to use the concept of parallax to measure distances to objects in the classroom. First they need to figure out how they will make the measurement. Install the ``ruler'' against one side wall. Have students work in groups of 3-4; in each group, have them take turns standing against the opposite wall, with a partner holding up a pencil while standing anywhere from 3 to 20 feet from the observer (i.e., less than half the classroom away). Have the observers blink eyes and notice motions against the background ruler. Have each observer look at objects at three different distances, and make sure that everyone confirms that the object appears to move less as it is placed further away. Make sure everyone has a chance to observe, then have them choose a ``qualified'' observer to make the real measurements of how many tick marks the object appears to move at each distance. Emphasize to them the need to try to make accurate measurements, and, most importantly, make sure they estimate the uncertainty in their measurement. You will probably find that students do not use fractional numbers in their motion measurements, and you can discuss with them what limitations that puts on their accuracies. Make sure the students leave their pencils at the distances they used so they can come back later and measure the actual distances.
They next experiment with the affect of a wider baseline. Now instead of looking with each eye in turn, have them look with one eye, then move a few feet to the side and look again. They can compare the apparent motion with that of the same object using the shorter baseline.
Finally, we move to trying to quantitatively measure the distance to their objects. To do so you need to discuss what we are actually measuring. In particular, you need to discuss how the observation of a changing direction to an object is really an angular measurement. Once they get this concept, you convert the measurement of tick marks to an angular measurement. Do this by ``calibrating'' the ruler; have students put a protractor to their eye, and extend lines (works well to use pencils) out toward the directions of the two ends of the rulers. They can then look up the angle, count the total number of tick marks, and divide these to get the angle per tick mark. Using this conversion, they can then convert their measurements of motion in tick marks above to angular measurements.
Students then need to determine the baseline of their observations.
Then you show them the parallax diagram and equation. I don't think you need to explain trigonometry, just say that you can quantitatively figure out distances using trigonometry and give them the equation. They can then figure out the distances to their objects.
They should then use their error estimates of motions to try to determine the possible errors in their distance measurements. Probably the best way to do this is to have them redo the calculation using their measurement with their error estimate added.
Then they get to compare the parallax distance with the true distance. Here the idea of errors will really be emphasized, as you will probably find that their parallax distances are not very good!
Finally, conclude the lab by showing how parallaxes are used in astronomy, i.e. how the baseline is the Earth's orbit, etc.