As muons pass through a substance, they lose energy, so you expect absorber materials to decrease the muon rate. We wish to see if there is a smooth rate of decrease in muon rate with absorber material thickness and to try to determine the relationship between rate and thickness.
Set the paddles one directly above the other at some set distance. Measure the counts for equal time periods with various amounts of material shielding the paddles. Ideas for materials include, but are not limited to: lead, drywall, paper, concrete, wood, ceilings of a building (the lower a floor you are on, the more ceilings there are above you).
Calculate the muon rate and the uncertainty in that rate.