Students use two methods in this little activity...
The one shown above makes use of the fact that at a critical angle, the force due to gravity mgsinq equals the frictional force mmgcosq.
Setting these two equal, and observing the critical angle yields
m=tanq.

In this part, students use a scale and drag a mass at a constant speed.
In this condition, the applied force (the one they read on the scale) mg equals the frictional force mmg.  The students set these two equal to each other and solve for m.