A piece of copper and a piece of germanium are cooled from room...

Copper is a metallic conductor. For metals, the temperature coefficient of resistivity is positive. As temperature decreases, the thermal agitation of atoms decreases, which increases the relaxation time of free electrons. This leads to a decrease in electrical resistance.

Germanium is a semiconductor. For semiconductors, the number density of charge carriers (electrons and holes) decreases exponentially with a decrease in temperature ($n \propto e^{-E_g / 2kT}$). This reduction in charge carriers leads to an increase in electrical resistance.

Thus, when cooled from $300\text{ K}$ to $80\text{ K}$, the resistance of copper decreases while that of germanium increases.

Answer: The resistance of copper will decrease while that of germanium will increase.