Why does the resistivity of a metal rise as its temperature rises?

1. Heating a metal makes its atoms vibrate faster and over larger distances. 2. A larger vibration amplitude means a moving electron meets an obstacle sooner and more often. 3. More collisions per unit length means more opposition to flow, so resistivity rises. 4. That is why the temperature coefficient of resistivity is positive for metals. 5. A rising free charge density would lower resistivity, which is what happens in semiconductors instead. _Source: OpenStax College Physics (CC BY 4.0), Ch 20 "Electric Current, Resistance, and Ohm's Law", section Temperature Variation of Resistance_