On steep slopes with loose rocks, take extra care. When choosing where to place your feet, the best surface is bare ground. But if it's rocky, bigger rocks are better, and rocks embedded in the ground are better yet. Bigger rocks tend not to move as much or end up rolling down the hill.
It is better to lead people diagonally up a hill to avoid dropping rocks onto others. If a rock is dislodged yell out "rock" so that people below have a chance to avoid it. Keep a safe distance between people depending upon the nature of the rocks and the slope angle.
If you find a dangerously loose rock, try to stabalise it and notify the people in your party of its location, otherwise if it remains hazardous, notify everyone around you and choose another less hazardous route. People below should attempt to get out of harms way.
Fire can loosen rocks that would otherwise be stable. Vegetation often holds the rock within the soil and a fire will provide plenty of loose rocks. Quick cooled volcanic rock like basalt areas are notorious as are conglomerate sedimentary and some sand stones and lime stones for breaking off and tumbling down hills.
In general rocks with coarser grains like granite provide easier grip than fine grain rocks like basalt. Lichens and algae on rock become extremely slippery with the slightest moisture. Rocks in shaded creeks can take weeks in cool weather to dry out from rain and remain slippery.
A tip when rock hopping is sometimes to step onto rocks just beneath the water's surface in flowing water. The water keeps lichen or algae from getting well established making grippier walking. (Also there is less distance to fall). Always keep a lookout for banks and riparian corridors where rocks can be avoided.
When rock hopping, walking sticks allow the walker to balance on slippery rocks without slipping by acting against the forces that leave you slipping down the rock.
Walking in creeks with slippery rocks can lead to walking speeds down to 300m an hour in the worst situations. Remember that just about all small creeks have many twists and turns that will also slow progress.
If a rock is coming down a chute it is usually bouncing out and down the chute. You have less chance of injury if you can anticipate its direction and avoid it but if this isn't possible, minimise the target by getting into a hunched position close to the ground. Put your arms over your head (just as in the crash position on a plane) as it is better to have broken arms than a crushed skull.
If the rock is rolling down the chute, being to big to bounce or not steep enough, you should risk a lesser injury by trying to move to one side of the moving rock as a perpendicular hit from the centre of gravity of the rock will inflict far more force and injury than its edges.