In their lodges (or other small teams) the Beavers/Cubs will build a den/shelter, using natural materials found in the woods. The idea is to build a shelter to keep them (or the leaders!) dry. The team that builds a shelter which keeps them/the leaders the driest, when a small(/or large!) amount of water is poured over the shelter will win.
Beavers/Leaders to scavenge wood/bracken in the woods.
Consult one of the many guides for building natural shelters. To make it simpler for Beavers, you could expand the allowed items to include a tarpaulin.