Observe
It helps that gray whales are born in the lagoons of Baja California Mexico. Here, scientists can more easily observe some behaviors. Caroline, a tour guide at San Ignacio Lagoon, described this scene:

"We are starting to see the moms teach the calves how to feed off the bottom. They prefer a sandbar by the mouth of the lagoon, 6 to 12 feet of water, where we see them turn sideways with a pectoral fin or tail fluke above water, as they vacuum up a mouthful from the bottom. Then we see the sediment-mud circle in the water as they surface and push their tongues against the baleen to expel the water and trap any food. Here it's just a little snack, I think, as birds aren’t following them to feast on critters that are stirred up and exposed. No birds following the whales tells me there’s not much prey in the bottom sediment."

Image: Caroline Armon