One of my favorite whale behaviors to watch is a mother and calf logging. This is when the mom and baby are lolly gagging at or near the surface and in a hurry to go nowhere. The mother may or may not be sleeping. I have seen several mothers float at 15-20 feet for 20-30 minutes while the calf is free to explore its world. If patient these encounters develop into mutual interactions where the mom is not nervous, and baby gets to come in close and check us out.
I have also seen mothers bring their calves very close as if to teach them not to be afraid of everything they see that is different. See more whale photos here.