My little guy, 22 months, is very independent -- always has been. Right now, as a matter of fact, he's downstairs in the (obviously, childproofed) living room sitting at his little table and coloring. Or playing with his trains. As long as I can hear him, I know he's OK and not getting into too much trouble.
We have a loose routine, but much of his day is playing by himself (although usually it's in the playroom/office with me). He will play with his blocks, arrange little cars and animals, zoom cars and trucks around, look at books, chase the cats, play with foam letters (we have about seven alphabets' worth of these), climb on things, run down the hallway and back, bang on his piano and xylophone. Or, if we're in the kitchen, he likes to stack and carry around the cans of cat food and whatever bits and pieces of appliances (like the bowl from the Kitchen Aid) he can get his hands on.
This isn't to say I don't play with him -- I do. But I've got so much else to do, between housework and WAHM stuff and writing and cooking, that it's tremendous for both of us if we can have together-but-separate time, or parallel activities. That is, if I'm vacumming, I'll give him a broom to push around. Or just make sure that he has something to hold his interest. If he starts to seem bored or restless, I'll either point out a toy, or suggest an activity, or start to play something by myself --he'll then come join in, 9 times out of 10, and I can either stay and play along or go back to my work. A lot of times, too, I comment on what he's doing: "Oh, what a tall tower you built," or "Gee, your bear puzzle! You haven't played with that in a long time!" or ask him to do play-tasks: "Can you find 2 red cars?" or "Where's the Q?" etc. That way we're connected, too.
Does this help?
As an aside, I'm curious what a bean box is -- I'm guessing it's just a box with dry beans in it, but how do you keep your DC from a) swallowing them; b) sticking them up her nose; c) throwing beans everywhere? I don't know if I could trust my little rapscallion with that!
~Nick