Conversations are the number one way children learn in an unschooling environment. At least that's been my experience. Pay attention to conversations. Here's one I had with my 9 year old daughter last week:
We were in the car driving somewhere. She's in the back seat buckled in and I'm, of course, in the front driving. Apropos of nothing she says suddenly:
"There are sixty seconds in a minute."
"That's right," I say.
"And there are sixty minutes in an hour."
"Yes," says I.
"And there are 25 hours in a day," she continues.
"Actually, there are 24 hours in a day."
"Oh! Twenty-four!" She mulls this over for a second or two.
"And there are seven days in a week."
"That's right."
There's a bit of a silence and I wait for her to go into how many weeks are in a month, but her mind moves in a slightly different direction.
"There are four seasons in a year."
"Yes."
"And there are four months in each season."
"Well, there are twelve months in a year and there are four seasons, so. . . "
"Oh, then there are three months in a season!" She's a little excited that she puzzled that out.
Me, enthusiastically: "That's right!"
Again, she pauses to think a bit.
"There are ten years in a decade."
"Correct!"
"And there are a hundred years in a century."
"Correct again!"
"And is there a word for if you have a thousand years?"
"Yes, it's called a millennium."
Child tries out this new word by repeating it carefully several times. It's a fun word to say.
"Is there a word for a million years?" She wants to know.
"Gee, honey, if there is, I can't remember it right now!"
She laughs, "That's because we haven't been around very long!"
Unschooling can make one feel rather insecure about whether a child is learning. Noting conversations like this is a wonderful way to 'see' the natural learning that is taking place.