I'm directing Challenge 4 this year, so as I was working in the kitchen one afternoon, folding laundry, doing dishes, etc., I was also listening to Wes Callihan introduce The Iliad on CC Connected.
The girls were working on their schoolwork in the living room.
The youngest (Foundations and Essentials) was working on a math lesson from her math book.
The middle (Challenge A) was making an outline from her science research notes.
Apparently, the two of them could hear enough of what Mr. Callihan was saying to get really interested.
So they quietly moved their stuff into the kitchen to position themselves to hear better as they worked.
In this way, I often find that what I am doing to prepare for directing Challenge 4 or whatever I am doing simply out of my own interests to learn something can enrich my daughters' homeschool days (and their lives) in ways that are totally unplanned, but very natural.
My lectures on The Iliad, podcasts about Shakespeare, Classic novels or poems on audio, sermons about the Bible, etc. all tend to become a part of the background in our homeschool and the content often enriches our lives in amazing ways I could never plan.