I enjoy reading examples of things HE families do. Sometimes it is presented as "what subjects did we cover today?" (I'm thinking of a Mumsnet thread, where this is crossposted)
But there are a couple of things which bother me, so I thought I'd put them out there to be gunned down or mulled over.
There might be a danger in cataloguing the "subjects" our children cover that we buy into the mythology that activities have to be cataloguable in terms of school subjects to be worth doing, to be educational. For school-at-home HE, it's kind of easy and obvious: "well, we did 30 minutes of our reading scheme and then 30 minutes of maths worksheets, a bit of our history project and then off to the HE science group after lunch" (I am oversimplifying just to make the point).
But for autonomous home educators, the activities of our children may well not at all look like school subject-specific activities.
1) there is the danger of focusing on, emphasising, noticing the activities which fit the boxes. Of breathing a sigh of relief when a child does something which we can present to the in-laws as educational and within the realm of what they'll recognise as such. Of interacting with the expectations of wider schooled society on their terms rather than ours.
2) we don't know when our children are learning or in what form. Someone recently said something about their children spending all day playing computer games. And it's accepted generally in society that that would Not Be Educational. But there is a stage in a person's life when they first learn to use a mouse alone. In what universe is that not a major thing to have learned? There is a stage when they first learn to navigate icons to their favourite games and activities. Again, how are they not, gloriously, learning? And the learning continues; computers are just a medium like any other, which can be educational depending on what is going on inside someone's head.
It might be in the "down-time" computer games that our children learn the most in a day. Or in the building of a large lego structure. Or in who knows what - it needn't look like school, it needn't be good LEA-report fodder, and maybe we as parents will never know what our children learned from colouring in 47 pictures of the Teletubbies one day aged 2 (that's a hypothetical).
There's a wonderful HE video on Youtube called "Learning all the time" which portrays some of that - that you can even make a video of unschooled children doing their thing, and there are glimpses of all sorts of wondrous learning going on, but it still can't be grasped and quantified. Poor old OFSTED, maybe that's why they tried so hard to shut down Summerhill.