
Biology:
Took a 6 hour round-trip road-trip to the Wild Center in the Adirondack Mountains; read all about the roles of fungi, bacteria, amoebas, and protistas in the lifecycles of the forest. This was a super cool explanation of the invisible things we'd been reading about in the biology book Helena requested. We also learned all about glaciers, alpine flora preservation, saw otters and trout, hiked, and climbed all over the Wild Walk - a walkway through the treetops with art, swings, lookout points to the high peaks, suspension bridges, a massive "spider's nest" of netting suspended high over the forest floor, and a life-size eagle's nest (MASSIVE) that you can hang out in.
Earlier today we were up at the lake and she was hanging out near a beaver's lodge wading and crawling all over downed logs; examining salamanders - we found two mating; playing with snails; discovered a massively huge snake (for NY); found a just dead woodpecker for whom rigor-mortis had not yet set in; found a spot where a bluejay had met his demise with only some feathers left; found a partial animal skeleton and decomposing animal fur in another spot. On the way home, we stopped to watch papa and mama goose with six perfectly fluffy and adorable goslings.
The other day she came out with me to do some field botany work and learned the difference between monocots and dicots and how to tell them apart in the woods. She looked at red trillium and noted all the series of 3's that characterize monocots. Then we talked about the role of each part: the pistil, stamens, anthers, style, petals, sepals and so on... She's also learning some new plants with me because now that I know them I point them out, "Oh there's more of that large toothwort plant in bloom!"
Tonight she did the spelling and vocabulary sections of the CAT test. Her vocab comes out well above 8th grade level. We've never done a single vocabulary worksheet, lesson, etc in her life. We read. We talk. :)
Math:
She occasionally recites some times tables for me. We've watched more Math Antics. We've talked a lot about converting decimals to fractions or comparing size of fractions with uncommon denominators and how to estimate this with a number timeline. We've played mental arithmatic games with this in the car. Tonight she did the first section of math on her CAT test. (NYS requires biannual testing for grades 4-8 homeschoolers.)
She's sorted her My Little Pony (MLP) collector cards categorizing them in more ways than I can keep track of. She's played Minecraft with all of its amazing spatial awareness and block counting and other skills it develops. She's also done a lot of spatial reasoning work with some interior design app that she downloaded.
Social Studies:
We've learned more about life in early 20th century Prince Edward Island through fiction. We read a biography about Blackbeard the pirate. We've talked about various social justice issues and about the Presidential campaign. She's learning about her own culture, childhood in this era, watching cartoons and hanging out with friends and generally being obsessed with MLP.
When kids unschool they often learn in cycles. Earlier in the year we explored so very many social studies topics, historical eras and so on. Now we're barely touching on it but she's delving very deeply into various science topics.
Arts:
She's currently doing a several hour film making class each week. She helps film the videos for my Online Herbal Summer Camp. She's also gotten very interested in architecture and interior design from watching Flip or Flop on Netflix. She found an interior design app to download and spends a good amount of time developing floor plans and furnishing them. Next time we're at the library we'll get out some books on interior design and maybe the history of design.

She does taikwondo 2x per week and a two hour swim and gym homeschool class 2x per week. She plays outside. We hike as often as possible. We are always talking about healthy food choices, nutrients and such. She does a daily guided meditation.
And that's just what I can think of off the top of my head in a couple of minutes. It's in no way reflective of EVERYthing she's done. :)