Its fun to be able to write this all down! It makes me see that we're actually doing alot, although I often worry that we aren't 'keeping up'. With a few exceptions (math and handwriting are the biggies), we try to have DS1 be as self-directed in his learning as possible...and isn't that the beauty of homeschooling? We are trying to help DS1 find ways to show his knowledge/work/learning without resorting to worksheets, and while keeping the work as interest-driven as possible.
Math: We use Mammoth math as a basic text and supplement with work in Unit Studies and mental math practice. He's about half-way though their 2nd grade book - just beginning carrying & borrowing. I completely agree with the importance of having those single digit number facts down solid! We did/do a lot of math games, oral review, skip counting while bouncing on the trampoline, etc. DS1 likes 'kinetic' math:) We usually alternate a few days of 'paperwork' with a day or two of project math (answering logic problems, etc.), math games (math bingo, cards, etc), and mental math.
Language Arts: Last year, our primary goal was for DS1 to become a completely independent reader & now he's in long chapter books. His reading is almost completely self-directed. The library is a highly anticipated outing :) Our goal for this year is for him to become an independent writer as well...to that end we encourage/develop as many writing tasks as we can all stand. We all journal every night and and DS1 is learning more formal writing as part of his unit study work. We alternate spelling words from the unit he's working on with lists that are mostly basic second grade spelling words.
Handwriting: We're reviewing print and are about to start cursive with Handwriting without Tears
Unit Study: We've found that Unit Studies are a great learning tool for our family. DS1 can do a tremendous amount of reading and research on his own, and his 3 yrd old brother can participate in many of the field trips etc. that deepen the work. The subject of the unit is always something that DS1 is really interested in studing. For example, right now we are working on a unit about owls. This developed out of DS1s love of the books The Guardians: Owls of Ga'Hool...which he discovered at the library a few weeks ago and has been devouring. He got out 'factual' books about owls, has been researching them, learning about taking notes, absorbing information and then recording the important pieces. We went to a zoo/farm and observed live owls, drew them and wrote poetry about our experience. We've charted their wingspan and created a scaled down chart to include in our report. DS1 generated a list of spelling words which he studies, has created word searchs and other games with for the grown-ups to do. DS1 has drawn and labeled diagrams of owls eyes and wings. I ordered owl pellets from Amazon that we can't wait to disect! Through this one unit (that's lasted about 3 weeks) we've covered: writing, research skills, library skills, reading, art, poetry, math (measuring, charts, etc), spelling, and LOTS of science. Our next unit (per request) is going to be on Ninjas - that one will have a big piece of geography, history, etc.
In addition: recorder, geography games, a giant time line that lives in our hallway and that we add to as we find interesting events to record, self-directed science experiments, tons of reading - both fiction and non-fiction, cooking, knitting, art, whew!...and that only covers the stuff we do at home!
Most of the actual 'school-work' happens in the early morning or late afternoon, with a piece after dinner with Daddy. Our out-of the-house schedule includes a homeschool Ninpo (martial arts) class, homeschool naturalist class, weekly library run bookgroup, 2 park days, a weekly meet-up with a group of 7 & 8 yr old homeschool boys we've connected with, and town soccer.
Enjoy your second grade year homeschooling! Have fun!