I can't help much with 1st grade but I am homeschooling my 3 year old (for now).
We went through a period when she just would not do anything that we suggested but she has mellowed out a little and even seems to enjoy thematic literature-based lessons so we have reverted back to that again although she spends 70% of her time doing her own thing, which sort of looks like project-based learning. Her latest project is to memorize as many songs as she can. I still try to be child-led so we went through a number of dance and music books that have animal theme. Those didn't last long so we're moving on to Jazz next. Then we'll go over a few classical works. Our field trip would be a live musical performance.
I don't know what we're doing after music but I'm thinking either Chinese culture or baking. Either way, it'd have some science and math.
One of the benefits of teaching thematically is that you can teach both a 1st grader and a 3 year old at the same time as long as you differentiate the expected output and pick topics that interest them both.
More "traditional" curricular materials we are getting her are:
Handwriting Without Tears
Singpore Math and RightStart Math
Montessori and traditional math manipulatives
Puppy Packet (music theory)
Geography and weather-related kits and such
These will go on her shelf as "free choice activities," replacing toys that she hasn't played with since last year. I might insist that she does 10 minutes of HWOT and Puppy Packet at least 5 days a week but we'll see how much she does them naturally on her own.
It might be helpful to print out the common core standards for both LA and math, just so that you know you're not missing anything major.