I speak from experience: if you have to shout often to get him to work, you're the one who has to change. BTDT.
What he's telling you in the best way he knows how is that either he's not on board with homeschooling in the first place or the approach you're taking is not working for him. Either way, you're not going to have luck with him until you change something. You can't change him, you can only change you.
Unschooling is totally valid, especially since he's had such a rough time the past year or so. Relax.
If you need more structure (I do), then I'd definitely recommend that you talk with him about what he wants to do. Do as much of the things he wants to do as you can do. Explain to him that there are certain things that must be done--writing, math, reading, etc.--but that HOW you complete those tasks is open for negotiation. Make an agreement *together* about what school will look like. Get his buy-in by letting him have more say, but then hold him responsible. He might be willing to do 10 problems a day if they're really challenging if he also gets to do something educational that's enjoyable for him.
Or dump math problems completely and go "off road" for a while. DS8 was growing to hate math when he was about that same age in our first year of homeschooling, mainly because nothing we were doing was hard enough. I finally threw my hands up and we started doing geometry. We liked "Painless Geometry" by Lynette Long. It's "real" geometry, not the "this is a circle" stuff, but it's accessible to HG+ young kids. Plus we did a lot of stuff with dice and pattern blocks. After a year or so of this, he was ready to go back to math problems. Think creatively.
Finally, I have finally (!) learned that when I don't challenge DS8 enough, he rebels. If you can find something that is truly hard for him, you might get better cooperation. It sounds to me like he's telling you he's bored.
If you want more specifics about any of this, let me know. I'm happy to help in any way that I can.
