Those reading worksheets look perfect! Thank you.
He seems to have skip counting down already and can do a lot of simple-ish math in his head (things like 26 + 7 are no problem). I didn't teach it to him. I'm not sure how unusual this is. DD has taught him the concept of multiplication, and he seems to get it, but is only able to calculate so far. I just asked him some double-digit addition and he wasn't able to do that in his head. I don't know if he can really do it without a scribe, since his writing is iffy.
I think that is really unusual.
Double digit addition: I think the way we will go about it is to steer her towards mental grouping. So with 17 + 26, I want DD to eventually see that there are 3 tens right off the bat then a 7 + 6. Then, I want her to see that 7 + 6 is 10 +3. So, hopefully, she will see that 17 + 26 is 3 tens (30) + 10 + 3, or just 40 + 3.
It is exactly what you do on paper, but I want DD to see it in her head first.
It is exciting because, like you, I have seen this big jump in mental math ability overnight. DD seems to have this advanced ability to see abstract things and keep the numbers all organized in her head. (She is the one that cannot do puzzles or play tic-tac-toe.) And, I think it gives us an opportunity to explore numbers before the school introduces algorithms.
So, even though she may have learned that 6 + 7 = 13 (because in her head this is plain as day for she has memorized that 6 + 6 + 12.) I really want to make sure she sees that 6 + 7 is the same as 6 + 4 + 3 (or 10 + 3). Because it is important to group ones into tens.
Obviously, this is something we do with the rods or in our heads lying in a dark room. I am not sure there is a curriculum that focuses on mental math long before learning to write the numbers and learning algorithms. If there is, I would want to take a look at it! Though, it does not sound like your DS would get much satisfaction out of it if he just wants to finish a worksheet. Personally, I agree that it would be better to stick with logic puzzles that deal with deductions, decoding patterns, relationships, and analogies for that. I am just not sure about the writing requirements.
I am with you, in that I feel like I do not want DD moving ahead in math--that is working through an actual curriculum. My feeling is that if we did that, I would have a lot of responsibility making sure she did not miss anything. And, I am just not that organized. And, she is just kind of all over the place. I really do follow her interests. And, even though I have good intentions of steering her toward things like grouping, she gets other ideas in her head, (like the recent obsession with skip counting and using multiples to solve addition problems.)
Your DS sounds awesome. I am really against it when it comes to my DD, but your DS seems a prime candidate for a grade skip!