Well, our pre-K teacher for the 4-5yo class was excited/worried because on the first day of class, pretty much all the kids already had 1-to-1 counting down pat, as well as IDing the letters and writing their names. Apparently this was very unusual, as she told us that she spent the first week trying to figure out what she was going to teach for the year! So I'm pretty sure those are not the norm for 3yos!
She did find some great things to do with them, and the class is a marvelous fit for DS4. I suspect nearly all of the 16 kids (including DS4) are at least MG, and I'd bet money that several are HG+. The moms are not hothousing moms either. It seems that lots of really smart kids (who all get along incredibly well, BTW. SOOOO much fun together!) all stumbled into the same class.

Bliss!
Ah, if only we could keep them all together for elementary school. *sigh* I fear this Nirvana only has a shelf life of about 5 more months. Then it will be back to the real world.

At least we found each other now, and maybe playdates will help. Four years later, I still arrange playdates for DS7 with a buddy of his from pre-K: a MG boy who was a year older, so the relationship has remained a pretty good fit. Maybe the same will happen for DS4...
Anyway, I digress. Sorry! My point is that I'm pretty doggone sure that 1-to-1 counting is advanced for a 3yo, and simple math is GT. I feel pretty confident in stating this is true.