Sounds like some of the same early stuff that HG+ DS6 was doing at the age of 3. DD4.5 started with the same math stuff closer to age 4. Both my older two chilren took an early interest to tangrams at school once they were in the 3 year-old and older classes and had exposure to them. I really think I should buy a set for DS2 and see how he does since he already loves counting various objects (does up to 3 reliably and as much as 5 or 6 if the mood strikes).
At around 3.5-early 4 both my older two loved playing the balloon game in the car. We would take turns asking how many balloons we would have if we started with 3 and someone came along and popped 2 or we started with 5 and someone came along and gave us 3 more.
I agree with Kriston, based on my limited experience with my own children and their GT status--I would agree that those type of things probably mean some level of GT. The more she initiates the stronger the correlation.
