I just read that list and the ones for 1-2nd grade and I am floored. They do not seem accurate based on my experiences, but maybe I don't know what typical is. My girls are more verbal than mathamatical, but still, my oldest was able to one to one count by 24 months, knows complex shapes by 1.5 years, and add and subtract, skip count, tell time, and that sort of thing at three. I really don't know what her friends can and cannot do. Think of it this way though: your friends probably have a similar educational background and perhaps even a similar IQ to you, so their children may be more like your children. Children with delays may be factored into this number too. It actually makes me feel a little nervous when I read things that suggest my four year old is doing things 7 and 8 year olds are starting to do...