That may hold true for much of the country, but in California the academic expectations based on CA standards starts pushing these skills way too early IMHO. Kindergarteners are expected to come into school already reading, and they are starting to teach algebra concepts in second grade. While some parents are giving their children a lot of exposure early in their child's life, most do not. Our 7 year old, now in 2nd grade, started Kindergarten able to read, and is reading at between a 3.5 and 4.0 level today. But, that is only because we took the time to start her reading way before she started school. Math, on the other hand, has been somewhat of a struggle for her. She is doing well on the basics, but when asked to use higher order reasoning to compute more difficult math reasoning problems, she struggles. I believe that this is because the brain of a 7 year old is just not ready for that level of reasoning. In CA we are pushing our children too hard, and this results in great frustration for the child, and the family, and might be worse than what the schools were doing before.
When I had my kid tested at 5th grade, she was reading at a grade 16 level but her math was at a grade 4 level.
Why was her math so low ? She couldn't do a lot of the problems w/o a calculator, and had never been exposed to basic equations like the concept of an unknown "x".
I agree that a 7yo has a great deal of trouble with abstractions, yet the very basics of algebra (x + 1 = ?) and sets can be handled successfully if presented correctly for the age group.
Go look at the Singapore math books or Ray's arithmetic if you want to see what average kids are doing overseas or did in the last century.