I remember my own frustration with elementary school math, echoed in the standards I read for DD a few years ago. They spent a full month every year on place value - increasing it one place per year: ones and tens in K, to 100 in 1st, hundreds in 2nd, thousands in 3rd... At a school math night I tried to express to a teacher that this was the SAME PROBLEM. It is not harder to add 10,000 + 30,000 than to add 1 + 3, once you understand place value; and if you don't get place value, then 100 + 300 is already too hard. The math teacher looked entirely baffled. I take from this that for many kids, I'm wrong and they actually do need to spend time learning that each new place also works on a tens system.
yes yes yes! This sounds so bizarre to me that I can't even take it on faith, but the curriculum does say they add one extra place per year for several years. IIRC it went to fourth or fifth grade or something insane like that ( I think the highest mentioned was 10,000, which would be fifth grade, but maybe they got ambitious and made them learn two spots in one year). A couple of teachers have claimed this, too.
But, I just don't believe it. Once you understand the differences between 1,10, 100, then if you can't extrapolate to 1000 and into infinity then you don't really understand the difference between 10 and 100. They must not be teaching it well enough.
ETA: I checked up, and second grade goes to hundreds, third grade go all the way to 10,000, fourth to a million. BUT, the second grade standard says they need to be able to do ordinals up to 20, which clearly isn't some watershed the way adding single vs double digits is, so these standards are obviously formulated as the floor for kids who do not understand at all and need to rote memorise it all. And they could just not have the space to add in memorising that fifty-second equals number 52 in line instead of understanding the pattern.
