It does vary state to state. Does your school have a curriculum night? We do at least once a year and they go over things.
My 1st grader is now doing double digit addition and subtraction. I'm not sure if they are routinely "carrying the tens digit" but mine knows how to do it. She explained it to me recently (Very proud of herself). I think one of the older girls in her aftercare showed her and the teacher reinfored it.
She also does a lot of word problems, money problems and lots of estimating.
How many ____ across is this item? (Feet, hands, fingers, pennies etc). Or if a large bag costs X and a small bag costs Y, how much does a medium bag cost?
As for reading - Pierre (who doesn't care) and Amelia Bedelia were in her recent reading logs.
They do a lot of science investigation - there was something about "counterweights" and clothespins in her recent work, but I wasn't totally clear on what they were doing. It was practical and hands on and she had to record her results (which are entirely written in 1st grade spelling with very little correction, hence my puzzlement).
Her social studies curriculum seems to consist of a lot of "High 5" expectations (courteous, etc), that feels endless.
There has been a lot of study of black history month in Feb. Ruby Bridges is a favorite. Read the story, answer questions, compare Ruby's school to yours. Describe how Ruby felt. And a little story called "White socks only" about a girl who took off her black shoes to use a water fountain and when she was called on it, all of the onlookers rallied around her and removed their shoes and drank from the fountain. And of course, MLK. There will be a school-wide presentation later this month that some grades will take part in.
She has a spelling test once a week, which concerns me. It seems so young. They take a 6-word pre-test on Monday and if they get 5 or more correct they will be given 10 new words to study for the Friday test, otherwise it's those 6. My kid is not really picking up on spelling, and she feels bad that she gets so many wrong. But she's 6! DH and I are both good spellers, but I can't say we were in 1st grade.
She also has these problems where the sentence is scrambled and you have to put the words in order to make a sentence. I find these a little tricky, but I guess I'm programmed to read gramatically correct sentences. She can almost do them faster than me!