In the US primary K-12 is required, and provided free to all children. An alternative is home schooling, which is gaining in popularity.

Beginning 7th grade students go to different classrooms with different teachers for their english, science, and other classes. 7th graders are 13years old, so it is a different scene than elementary school. Starting in 9th grade, and through high school, students have options to pick their classes, to choose electives they are interested in, such as music, theater, and languages. In my high school you could get 4 years of French, or 3 years of Spanish or German. Some subjects such as math and english offered different levels. Basically there was a 'standard' and a 'college-bound' version of each. It wasn't exactly dividing across class lines, working class and middle class, but it was close. (I had no clue about this at the time) Later on the advanced classes became called AP (advanced placement) since their goal was to help college-bound students get better test scores. I took AP English and AP Physics and AP Math, which regrettably stopped just short of calculus. This hurt me- at college other kids had had Integral and Differential Calculus, and I had to scramble to catch up. That's about how it works fo public K-12 primary school in the US. Back in my day there was more fiudnign for art and music and theater programs, I doubt those are as fortunate today. There is also a huge debate about US public schools- (and let's not argue it, but here's the point:) poinhting out that since the institution of national compulsory achievement exams, schools in order to get funding have focussed entirely of making students who can take that exam well- not necessarily to give them skills or teach them to think. Many people feel US public schools have become much worse than they used to be. I can solve that entire problem: simply pay all teachers as well as lawyers. Then you would have the best and the brightest lining up to pass along the benefit of their wisdom. Poor underpaid teachers as usual are working the best they can with what they have.

As for American schools, public primary school is K12 (Kindergarten plus grade 1 through 12) Many children receive some private schooling before this, either as part of a formal 'nursery school' or as part of daycare activities or church groups. Many children learn at home, too. I learned to read and do math from my parents several years before I starter public school. 5-year-olds attend Kindergarten, which is a half-day (4 hours) in the mornign or afternoon. Numbers and alphabet and some basic social skills are the curriculum. 6-year olds 1st grade, in which you get your own desk and start to learn to read and do arithmatic. There's a lot more taught besides just those basics, but that will give you an idea of levels. And it goes on up through 6th grade. K-6 grades are usually taught at a 'elementary school'. Each grade will be made up of a couple dozen kids in a classroom with one teacher, and they all stay in that room with that teacher and those other kids for their schoolwork. 7th 8th and 9th grade are taught together in their own 'junior high school'. In some places 7th and 8th only are called a 'middle school'.

there is no western education, there is national educations. so, focus on one country and ask them about their system.