They usually don't learn much in primary schools. I understand you about the Chinese, as I was also bad at languages, especially at writing. When I got a writing assignment, I was always confused, but thanks to https://www.trustmypaper.com/ I didn't have to bother about the assignments, this service could always do it for me. It would also be useful for those who need a trustworthy service.
Basically they learn deeper, and more elaborate Mandarin. If you are not good in Chinese language, like myself it's not so easy to teach them. They will be learning more vocabs, more difficult words, letter writing, composition, situational writing etc. But don't worry, there's classes out there for higher Chinese tuition. And you r so blessed that you child can do so well in academics. :)
It depends on school, every school has its own program.
Zijia Pan