FOR her mother. To provide FOR someone. As to "in eleventh grade" versus "in the eleventh grade" - it has become more common to leave the article 'the' out. The use of the article 'the' peaked in the 1940s and has now declined to the point where, it seems, the article is commonly dropped. Have a look at the Ngram viewer graph of phrase frequency.

Well done. Just two small corrections…. You need the article before 11th grade…she is just in the 11th grade! And it’s provide FOR her mother.

Correction: Is it grammatically correct and natural? She is a very ambitious person. She is just in eleventh grade but she wants to become a successful entrepreneur and provide for her mother in the future .