Academies are for educational purposes. Ihave three after school projects, and three academies. My after-school projectsare table tennis, badminton, and basketball while my academies are piano,swimming, and English. Some  of myfriends have four of five academies. Whit so many academies my friends lookstired. 

Student's sentence            Corrected sentence            Grammar explanation          Better sentence     

Student's Sentence: Academies are for educational purposes. 
Corrected Sentence: Academies are for educational purposes.
Grammar Explanation: The sentence is grammatically correct. It clearly states the purpose of academies. 
Academies are designed to help students improve their knowledge and skills.

Student's Sentence: I have three after school projects, and three academies.
Corrected Sentence: I have three after-school activities and three academies.
Grammar Explanation: "After-school" should be hyphenated because it is a compound adjective. "Activities" is a more appropriate word than "projects" for sports and clubs. The comma before "and" is unnecessary.

Better Sentence: I participate in three after-school activities and attend three academies.

Student's Sentence:  My after-school projects are table tennis, badminton, and basketball while my academies are piano, swimming, and English.
Corrected Sentence: My after-school activities are table tennis, badminton, and basketball, while my academies are piano, swimming, and English.
Grammar Explanation: Use "activities" instead of "projects." Add a comma before "while" because it joins two independent clauses.
Better Sentence: My after-school activities include table tennis, badminton, and basketball, while I attend piano, swimming, and English academies.

Student's Sentence: Some of my friends have four of five academies.|
Corrected Sentence: Some of my friends have four or five academies.
Grammar Explanation: Use "or" instead of "of" when expressing a choice or an approximate number.
Better Sentence: Some of my friends attend four or even five academies.

Student's Sentence: Whit so many academies my friends looks tired.
Corrected Sentence: With so many academies, my friends look tired.
Grammar Explanation: "Whit" is a spelling mistake and should be "With." Add a comma after the introductory phrase "With so many academies." Since "friends" is plural, use the plural verb "look."
Better Sentence: With so many academies to attend, my friends often look tired and exhausted.

Better Paragraph

Academies help students learn new skills and improve their knowledge. I participate in three after-school activities: table tennis, badminton, and basketball. I also attend three academies where I study piano, swimming, and English. Some of my friends attend four or even five academies. With such busy schedules, they often look tired and exhausted.