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* Correction:     Student's sentence        Corrected sentence        Grammar explanation       Better sentence    

My favorite day is Saturday and Sunday because I get to enjoy my free time even more. Sometimes doing nothing is a good thing to do. On Saturday I should spend more time with family but I go to time with friends more. I hope to do more sports so my healthy is good.

My favorite day is Saturday and Sunday because I get to enjoy my free time even more.

My favorite days are Saturday and Sunday because I get to enjoy my free time even more. 

Use the plural form "days", followed by the -be verb is. Take note of the basic rule: a singular subject takes a singular verb, whereas a plural subject takes a plural verb. 

Sometimes doing nothing is a good thing to do. 

Sometimes, doing nothing is a good thing to do.

 Place a comma (,) after sometimes if you're going to place it at the beginning of your sentence. 

Sometimes, doing nothing is a good thing. 

Sometimes, doing nothing is good.

Not doing anything is sometimes a good thing. 

On Saturday I should spend more time with family but I go to time with friends more. 

On Saturdays, I should spend more time with my family, but I go out with friends instead. 

The plural form of Saturday" is Saturdays, which means every Saturday.  

 Go out or hang out is the correct expression when you are spending time with friends. 

Instead means "by choice", as you choose to hang out with your friends than with your family on Saturdays.
On Saturdays, I should spend more time with my family, but I choose to hang out with my friends instead.

I hope to do more sports so my health is good.

I hope to do more sports so my health gets better. 

Gets better is the proper expression, which means to improve.