Okay so is it possible to go to public school for half a week and the be home schooled for the other half/?

Sounds like you're in the UK. You might want to go to a site such as a href="http://www.educationotherwise.org" rel="nofollow"http://www.educationotherwise.org/a to find out about the options in the UK. I rather doubt a school would be willing to take on the sort of schedule you mention, though you never know for sure unless you ask.