Just got back to this thread. Sorry if my first post was unclear.
To clarify: you are teaching 0.5
A teacher who wants to work part time like this, quite understandably wants to have this as a block of time - ideally in school continuously for 2 and a half days, and then off for 2 and a half days.
Problem is, school timetables don't work like this. If you are teaching, eg English, the school cannot squeeze all the English lessons for your classes into the days that you want to come to work! Pupils need to have a good balance in their timetable. So the alternative is to split your classes - ie: you teach them some of the time, and other people the rest of the time.
Problem with that, is that it isn't alwayss best for the pupils, and it definitely creates more work for colleagues. Even where it works well (and I accept that in some cases it can be good for pupils to have fresh input) you can't deny that it creates extra work for colleagues, as to plan effectively, assess effectively, write reports, ensure continuity etc, it actually means quite a lot of liaison. And for some classes, it is definitely not best anyway. I teach, and currently share a couple of classes to accommodate part time staff, and I actually feel it's very unfair on the children. They are Year 7, so getting used to dealing with large numbers of teachers rather than one class teacher anyway, and to throw two teachers into the mix for one subject just creates extra pressure on them.
S0... to be honest, if you have 0.5 across 3 days, I actually don't think you're doing badly at all! I think it's very dodgy that the school are telling you that you can't leave the school site during times that you're not actually paid. But other than that, I think you'll have to just put up with it or find another job.
Someone suggested that the school ought to *'find you something else to do' to bring your hours up to 0.6, but I totally disagree. It isn't an employers job to 'find' things for the employee to do to fit exactly the hours they would like to work! The world of work doesn't operate like that!