insulating wooden floor above garage- vapour barrier needed?

[Hazelb]

I'm off to my mum's next week and one job I have is to insulate the bedroom floor ( it is above a cold garage ). I'm going to lift as few floor boards as I can. I was planning on using rock wool slabs or the roll insulation.

Should I leave an air gap on both sides of the insulation (between the insulation and bedroom floor, as well as between the insulation and the garage ceiling.

Do I need to include a vapour barrier? ( is that on the 'warm side' of the insulation)?

 

[ModernMaterials]

i would put the plastic in as well. not only will it stop draughts but it will keepcar fumes out of the bedroom. I dont really think it matters which side you put it although above the joists would be easiest