Reservations

I am planning a trip to Japan. I will be flying in to Sapporo and training down to Hakodate. Then from Hakodate to Tokyo, kyoto and other cities. My question is I will be traveling with my family (6 total) I will be in Japan over golden week (yea I know not great timing on my part. I did not know that Japan had a week vacation). Anyway If I get the Green JR pass can I make reservation on the trains that the JR pass work on in advance? Say a month before I arrive? I have all my hotel accommodations set up its a busy time to travel and I am worried that all of us (6) will not be able to get on the trains we need to get on.

Thanks