I worked this problem out by folding the piece of paper and then writing down the sequence. I then wrote the sequence backwards as, if I turned the paper upside down, it would be the same. I kept doing this until I came up with a sequence that I had already found, and couldn't find another way to do it.
This is what I came up with: BACD, DCAB, CDBA, ABDC, DBAC, CABD, ACDB, BDCA.
So that makes eight different ways to fold the map.
Emily also worked on finding the fold sequences for the larger map and found these twelve sequences:
CBADEF, FEDABC, DEFCBA, ABCFED, EFDACB, BCADFE, DFEBCA, ACBEFD, DCFEDA, ADEFCB, DABCFE, EFCBAD.
BUT ... there are more ways than this to fold the map! Can anyone find them all?