It may be a bit hard to determine the day of the week.
You have a list of numbers: 1 2 3 4 5 | 6 7 8 9 10 11 12 | 13 14 15 16 17 ...
So -knowing that the pipe splits Sunday from Monday- you have to go back from that to find out that the 1st of May is actually Wednesday.
We could prepend a couple of empty squares, or simply put the days of the previous month, ie. 29 30 1 2 3 4 5 | 6 7 8 9 10 11 12 | 13 14 15 16 17 ...