Yeah, this is what I do. Or used to do. I followed an interesting progression with it -- at some point, I stopped having to actually look at or touch my knuckles to do it, then after a number of years, I found that I (mostly) just have the months lengths memorized.
Also in case you did not know, the leap year is not on even hundreds of years, i.e. 1900 was not a leap year, and neither will 2100 be under the current calendar.
The exception is every four hundred years, which means 2000 was a leap year, as would 1600 have been, and 2400 will be.
This means the year is on average 365.2425 days long[1] -- a constant that I've found surprisingly useful to memorise.
The number of days in a month sits in a nice space of complexity for me - it's hard enough to be non-trivial, but simple enough you feel you should know it.
Probably the easiest thing to remember is that short and long months generally alternate (the exceptions are December/January, and July/August).
I like the 'use the knuckles of your hands' technique - put your hands next to each other, and count the months using your knuckles and the spaces - so January (knuckle - high so long-month), February (space - low so short-month), March (knuckle - high so long-month). When you reach July, you get your left-and-right knuckles next to each other, so two long months in a row. [EDIT: I can now see that I'm about the fifth person to mention this!]
Back in primary school the knuckle method that we were taught seemed too complex and slow, so I made up a word instead from the 30-day months: "apjuseno".
In Portugal (idk about other countries) we use something like:
- Use knuckles and spaces between them
- Start with left-most pinky knuckle (in
- Count across hand: knuckle (31), space (30), knuckle (31), etc.
- Jump to right hand's index finger knuckle after left index (so it's two times knuckle, when passing from left to right hand (for July and August) and continue.
[0] https://en.wikipedia.org/wiki/Knuckle_mnemonic