We do physical rote learning in my Y2 class(IYSWIM):
once (touch head)
two (touch shoulders)
is (touch knees)
two (touch toes)
2 (H) 2s (sh) is (kn) 4 (toes)
etc
It's a good way of teaching multiples as the multiples land on your toes (and getting some exercise!).
We recite as an orchestra. I'm the conductor and wave arms in time to the recitation. I go quicker and slower and the chn have to keep up. (All this after 'tapping the music stand and mouthing 'are you ready?' - making a bit of a show of it!)
After finishing a series of quick adding tests to 100 they start their x tables tests (from 2) which continue up the school and include division).
We also play 'shoot the sheriff' where we arrange a duel between 2 cowboys and the quickest to recit a table shoots the other. One boy last year beat me at the twos!
I tell them to learn them with background noise so they know them without thinking. We also recite them in some way every day.
We are doing 2s, 5s, 10s, but will soon move on to 3s.