One thing I have really enjoyed doing with K in the last year is learning (remembering) old songs and nursery rhymes.
The Slovak has always sung her a lot of SK folk songs, since he knows more of them than classic children's songs. We did learn a lot of SK children's songs from CDs, though, and K learns even more CZ ones at school.
She would come home singing a fragment of a song and want me to finish it with her, not accepting "I don't know the rest of that song" as an answer. For instance, I knew the first line of "Skákal pes" but not the rest, so I couldn't help her get past that first line. She did not understand that there could be a song I don't know. After a while I had the (belated) good idea of looking it up online, and found it straight away of course. The look on her face when I started singing the whole song - awed. "HOW DID YOU DO THAT??" she wanted to know. Internet access + ability to read = superpower.
I always get kind of a kick out of a Slovak-American kid singing "Já jsem muzikant a přicházím k vám z české země" or "Okolo Hradce" or other very Czech songs. The first one is a call and response song that involves pretending to play on various instruments (drum, piano, violin), though the Slovak and I have improved it by adding verses like "na ukulele", "na zadek" and "na nervy".
For a long time K's going-to-bed song was "V hlbokej doline", every night, all five verses. The Slovak started singing it to her when she was very small and eventually she didn't want anything but that. I always thought it was a funny choice for a lullaby as it is really not for children. I also wondered how many Americans (or, indeed, Slovaks) there are out there who sing "V hlbokej doline" to their child every night. She made me laugh once when I asked what the song is about (to see if she knew) and she answered, "um, a doll" - it does mention "panenka" but in reference to the maiden in this case, not a doll.
The Slovak also taught K a song in eastern dialect called "Dža volky". It is very fun to sing because it gets progressively faster on each repetition. K can go longer than I can, and the Slovak can go longest of all. She once requested that song by calling it "the song with those wolves", which took me a minute to process because the song is actually about oxen (volky) while wolves is vlky (vlci). But she really thought she was singing a song about wolves hitched up to a wagon, I guess. (haha)
Between school and the Slovak's rich repertoire of SK (and the occasional Russian) songs, K knows a whole bunch of CZ and SK songs. Whether she understands all the words is obviously a different story. At some point, though, I realized that we hadn't really moved beyond "Twinkle Twinkle" and "Wind the Bobbin Up" in English. And of course I couldn't allow that to continue...
I started refreshing myself on all the nursery rhymes I could remember and teaching them to K. She has a good memory and enjoys reciting them for whoever will listen.
Just like in Slovak, she doesn't always understand all the words or concepts, but it is a good vocabulary enhancer. She can never remember that Jack and Jill "fetched a pail of water" - usually it is something like "went up the hill to get a package of little water". I tried to explain about wells and pails and indoor plumbing but I think packages of bottled water from the store is still more familiar to her!
She also started asking me to sing her "one of YOUR songs Mommy, a NEW song" several months ago, so I sang her every bedtime-appropriate song I could think of and then some. I often couldn't remember the words so had to look them up during the day so I'd have something new to sing at night. I was debating what kind of songs to claim as "my" songs - songs from musicals? Movies? Radiohead didn't seem very appropriate somehow.
I decided to take the opportunity of introducing some English folk songs, along with the occasional spiritual or other song (Over the Rainbow, Sarah McLachlan's Ice Cream). Pretty much anything I think might have some cultural or historical value or just that she will enjoy. We do several every night at bedtime. K's favorites are I Gave My Love a Cherry, Danny Boy, Greensleeves, The Water Is Wide, Wayfaring Stranger, Early One Morning, Black Black Black, He's Gone Away...
She makes up her own songs as she's playing during the day and I love hearing how they include "parsley, sage, rosemary and time" or other lines or melodic influences from these traditional songs. Pretty much if I notice that all her songs start to be about her lost love and sung in a minor key I'll know my work here is done.