I've blogged before about "choose games". Today's "choose game" is an even simpler version, but is fun none-the-less. Simply print off pictures of a shamrock (or any other St. Patrick's Day themed image: pot of gold, leprechaun, rainbow, Ireland, etc). Place a stick on some of the shamrocks and turn them all over. Have the child do some work (with whatever goal you are targeting) and then let him/her choose a shamrock. You choose a shamrock on your turn too. Whoever has the most shamrocks with stickers on them, wins! Isn't that easy? I didn't have any stickers (I was at work when I made the game) and so I drew a star on each one.
If your child needs a little more movement than simply putting the shamrocks on the table, then you could also tape the shamrocks (sticker side down) on the wall. Have your child throw a bean bag at the wall. Whichever shamrock he/she hits (or is close to hitting), let him/her pick that shamrock. That can make the same game seem very different to a child.
If you have access to ellison cuts (dye-cuts) at a school, then cutting out shamrocks using the dye-cut would be a lot faster! I laminated mine to help with durability.