Some days I do a terrible job improvising with my child.
Let me back up. I teach improv at the UCB Theatre in NYC. One of the central rules of improvisation is “Yes And.” It’s a simple rule. Basically, if someone says something to you, you say “yes” to their idea and you “and” it by adding more information. In this way, you create a scene from nothing.
Here’s a quick review in case your last improv class was awhile ago (or never):
A: “The bakery sure is slow today”
B: “Nobody comes here anymore [yes]. I think the smells from the fish store next door are driving them away; nobody wants a croissant that smells like a flounder! [and]”
Now, without getting too deep here I want to note that it’s also okay to disagree with people’s opinions. You don’t have to literally say “yes.” What you are “yessing” is the idea of the bakery:
A: “The bakery sure is slow today”
B: “Are you crazy? [yes, though opinions differ] We’ve had 20 customers and it’s only noon! [and]”
When you’re creating something out of nothing, the important part is to get on the same page. This here’s a bakery scene. You “yes” the idea and add more information (fish store next door, 20 customers). You approach the scene with a sense of play, an open-ness to do the scene your partner is starting.
This is sooooo applicable to parenting. When I’m not in the mood, when I’m feeling very much the dad-in-charge, I forget to play with my kid in the way that works the best: I forget to yes-and her idea and play by her rules.

Right now I’m typing this in my office which has a sign on the door: “Kids offise!!!!!” because the other day she and her friends took it over and kicked me out. That same day, the bathroom had a sign “Kids potty” and basically the whole place was taken over by kids. The lunatics love running the asylum, and in the spirit of improv, letting them do so is sometimes the best thing you can do.
As an example, the other day she was clearly bored and I proposed a bunch of stuff: let’s play a card game, make some art, do a project, go try out the bike…all of which were TERRIBLE ideas apparently. She proposed making her Winnie the Pooh and her Dragon, Lily, into acrobats. I had about 60 really good ideas and she had one that made no sense. Normally, in a very non-improv way, I try to steer her towards a game that actually exists. But I decided to yes-and her choice and we played acrobats.

Ya know: you throw Winnie the Pooh or Lily to each other over the Frog and if they hit the frog at all - scratch that - if they hit the Frog on the belly, then you lose. Oh, and it’s best out of three. Or five. Or basically until Dad loses.
This game still made no sense, but she was dying laughing, having a blast. We were violating a no-throw zone in the living room, playing something she cooked up. And predictably, it all spiraled out of control until I had to shut it down. But it was probably the highlight of her day.
One of my improv teachers, Matt Besser, once gave us the note “If you’re not looking like a jackass, you’re not doing it right.” And the hardest parenting days are the ones where you’re too-cool-for-school, not giving into the idea at hand, not working under the kid rules. So don’t forget to look like a jackass, be a good yes-ander and improvise with your kid!