It's an amazing idea! I'm always looking for screen-free activities related to problem solving with my daughter. By the way, if someone happens to have other examples, it would be great to share!
My four-year-old grandson and I enjoy playing with go stones on a go board. The black and white stones and board’s grid lines inspire a lot of counting and geometric-shape activities. Similar things could be done with other types of objects, of course, but I had the stones and board from when I used to play go forty years ago.
My daughter wants me to teach him how to play go at some point, but he’s not quite ready for that. He hasn’t yet learned the concept of winning or losing at games, and we don’t see any need to force that on him early. In the meantime, playing with and talking about the stones seems to have boosted his understanding of numbers.
I think the "Peanut Butter Sandwich Instructions" game could fit into this category as well. For kids who can't write, you can do the actions in real time. For kids who can, have them write down instructions first then "run" the program. Teach them to "debug" or test their program along the way.
Every year I teach a few weeks of "coding" at my kids elementary school. I always start with the Peanut Butter Sandwich and it's a huge hit. For time's sake, i print & cut out 30-40 random instructions like "openTheBag();" or "holdJellyOverBread();". They get in 4 groups, choose which instructions to use, and put them in order.
I have a short collection of ideas here.[0] The biggest thing I've done is tell bedtime stories (often collaboratively) that incorporate topics like functions, negative numbers, and debugging. Here's one where we did FizzBuzz together. [1]
My daughter wants me to teach him how to play go at some point, but he’s not quite ready for that. He hasn’t yet learned the concept of winning or losing at games, and we don’t see any need to force that on him early. In the meantime, playing with and talking about the stones seems to have boosted his understanding of numbers.