[WorldMaker]

One silly, maybe extreme, direction to move to try to explore building functions together is Alligator Eggs: https://worrydream.com/AlligatorEggs/

[PebblesRox]

Thank you for sharing! I tried it out with my 7yo, who was interested. Unfortunately we had some issues with the toddler interfering so our session got interrupted.

I did find an online version here, for anyone who wants to try it without cutting out a bunch of alligators: https://tibordp.github.io/gator-calculus/

I am also on the search for more puzzles/challenges to do with it.

[PebblesRox]

This blog post [0] has a few more examples, and I like how the author's alligator calculator [1] translates from traditional notation into alligators.

[0]https://propella.blogspot.com/2011/09/yet-another-alligator-...

[1]https://metatoys.org/alligator/#!/(%CE%BBx.x)%20y