Everyone's favorite preschool activity is finding things to count. Following the general idea of finding things for parents to program with their kids, I was showing my kids some cellular automata. The first thing they wanted to do was count the black cells. They were unstoppable. Here is rule 250.
As you can see in the attached notebook, this leads naturally to Map and Total and then after a ListLinePlot they can guess the next elements and together we wrote a function for predicting the answer.
Another way to approach cellular automata, for older kids, is to use Wolfram Alpha, e.g., look at its results for the different rule numbers. http://www.wolframalpha.com/input/?i=rule+250 not to mention reading the New Kind of Science book by Stephen Wolfram.
(More advanced students and adults interested in cellular automata should consider applying to the Wolfram Science Summer School.)
(An earlier post on projects with kids was about writing letters.)
Yes, I was surprised too, but then realized that it was not too surprising. It's not too uncommon for kids to count things. They also like counting the tick marks when Axes->True.
Some things should be simple enough for the youngest kids, as complicated as counting, and CA is probably one of them, though we haven't done the rules for anything more complicated than rule 254. Some of the common primitives of Wolfram Language are like that too. I am intrigued by the question of what conceptual primitives are prerequisites.
Of course, the white-to-black cell ratio is quite an important metric in cellular automata. It's interesting that your children instantly recognized this as a countable value.