Given the societal impact, I think a simple recommender system would be really important. Recommender systems literally shape the world we see.

Poll anything they might have a preference on (and not all the same) - movies, music, internet celebrities or what not - and build a system that asks someone's opinion on 5 things and then outputs suggestions.

I don't think you need anything fancy, but just counting "same entries" in the preference matrix would work to get basic collaborative filtering. Depending on the depth allowed, you can cast that more mathematically and maybe even discuss the idea of rank 1 factorizations (i.e. assign each person / thing a vector and attempt to approximate the matrix entries as scalar products) or optimization of that stuff.

As outlook, you have word2vec that works similar but has the added complication of the matrix being huge. Use that for a information retrieval or toy chat bot or whatever.

I did teach this to non-experts, but not high school kids. I imagine it would work similarly. Unfortunately, I don't know of a website that covers this for school kids.