I alluded in a couple of earlier posts, here and here, to the fact that our high school mathematics curriculum is in a rut focusing mostly on basic algebra and that many algebra skills will only be useful in calculus and the physical sciences. I also mentioned that there are plenty of cool topics in mathematics that are not algebra based.
Recently I ran across the project below that explores the concept of minimal spanning trees. I constructed it as part of an assignment for a weekend class at Chico State University that I took many years ago. At minimum it can be treated as just an exercise in addition. I like it because it exposes students to a non-computational algorithm and easy but clever proof.