There are some cool little formulas you can "prove" by putting together a 3d block puzzle. For example, the formula for the sum of the first n squares can be seen by putting together 6 puzzle pieces to form a square prism with sides n, n+1, and 2n+1. Here, each piece is a "staggered square pyramid" of volume 1+ ...+ n^2. (Suggestion: Take n=5) There are other such puzzle-ready formulas like the sum of triangular numbers. I believe "The Book of Numbers" by Conway and Guy has some. You could build nice big soft ones that schoolchildren can play with and grownups can appreciate.
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