I've spoken about the "puzzles" that Terry Tao and I developed for Schubert calculus, like the left two here:
I handed out pieces (the 0-triangles, 1-triangles, and rhombi) for the 3rd graders to assemble, in groups, telling them to make triangles. Then made a table with n = #edges on a side (any side, since they're equilateral), k = #1s on a side (theorem: any side), n-k, #1-triangles, #0-triangles, #rhombi.
Different groups made different puzzles, and I included some little ones (n=0 and 1) in the table. Then asked if anyone saw patterns. I got the answers I wanted, which were that #1-triangles = $k^2$, #0-triangles = $(n-k)^2$, #rhombi = $k(n-k)$.
It works nicely with younger children, too, but they're less likely to guess these formulae.