I recently found a couple of c. 1900 Milton Bradley Kindergarten Blocks sets designed by Friedrich Froebel, which the box and the blocks on this set remind me very much of. I have not been able to find another set like this one out there, which I assume were made to teach the concept of fractions, with five slots in the box corresponding to five sets of blocks, dividing a sphere into 2 then 3, 4, 5 and 6 sections. I can't say for sure that these were made by Milton Bradley, as there is no label on the box, but I might guess that they were and that they date to about the same time.
The wood on the box here has seen better days, with plenty of wear to the finish, though it remains in good structural shape, with all of the dividers in place and the slide top lid working fine. The blocks show some spotting/darkeing but are in overall good shape, a few with hand-written numbers in pencil on them. Box measures 16"l x 3 5/8" w x 3 3/8" t. Spheres formed by blocks are 2 1/2" in diameter.