Montessori is great for beautifully made manipulatives.
I finally found a good excuse to order the binomial and trinomial cube puzzles.
This site which explains how to use them recommends them for the youngest children; but I seem to remember working on these cubes (and finding the trinomial very challenging) in both my Lower Elementary (1st-3rd grade) and Upper Elementary (4th-6th grade) classrooms.
Personally, my excuse for ordering them is a group of high school students who are studying polynomials. I think we never outgrow good visuals.
I handed the boxes to my second grader, told her they were puzzles, and let her figure out on her own how to solve them. She found them an absorbing and pleasant challenge.
(The math-genius grown-up of the family walked in, took one look at the trinomial and, without stopping to think, FOIL'd it and built up all three layers at once, diagonally.)
A significant part of the Montessori philosophy is that children are sensitive to beauty, so their learning materials should be beautiful. The school I attended used, I remember, beautifully crafted, polished Montessori materials.
I ordered the (relatively) cheap version of the puzzles from China. I'm satisfied with the quality. They're still lovely and curiously attractive (like Uncle Andrew's magic rings) and satisfying to handle.
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