My favorite materials in the Montessori sensorial area are the algebraic cubes. Because this is a post for B, I guess I need to focus on the Binomial Cube.
Forgive me. I forgot to take pictures of my planned posts before spring break. I can't get a picture until we return next week, and can't seem to find one quickly in my collection. So, I am going to refer you to links with pictures that will pop open in other tabs, to help explain a few things.
The equation for the Binomial Cube is (a+b) cubed. (I again apologize, because I don't know how to make the little 3 for the cubed sign.) Montessori for Everyone has some cards that can be used with elementary students who are learning the equation. They also explain how the colors correspond to the equation. See the picture here.
At my age level, though, we do not expect the children to memorize these equations, nor even know what they are. The cubes are a concrete representation of the algebraic equation. Children learn how to put the cubes back together like a puzzle, using the colors, sizes, and shapes of the various blocks. By doing so, they are mapping out later algebraic studies in their brains. When they have done it enough times, they should be able to put it together even when wearing a blindfold. I like to impress the kids by putting together the trinomial cube with a blindfold, to inspire them to try to do the same.
Take a look at kids doing the cubes in this post by Montessori MOMents.
Does this really work? I tell parents time and time again that I truly believe that my experiences with the Montessori materials helped to shape my love for and ability to do advanced math in high school and beyond. I was able to better visualize the equations, and firmly believe it is due to having used these materials as a child. Others back me up on this.
Visit a Montessori classroom some time and see if you can put these together, yourself.