In Montessori classrooms, children work with a particular set of manipulatives to make sense of the algorithms we use for addition, subtraction, multiplication and addition. In the process, they develop deep understandings that support their learning of other areas of mathematics like algebra and number theory.
The Montessori math materials, lessons, and activities aid in the development of a complex web of declarative and procedural knowledge. Currently, I'm trying to develop teacher resources on long division and finding the cube root of large numbers with the trinomial cube. As time permits, I will add pages on other nodes in the Montessori math web.
NOTE: The use of manipulatives for teaching math is not unique to Montessori classrooms. To get a sense of the differences in manipulative design and use in Montessori and other environments, see Learning Math with Manipulatives.