One of the fundamental Montessori math works is the Forty-five Layout. This is the student’s introduction to place value and the foundation of the decimal system.
The Forty-five Layout is a “big” work. Literally, it takes up a lot of space; it requires a lot of time; and in a class of mixed-ages, it is typically a big kid work.
The manipulative materials are proportionally designed, which allows the student to see and feel the mathematical value. This concrete, hands-on approach builds a strong foundation for abstract application.