As we grow and learn and explore and reinforce, so do Montessori's amazing materials. Abstraction becomes a natural progression as the student moves through the Montessori Elementary curriculum. While materials are still available for taking fractions into decimals and percentages and for working measurement through new levels, the materials become more detailed and complex allowing for easier abstraction as the foundational functional activities are, by now, well retained.
The decimal checker board while colourful and large and appealing to use, nows draws on earlier lessons - the coloured beads from CASA, the bank and stamp game. The colours are lighter as numbers become percentages of numbers and as such really, really small numbers. Squaring and square roots with the algebraic pegboard helps the student realize that squares of numbers are actually "squares". Enjoyable, engaging manipulation of materials still draws and holds the interest of these pre-teens. Replicating these numbers on graph paper with their representative numbers make for worthwhile documentation.
Math made - not only easy but - interesting, engaging and logical. As reiterated over and over, Maria Montessori has the mind of a genius and a love of educating the young mind that has yet to be duplicated. Copied yes - watered down yes - but Montessori's materials - the math in particular - are a scientific journey that is as exciting to take as it is to share.