**Stage 1 – Montessori Math Materials**

Montessori took the idea that the human has a mathematical mind from the French philosopher Pascal. Maria Montessori said that a mathematical mind was “a sort of mind which is built up with exactity.” The mathematical mind tends to estimate, needs to quantify, to see identity, similarity, difference, and patterns, to make order and sequence and to control error.**Mathematics: The Preschool Years**

Although preschool students have had several years working with numbers and mathematical concepts, children do not immediately begin working with the math materials in the Montessori preschool environment. Instead, the child is indirectly prepared for later mathematical works through the Montessori Practical Life and Sensorial activities where she develops the fundamental abilities necessary for higher level mathematical concepts: discrimination, recognizing similarities and differences, constructing and comparing a pattern or series, finding relationships, and understanding terminology.

These materials develop visual and muscular perception leading to an understanding of three dimensional size.

- The Pink Tower also prepares the child for maths; the largest cube would hold 1 litre and the smallest 1 millilitre.
- The Long Rods vary in length with height and width constant (2sq cm), the longest rod is one metre.
- The Binomial Cube provides preparation for algebra and the proof of (a+b)3. The faces are coloured: a square is red, b square is blue and ab is black.
- Large Number Rods introduce the child to fixed quantity and awareness of the sequence of numbers 1 to 10.

- Seguin Board teaches quantities 1-19 and symbols 11-19 and combinations of quantity and symbol.
- The Golden Bead Material teaches the names of quantities and gives the child an understanding of the decimal system.

- Addition Strip Board furthers the child’s experience in addition and reinforces number bonds.

Some of the Sensorial Material is mathematical material. It is presented with exactness and will be used by the child with exactness. The activities call for precision so that the child can come into contact with the isolated concepts and through repetition, draw from the study of each and have a clear abstraction. Sensorial work is a preparation for the study of sequence and progression. It helps the child build up spatial representations of quantities and to form images of their magnitudes such as the Pink Tower.

Many of the Montessori Sensorial materials are based on the concept of 10, which helps children visualize and comprehend our decimal system.

By understanding the decimal system and place value, the child is introduced to geometry: a point (Golden Bead) is a unit, a line (Golden Bead 10-bar) is 10, a plane or square (Golden Bead 100-square), and a cube (Golden Bead 1000-cube) is 1000. With this understanding, Montessori preschool/kindergarten students are able to add and multiply to form larger numbers and subtract and divide to make smaller quantities. Because they first experienced these concepts through their senses, Montessori students are able to understand the true nature of the operations.