The perceptual skills already acquired through materials in the Sensorial Area are now laying the foundations for counting and arithmetical operations which are to be developed in the MATH CURRICULUM AREA.

THE MONTESSORI MATH MATERIALS  were designed to allow the child to explore a concept in the concrete form. The sequence of presentation begins with simple to more complex and from concrete to abstract. Children will progress through concepts at their own developmental rate. The materials themselves contain the pattern for presentation as well as understanding. The sequence for presentation and learning is :
1. Concrete before Abstract.
2. Quantity.
3. Symbol.
4. Quantity and Symbol Association.
The layout for  presentation of math materials - left to right and top to bottom (reading presentation) except when working with place value which is right to left as in computations/operations.

Color beads

"The idea of quantity was inherent in all the material for the education of the senses...The conception of identity and of differences form part of the actual technique of the education of the senses. It (the teaching of arithmetic) should start with sense perceptions and be based on knowledge of concrete objects." Maria Montessori

Number Rods

See a sample of Montessori Math from my album in PDF format.

In the Montessori areas of Practical Life and Sensorial, the child is introduced to premath concepts such as temporal relations, spatial relations, and one to one correspondence. A child's perception is enhanced by asking him to match, order, contrast, and compare. Premath concepts of one to one correspondence, class inclusion, seriation, and equivalence are fostered in all of the sensorial apparatus. These areas prepare the child to work in the math area.

My lesson plans for Montessori premath

"This system in which a child is constantly moving objects with his hands and actively exercising his senses, also takes into account a child's special aptitude for mathematics. When they leave the materials, the children very easily reach the point where they wish to write out the operation. They thus carry out an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations." Maria Montessori - The Discovery of the Child, ch.19.

Further Development in Arithmetic.