Mathematics is developed with the use of concrete learning materials. The sensorial area is the preparation for mathematics. Hands-on materials are used such as number rods, sandpaper numbers, number boards, spindle box, number tiles, beads, and games. Each exercise builds upon another and the child gradually moves to from concrete to abstract areas such as place value, addition, subtraction, multiplication, and fractions. Math is taught in this order: numbers through ten, the decimal system, counting beyond ten, memorizing the arithmetic tables, passage to abstraction (working with more symbols on paper and with less of the concrete math material) and fractions. There is overlap amongst the last groups of lessons.
The Practical Life and Sensorial Montessori material prepare a child’s mind for Mathematics. Practical Life work offers sequence, and practice with processes. It appeals to a child’s intellect because it has a purpose and a child completes it with order and precision. Sensorial work is done with exactness. It engages a child’s mind to classify experience and this classifying (using the five senses to discriminate by dimension, weight, smell, etc.) enables a child to draw conclusions. Further, sensorial work lays the foundation for math by preparing the mind for the study of sequence and progression.