Learning mathematical concepts in a Montessori classroom begins concretely and progresses towards the abstract. They are developed from simple to complex. Process is taught first and facts come later. Order, coordination, concentration, and independence are experienced by the child using these materials. The math activities are organized into five groups. 

Group one introduces sets of one through ten which prepares the child for counting and teaches the value of quantity. Children begin to associate numeral and quantity with number rods and number cards. A child will gain a growing understanding of sequence. Spindle boxes, cards and counters, the short bead stair, and other 1- 10 additional counting activities a teacher may add, reinforce the one through ten numeral concept. 

Group two involves the decimal system using the golden bead material. The child will become familiar with the names of the decimal categories; units, tens, hundreds, and thousands. A concrete experience with each category is represented by beads. Quantity will be followed by symbol and association. 

Group three deals with the operations using the golden bead material. The concept and process of addition, subtraction, multiplication, and division are presented. Children work with each other and benefit from these exercises using the bank game. Progression then continues using operations with the stamp game. 

Group four consists of linear counting. Quantity is presented using the teen and ten boards followed by symbol and association. The one-hundred board and bead chains develop number concepts and recognition of numbers one through one-hundred. The bead chains also introduce the child to skip counting; five, ten, fifteen, twenty, etc. 

Group five contains activities such as strip boards, snake game, and memorization of facts. Fractions are also a part of this group. Fraction skittles and insets serve this purpose.