Infant/Toddler
Math is learned indirectly at this level through one to one correspondence activities, such as counting out place settings for snack. Some children may work with additional activities that build a greater understanding of quantity and symbol (1-10).

Children's House
The Montessori math curriculum is presented to children first through concrete materials that allow for hands-on exploration of a concept. The goals of the math curriculum are quite extensive, beginning with an understanding of quantity and symbol, progressing to place value and experiences with the four operations of mathematics (addition, subtraction, multiplication, and division). When children at this level demonstrate a concrete understanding of these math concepts, they may be ready to move on to the more advanced exercises in memorization, abstraction, and fraction work.

NUMBERS 1-10

One to one correspondence, quantity, symbol and sequence of numbers one through ten are taught through the use of materials such as rods, spindles, and cards/counters (numeration with objects).

DECIMAL SYSTEM

Categories of unit, ten, hundred, and thousand are introduced with bead materials. The processes of addition, subtraction, multiplication, and division are experienced with the manipulation of the materials, giving the impression of the four operations in math.

TEENS AND TENS

The teens are introduced through the manipulation of gold beads, colored beads, and cards to represent quantities and symbols of numbers 11 through 19. Numbers in the tens are explored with the emphasis on the change from nine to the next ten (e.g., 39-40) by building the numbers with beads and cards. Bead chains provide concrete practice in counting and recognizing numbers and patterns. Exercises using the chains include the introduction to multiples of numbers and the concept of squaring and cubing.

MEMORIZATION WORK

The exploration of math facts occurs through a series of beads and boards work, offering repetition.

Further understanding of math facts occurs as children memorize math facts in addition, subtraction, multiplication, and division.

PASSAGE TO ABSTRACTION

Some children move to abstraction in math through

the use of an abacus-like bead frame, enabling the child to perform math operations with very large numbers.

FRACTIONS

Students may begin manipulation and exploration of fraction inset materials through introduction to the language and writing of fractions and their relationships to each other.

GEOMETRY

Sensorial exploration of plane and solid figures at the Primary level (Ages 3 to 6):  the children learn to recognize the names and basic shapes of plane and solid geometry through manipulation of special wooden geometric insets.  They then learn to order them by size or degree.

Stage I:  Basic geometric shapes.  (Age 3-4)

Stage II:  More advanced plane geometric shapes-triangles, polygons, various rectangles and irregular forms.  (Age 3-5)

Stage III:   Introduction to solid geometric forms and their relationship to plane geometric shapes. (Age 2-5)

Study of the basic properties and definitions of the geometric shapes.  This is essentially as much a reading exercise as mathematics since the definitions are part of the early language materials.

More advanced study of the nomenclature, characteristics, measurement and drawing of the geometric shapes and concepts such as points, line, angle, surface, solid, properties of triangles, circles, etc.
Congruence, similarity, equality, and equivalence.

The history of applications of geometry.

The theorem of Pythagoras.

The calculation of area and volume.