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The goal is for
students to understand the relationship between number symbols and
quantities. The children will be able to count, recognize, represent,
name and order numbers of objects from one to ten. The Number Rods,
(ten wooden rods in graded lengths, each rod divided into sections
representing the number of the rod) are used to help children learn
the names of numbers, to help them see that each number is a separate
entity in itself, to help them learn the sequence of one to ten and to
make the association between spoken number and quantity. After an
understanding of quantity is attained, number symbols are taught.
The final step in work with numbers from one to ten is associating the
symbol and the quantity. The Montessori materials such as the Spindle
Boxes, the Shell Game and the Colored Bead Stairs support this process.
Extensive work with the numbers from one to ten provides a foundation
for all further mathematical endeavors. Children who are ready may be
introduced to the teens. The difficulty with learning the teens is in
the language: irregular names like eleven and twelve, thirteen and
fifteen, as well as inverted sequences (twenty-seven sounds like 27,
eighteen doesn't sound like 18) can be confusing. As with earlier
work, a progression is made from quantity to symbol. Children learn
that teen numbers are based on ten and a certain number of units.
Unit beads and ten bars are used to introduce teen quantity and other
materials such as Cuisenaire rods are helpful tools in promoting the
leap from units to teens.
Students gain an understanding and practice simple addition and
subtraction by using concrete objects (beads, Unifix cubes,
manipulatives, etc.) to determine the answers to problems. Children
will be introduced to mathematical language symbols (+, -, =) and will
gain experience with written addition problems. The Addition Strip
Board and Addition Finger Charts as well as a variety of dice, card and
domino games provide additional practice with addition and the learning
of addition facts (1+_ =10, 2+_ =10).
Children prepare for mental math by learning to visually grasp number
patterns without having to count individual dots or objects. Thus,
they can recognize that a ten-bar always represents 10, and that a
certain arrangement of dots on a domino always stands for a
The children are introduced to the decimal system, learning the
relationship of units, tens, hundreds and thousands. The Montessori
Golden Beads offer a concrete representation of the decimal system.
For many children, the Hundred Board represents a milestone in their
work with numbers. In addition to demonstrating facility with number
sequence, it is another vehicle that allows children to glean a sense
of the patterns of the decimal system. The material can be used to
learn to count by ones, twos, tens, etc.
Children may also compare sets of objects and recognize which set
contains more than, less than, or is equal to another set.