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Preschool/Kindergarten Curriculum:
Mathematics:  Number Sense

Preschool   pre-K
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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 corresponding number.

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.


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