# Introduction to the Decimal System

After the child has been introduced to the numbers one through ten, the child has understood the concept of quantity and the names of the symbols that represent these numbers over repeated work. The child can also grasp the idea of zero and decipher associations of quantities and the symbols. Through work with the number rods, the child receives the first impression of the four operations; addition, subtraction, multiplication, and division.

Once the child has had sufficient work with the numbers one through ten, we can go to the decimal system. It is not necessary to introduce the children to the teens and tens numbers such as nineteen and twenty-three. Children have a deep interest in working with large quantities, thus, why the golden beads were created. By using a sensorial approach to the decimal system, children are able to engage their sensitive period of order paired with exploring their human tendencies of abstraction and mathematical mind. The child also refining her senses of language and movement.

When the child knows zero and one through ten, we introduce hundred and thousand through the decimal beads. The decimal beads give the child a sensorial impression of the obvious differences between the quantities by looking at the beads being bound together or unbound. By binding the beads together, the child can more easily count the beads and see the relationship to the other numbers. One challenge children sometimes face is understanding the difference between one hundred and one thousand. To support the children, we offer exercises that allow built in repetition. Children learn through the change game how to exchange ten of one category for the next category such as ten units change into ten and ten tens change into one hundred and so forth. The golden beads introduce the operations in a sensorial, manipulatable way and are reinforced through games such as the dot game, stamp game and work problems.

There are six points to remember with the decimal system. The first is category vs hierarchy. Within each hierarchy there are repetitions of the categories. The categories are units, tens, hundreds. The firs hierarchy or simply hierarchy is one, ten and hundred. The next hierarchy is thousand, ten thousand, and one hundred thousand. The next hierarchy is a million. The second point to remember is we do not move onto the operations until the child knows the different categories. The third point is that children often confuse one hundred and one thousand with the cards so it is helpful to point out the zeros. The fourth point is that we never use the word and when naming a whole number. The fifth point is to not rush onto the stamp game without sufficient golden bead work. The work with the golden beads is what supports the child with the impression of the operations. The sixth point is that we give the keys to math and understanding math is dependent on building up knowledge from previous knowledge.

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