The teacher explains to the children that to count large quantities of Units is awkward and time consuming. Therefore, whenever they have 10 Units they exchange them for a Ten Bar. When they have 10 Ten Bars they replace them with a Hundred Square, and whenever they have 10 Hundred Squaes they exchange them for a Thousand Cube.
The picture also shows the corresponding numerals cards printed in different colors to indicate the columns of the decimal system. The Units are printed in green again (because Thousands are actually Units of Thousands, followed by Tens of Thousands, etc.)
The children are introduced to the decimal system with three basic exercises. First they build quantities with the bead materials. The teacher starts with simple numbers. She says, e.g., "Bring me 3 Units." Soon she can combine numbers in different columns: "Bring me 5 Tens and 7 Units."Eventually the children enjoy accumulating large quantities on a tray, such as 8 Thousands, 4 Hundreds, 3 Tens, and 7 Units.
In the second exercise, the children find cads to represent the numbers the teacher gives them orally, such as 8 Tens and 3 Units. Finally they learn to combine the numerals on the cards with the corresponding quantity of bead materials. With the Seguuin Boards the children learn to translate the numbers, such as 7 Tens and 1 Units, into 71.
The Numeral cards may be combined in an interesting way. When the figure 1 is placed on top of 10, it will be read 11. When the 11 is placed on top of the 100, it will be read 111, and 111 placed on top of 1000 reads 1111, the total quantity illustrated by the material in the preceding photograph.
THE THOUSAND CHAIN
The Thousand Chain shows how the Thousand Cube would look if all its beads were laid in a single row. The chain, which is actually made up of 100 Ten Bars, is used as an exercise in counting by ten up to 1000. The numbers 10, 20, 30, etc. up to 990 and 1000, are written on small cards that the child in the photograph is placing in order beside the chain. Because the chain is 27 feet long, the child is impressed with the great size of 1000.
THE BANK GAME
Any exercise involving the exchange of the Golden Beads (or duplications of them) is usually called the Bank Game. The large quantity of material, that the children use as a source for the game, is referred to as The Bank. The children use The Bank whenever they want to change Units to Tens, Tens to Hundreds, Hundreds to Thousands, or vice versa. Adding, subtracting, multiplying and dividing four place numbers can all be done with the quantities in the Bank.
If two children wish to add, each one puts a quantity of bead material on a small tray and selects the corresponding cards to represent the quantity. They then combine the two quantities on a larger tray and select larger cards to represent their total.
For subtraction, the teacher places a large quantity of bead material with the corresponding large cards on a large tray. She then gives the child a smaller tray with a number printed on a smaller card. The child "takes away"this quantity of bead materials from the larger tray is the answer. The child then finds the numeral cards to represent this remainder. With this process the children learn that subtraction is the breaking up of one large quantity into two smaller ones.
When learning division, the child is taught that division means sharing and that the answer (quotient) is always what one person receives. If he has the problem 1294 divided by 3, he, serving as the Banker, asks three other children to get empty trays while he gets materials to represent the quantity 1294. He wants to share this amount equally among the three children, beginning with the One Thousand Cube.
Since he obviously cannot divide the single cube, he changes it at The Bank for 10 Hundred Squares. He now has 12 Hundred Squares-these 10 plus the original 2 in the number 1294-and he begins to share them among the 3 children. Each child receives 4 Hundred Squares. Next he divides the 9 Ten Bars; each child receives 3. Then he divides the 4 units; each child receives 1. One unit remains which he cannot divide. The answer is what one person receives, 431, with a reminder of 1.
THE FRACTION MATERIAL
Sometimes a child asks if the one remaining Unit can be divided. This is an ideal time to show him the Fraction Material that illustrates how the Unit can be broken down. There are 10 large red discs. The first is whole. The second disc is divided into two halves, the third disc into three thirds, and so forth, up to the last disc which is divided into ten tenths. Each fractional piece has a little knob so it can be manipulated easily.
This material can show a child concretely that 1/4 is smaller than 1/2; or that 5/5 is the same as 10/10. If he takes the disc that is divided into two halves and removes one half, he can fit two 1/4 sections exactly into this space. He can now see that 2/4 = 1/2. Many more fraction facts can also be demonstrated. Whenever he is interested, the child learns how to write the fractions and how to do simple combinations.
This material can show a child concretely that 1/4 is smaller than 1/2; or that 5/5 is the same as 10/10. If he takes the disc that is divided into two halves and removes one half, he can fit two 1/4 sections exactly into this space. He can now see that 2/4 = 1/2. Many more fraction facts can also be demonstrated. Whenever he is interested, the child learns how to write the fractions and how to do simple combinations.
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