Dynamic Operations in the Decimal System


Age: 4-7

…to further understand the concept of addition, subtraction, multiplication, and division

…golden bead material
…large and small numeral cards
…symbol cards for the operations
…problem cards for each operation

a. Introduction to the Change Game:
Individual Presentation. A large quantity is placed on the tray and the child is invited to count it. Beginning with units, the child counts, but is stopped at 10. Ten units cannot remain loose; they must be changed for a ten-bar. The ten beads are traded for one ten-bar from the bank. The child continues counting units and placing the correct large numeral cards on the try. So on to thousands. The cards are arranged and read. The child does many exercises.
Aim: to exchange equal quantities of different hierarchies
to reinforce the rule: only 9 units can remain loose
to reinforce knowledge of the composition of each hierarchy (ten tens=100)

b. Presentation of Addition:
The teacher reads a task card. The child performs each command as it is read. The teacher controls.

c. Presentation of Subtraction:
The teacher reads a task card. The child performs each command as it is read. The teacher controls.
The teacher presents the thousand cube (golden bead) and wants to take away 1 unit. This may be symbolized with the large and small numeral cards for emphasis. How can this be done? The thousand is changed to 10 hundreds. Now can we take away one unit? Not yet. So on until one unit can be taken away. The remaining quantity is counted and represented with small cards.
Aim: to realize that one unit revolutionizes a large quantity.

d. Presentation of Multiplication:
As for addition task cards are prepared.

e. Presentation of Division:
Group Presentation. As with static division the child sets about distributing. When he finds that he doesn’t have enough for one hierarchy to go around, he must exchange for a lesser hierarchy.
When there is a remainder, the corresponding small numeral cards are brought and placed after a small card with the initial r to the right of the result (quotient)


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