Dynamic Operations in the Decimal System

Age
4-7

Materials

 * Golden bead material
 * Large and small numeral cards
 * Symbol cards for the operations
 * Problem cards for each operation

Preparation
This is an individual presentation.

Presentation
The Change Game:


 * 1) A large quantity is placed on the tray and the child is invited to count it.
 * 2) Beginning with units, the child counts, but is stopped at 10.
 * 3) Ten units cannot remain loose; they must be exchanged for a ten-bar.
 * 4) The ten beads are exchanged for one ten-bar from the bank.
 * 5) The child continues counting units and placing the correct large numeral cards on the tray.
 * 6) So on to thousands. The cards are arranged and read.

Addition:


 * 1) The directress reads a problem card. The child performs each command as it is read.

Subtraction:


 * 1) The directress reads a problem card. The child performs each command as it is read.
 * 2) The directress presents the thousand cube and wants to take away 1 unit.
 * 3) This may be symbolized with the large and small numeral cards for emphasis.
 * 4) How can this be done? The thousand is changed to 10 hundreds.
 * 5) Now can we take away one unit? Not quite yet. Continue on until one unit can be taken away.
 * 6) The remaining quantity is counted and represented with small cards.

Multiplication:


 * 1) As for addition problem cards are prepared.

Division:


 * 1) As with static division the child sets about distributing.
 * 2) When he finds that he doesn't have enough for one hierarchy to go around, he must exchange for a lesser hierarchy.
 * 3) 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.

Control Of Error
The directress.

Purpose

 * 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)
 * To realize that one unit revolutionizes a large quantity.
 * To further understand the concept of addition, subtraction, multiplication, and division