3-6 Math Album – Static Operations in the Decimal System


…golden bead materials including wooden hundred squares and thousand cubes
…large numeral cards
…three sets of small numeral cards
…a box containing symbols for operations +, -, x,÷
…small pieces of paper
…a thin rod to be used for the = line
…a soft cloth.

a. Presentation of Addition:
Small Group Presentation. Each of two or three children takes a tray. The teacher states a different numeral for each and they find the appropriate small numeral cards and the quantity, placing the cards on top of the respective quantity. The teacher controls. The child arranges the cards, places the numeral on the table and dumps the quantity on the cloth. When all the quantities are on the cloth, the teacher gathers up the cloth, mixing all the quantities together. The cloth is opened and the materials are sorted. The child begins with units counting the quantity and bringing the large numeral card. When all has been counted, the child arranges the cards and reads the quantity that the combination has produced. Pointing to small numeral cards: ‘The children brought these small quantities. When we put them together we made this large quantity.” (indicating the large numeral cards which is seperated from the addends by the thin rod) ‘We have done addition.’
The numerals are arranged in a column. The plus sign and its function is presented. The line (which was formed by the thin rod) is equivalent to the = sign. The teacher reads the problem (equation) ‘2,512 plus 1,234 equals 3,746.’

b. Presentation of Subtraction:
Group Presentation: Initially the teacher may play the “Rich Man, Poor Man” game to demonstrate the concept of “taking away.” The teacher has a large quantity from which several children take away small quantities until there is nothing left. The purpose of this game is to make the impression of taking away and nothing remaining.
The child has an empty tray. The teacher has a large quantity on his tray. The quantity is counted beginning with the units and large numeral cards are placed on the quantities. The child arranges these cards and reads the numeral. Offering the child some of this large quantity, the teacher chooses some small numeral cards. The child arranges these cards and reads what shall be taken away. The teacher counts out this quantity from what is on the tray, beginning with units. What is left? This quantity is counted and small numeral cards placed on the quantities, arranged and read. What remains on the tray is the result of subtraction. When we take away, we are subtracting. The problem is set up with the minus sign and read. The large cards tell us the large quantity; the smaller cards are for the small quantity that was taken away and the small quantity that remains.

c. Presentation of Multiplication:
Group Presentation: Each child is given a tray and is asked to get the cards and quantities for a stated number. The teacher controls each child’s tray; the cards are arranged, the numeral is read and the quantity is placed on the table. As in addition the quantities are put together, sorted, counted, labeled and the sum is read. The problem is then set up as in addition with the plus sign.
Now it is observed that in this ‘special’ addition, all of the quantities put together (addends) are the same. This special addition is called multiplication. Taking one small numeral : ‘We can say that we took this quantity three times.’ The times sign is presented and the numeral three is written on a blank piece of paper. The result has not changed; this is just an easier way to write the problem.

Note: After this initial presentation, the child no longer sets up the addition problem first.

d. Presentation of Division:
Group Presentation: The children are seated in a circle. One child is asked to pick up the large numeral cards for the stated quantity, and he brings the golden bead material. ‘This large quantity must be distributed to each of these other children equally. ‘Starting with the thousands, one thousand for you, one thousand for you, another thousand for, another thousand for you’… until all of the quantity has been distributed. The children who received count their quantity to be sure that everyone received the same amount. One child is asked to get the small numeral cards. It is emphasized that each child received this amount. When we distribute equally to many others, we divide. The division problem is set up, using a small piece of paper for the divisor, and it is read. The result of division is what one child receives.

After each problem has been demonstrated and set up with numeral cards and symbols, the child may write this in his notebook, preferably on paper with columns and in colors for the hierarchical orders.
After all of the operations have been presented, it is important for the child to understand the function of each operation. ‘What is addition?… putting together…etc.

Age: 3-7

Control of Error: The teacher checks the quantities counted.

…to realize the concept of addition (putting together), subtraction (taking away), multiplication (adding the same number many times), and division (distributing equally)