Operations with the Golden Bead Material

Division 1


As for addition


To help the children understand division
To teach the vocabulary division, dividend, divisor, and quotient


5 years onwards


A small group of children.  The material is arranged as for addition.  One child is in charge of the golden bead material.  Another child is in charge of the large number cards, and another is in charge of the small number cards.  There are as many children to do the division as the divisor (for example, two if the divisor is 2, three if the divisor is 3, etc.).  The teacher tells the children that they are going to work division problems.  The teacher thinks of a problem that does not involve exchanging: e.g. 4862 ÷ 2.  The teacher makes 4862 in golden bead material and the large number cards and places them on the mat on the table.


She tells the children, "I have 4862.  I am going to divide it between two children.  They will each get exactly the same amount."  She gives a tray to each of two children.  They stand in front of her holding their trays.  The teacher says, "I will divide the thousands between you first.  There are four thousand."  She puts a thousand on each tray; then, a second thousand on each tray.  There are no more thousands.  Each child has two thousand.  The teacher puts a small number card 2000 on each tray.  She says, "You each have two thousand.  You each have the same. Now I will divide the hundreds between you."  There are eight hundred.  She divides the hundreds, one by one.  There are no hundreds left.  Each child has four hundred.  The teacher gives them each a small number card 400.  She says, "You each have four hundred.  You each have the same.  Now I will divide the tens between you.  I have six tens.  We will see how many you each get."  She divides the tens, one by one.  Each child gets three tens and is given the small number card 30. The teacher says, "You each have three tens.  I have no tens left, so I will divide the units between you."  There are 2 units.  She puts one unit on each tray.  Each child is given the small number card 1.


There is nothing left.  The teacher asks the children to superimpose the small cards on their trays.  They do so.  She asks each in turn to read his or her number.  Each reads 2431.  The teacher says, "You each have 2431."  She takes the small cards off one tray and places them over the large number cards at the top of the table, forming the quotient.



This is partition (equal sharing).  The answer is what one person gets.  The teacher re-caps, "I had 4862.  I divided it between two children.  They each got 2431.  There was nothing left."  More problems are worked in this way.
Note:  Large number cards are used for the dividend and small number cards for the quotient to give the impression that a larger quantity is broken down into smaller equal quantities.  The teacher stresses the fact that the division will be an equal one, because one can divide unequally.