Operations with the Golden Bead Material
- 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.