Operations with the Golden Beads

Division 2, with Exchanging


As for addition


To help the children understand division


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.  One child is in charge of the large number cards.  Another is in charge of the small number cards.  The teacher tells the children that they are going to work division problems.  The teacher thinks of a problem that will require exchanging:  e.g. 5672 ÷ 2.
The teacher makes 5672 in golden bead material and the large number cards and places them on the mat on the table.



She tells the children, "I have 5672.  I am going to divide it between two children.  They will each get exactly the same amount."  She gives a tray to each of the two children.  They stand in front of her holding their trays.  The teacher says, "Here are five thousand.  I will divide them between you."  She gives each child a thousand, and then a second thousand.  There is one thousand left.  The teacher says, "I cannot give this thousand to either of you, because then the other would not get one.  You each must have the same amount.  What can I do with this thousand?" Occasionally a child will suggest changing the thousand for ten hundreds.  Otherwise, the teacher explains that a thousand is the same as ten hundred, and can be changed for ten hundreds.  She asks a child to take the thousand to the child in charge of the golden bead material and exchange it for 10 hundred squares.  The child does so and brings the hundred squares back.  The teacher takes them and puts them above the hundreds on the table, indicating that these are hundreds obtained by exchanging.


She says, "We have 10 hundred and 6 hundred which make 16 hundred.  I am going to divide the 16 hundred between you two."  She divides the hundreds one by one.  Each child gets 8 hundred and is given a small number card 800.  The teacher says, "Now, I will divide the tens between you."  There are 7 tens.  Each child gets three tens and there is 1 ten left.  The teacher explains that there are not enough tens and that the ten must be exchanged for units.  She gives a ten bar to a child who is watching and asks him to change it for 10 units.  He takes the ten bar to the child in charge of the golden beads and receives 10 units in exchange.  He brings them back to the teacher.

The teacher puts the 10 units above the units on the table mat and says, "We have 10 units and 2 units, so we have 12 units altogether.  I will divide 12 units between the two children."  Each child gets 6 units and is given a small number card 6.

The teacher asks the children to superimpose their small number cards.  Each child tells her how much he has.  Each child has 2836.  The teacher takes the small cards off one tray and puts them above the large number cards on the table.  She re-caps. "I had 5672.  I divided it between two children.  They each got 2836."  More problems are worked in this way.