Operations with the Golden Beads

Subtraction 2, with Exchanging


As for addition


To understand subtraction


5 years and older


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 and another of the small number cards.  The teacher thinks of a problem, e.g. 3273 - 1528 - 487.  She makes the minuend, 3273, with the large number cards and the golden bead material, and places them on the dark green mat.  She makes the subtrahends, 1538 and 487, from the small number cards and places them in the upper right hand corner of the felt lined trays.  She gives a tray to each of the children who will be doing the subtraction and asks them to read their numerals.  They do so.


The teacher, indicating the minuend, says to the children, "Here is 3273.  Tim is going to subtract 1538.  How many units will you subtract, Tim?"  Tim says, "Eight units."  The teacher says, "I do not have enough units.  I only have three units.  What can we do?"  She pauses and then explains that a ten bar equals 10 units.  There are seven ten bars so one of them could be exchanged for ten units.  She gives a ten bar to one of the children.  He exchanges it at the bank for ten units.  These are brought back to the teacher.  She takes them and puts them above the golden beads on the table.  She says, "Now we have 10 units and 3 units, so we have 13 units."



"Tim you can subtract 8."  Tim does so.

Tim needs five hundred.  There are only two hundred.  What can be done?  The teacher explains that a thousand equals 10 hundred, and that one of the thousands could be exchanged for ten hundred.  One of the children takes a thousand to the banker who gives 10 hundred squares in exchange.  The teacher puts the 10 hundred squares above 2 hundred on the table.  She says, "We have ten hundred and two hundred, so we have twelve hundred.  Now Tim can subtract 5 hundred."  Tim does so.  There are 7 hundred left.  There are 2 thousand on the table.  Tim subtracts 1 thousand.  There is 1 thousand left.



The second child subtracts her subtrahend from the quantity remaining on the mat.  When necessary, one of a hierarchy is exchanged for ten of the next lower hierarchy.


As the subtraction is completed in each hierarchy, the number remaining on the mat is counted, and the corresponding small number card is placed beside it.
The teacher superimposes the small number cards.  She places them under the large ones and re-caps.  We had 3273.  Tim subtracted 1528.  Mary subtracted 487.  So, the difference is 1248.  More problems are worked in this way.