How To Use An Abacus 

William Gordon                 John Hope Academy
                               5515 S. Lowe 
                               Chicago, Illinois 60621
                               312-962-2760

Objectives:

The students will be able to:
   1. Demonstrate the properties and operations of a number system
   2. Develop an understanding of the commutative, associative and 
      distributive properties of the mechanics of the abacus
   3. To understand the place value of whole numbers using an abacus

Materials:

Chinese Abacus (Suan Pan or Soo Pain)

Strategy:

   A typical Chinese abacus consists of columns of beads.  A crossbar separates 
the beads.  Each column has two beads above the crossbar and five beads below 
it.  Each upper bead represents five units and each lower bead equals one unit. 
   The first column on the right is the ones' column; the second column is the 
tens' column; the third column is the hundreds'; the fourth column is the 
thousands'; and so on.  The ones' column represents numbers from one to nine.  
Each bead below the crossbar has a value of one (1) and each bead above the 
crossbar has a value of five ones (5).  The tens' column represents numbers from 
10 to 90.  Each bead below the crossbar has a value of ten (10).  The beads 
above the crossbar has a value of fifty (50).  The hundreds' column represents 
numbers from 100 to 900.  Each lower bead equals 1 hundred (100) and each upper 
bead equals 5 hundred (500). 
   To place a number on the abacus, move beads to the crossbar.  When beads are 
moved away from the crossbar, they are cancelled.  This means a lower bead is 
cancelled when it is lowered from the crossbar and an upper bead is cancelled 
when it is raised from the crossbar. 
   To place the number 3,684 on the abacus, raise 3 of the lower beads in the 
thousands' column.  Then lower one upper bead and raise one lower bead in the 
hundreds' column to represent 6 hundreds.  Next, lower one upper bead and raise 
three lower beads in the tens' column to show the 8 tens.  Finally, in the 
ones' column, raise four lower beads for the 4 ones.  Now the abacus shows 
3,684.