In the model we use for
subtraction, the minuend (the top number) is represented as quantities of balls
color coded by place value as for the addition model. The subtrahend is represented as quantities
of holes organized by place value which are to be filled from the corresponding
balls above. The process of filling the
holes procedes from right to left starting with the “ones” column. Each step is effected
by clicking on the “minus” button which changes color as the hole filling is
completed for each place value. For each
placevalue the process begins with a request from the subtrahend column for the
requisite number of balls. If there are
enough balls in the corresponding minuend column, the required number of balls
are dropped down to fill the holes and the count of the remaining number of
balls is recorded in the proper place value of the result. Otherwise, a “reqrouping request” is made to
the next place value column. If the next
column has any balls, one will be removed and passed to the requesting column
where it is exchanged for 10 balls of the placevalue for the requesting
column. If the next column has no balls,
it makes a request to its left neighbor and so on until ultimately the requests
are satisfied and the original request is satisfied. There is also a button which displays the
answer to the problem so that students can try the problem on their own and
check their answers.