What Is The Counting Up Method?

"Counting up" is a method of adding (or subtracting) a small integer to (or from) another number. It is accomplished by counting up (or down) from the number the integer number of counts. It is often most useful where a carry (or borrow) might otherwise be involved.

Example
  49 + 3 is computed by counting 50, 51, 52. (3 counts)
  31 - 2 is computed by counting down 30, 29. (2 counts)

This method requires a certain mental agility, as you must keep track of both the current count and the number of times you have counted. Because of this, concentration is essential, and distraction will often result in the wrong answer. Clearly, it is most useful when the number of counts is small.

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A variation of this method is used for counting change (when change is actually counted).
Example
  A customer offers $20.00 for an item that costs $0.37.
  The change is counted (by pennies) .38, .39, .40 (3 pennies), and .10 (1 dime) makes .50, and .50 (1 half-dollar or 2 quarters) makes $1. Then the bills are counted, $2, $3, $4, $5 (4 one-dollar bills), and $5 makes $10 (one $5 bill), and $10 makes $20 (one $10 bill).
Total change is $19.63, consisting of 3 pennies, 1 dime, 2 quarters, 4 ones, 1 five, and 1 ten-dollar bill.