VISUAL METHOD

The concept of subtraction (with "borrowing") can be shown visually using Base Ten Blocks. The visualization used for this subtraction example is the "Take-Away" visualization.

EXPANDED NOTATION METHOD (words)

The concept of subtraction (with "borrowing") can be shown using words to identify the values in the arithmetic problem. This method directly relates to the visual method and can be used as a transition to a method using numbers.

EXPANDED ALGORITHM METHOD (alternate method)

The concept of subtraction (with "borrowing") can also be shown numerically in such a way to identify any numbers that need to be "borrowed" and why. This method works well for addition and multipication, but it results in negative numbers under subtraction, and therefore is considered an alternate algorithm for subtraction. This method can be used to show subtraction can be worked from "Left to Right" as well.

A subtraction problem that requires "borrowing" (trading) can be worked by "adding" the same value to both the minuend and the subtrahend to avoid "borrowing". This method yields the correct answer because you are really adding a number to the minuend and then adding its opposite to the subtrahend, which results in adding a value of zero to the problem (which does not change the final difference). This method only works under subtraction.

UP-THE-HILL METHOD (alternate)

Subtraction, especially with larger numbers, can be done by counting forward from the smaller number (subtrahend) to the larger number (minuend). The amount "counted forward" is the difference between the numbers. This method also alleviates the need to "borrow" (trade).

*BACK TO WHOLE NUMBERS