Certain principles are true of subtraction regardless of the way the concepts are understood or expressed. First, subtraction is the inverse of addition. This means that while addition focuses on combining smaller numbers to give us the one larger number or sum for the answer, subtraction has a larger number or sum removing a smaller number to find the difference. I encourage students to utilize their knowledge of addition when solving a subtraction problem.
The algorithm predominantly taught in schools today is the Decomposition algorithm, also known as the borrowing method. The Decomposition algorithm may be the most common method employed to solve subtraction problems, but it is far from being the simplest method.
There is a more efficient method for subtraction called the Austrian algorithm. While the Decomposition algorithm can get bogged down with borrowing, renaming, and confusion over place values, the Austrian algorithm looks practically untouched by the time the student has solved the problem. The Austrian algorithm borrows a power of 10 from the digit in the minuend directly left of the number in need, making a mental note the number in need of enhancement is now a teen. However, rather than slashing through both the number borrowing and the number borrowed from and rewriting them as different numbers overhead, students simply must place a crutch of a small numeral one below the subtrahend digit in the next place value. The crutch reminds students that they have borrowed a power of ten to make the minuend place value in the column to the right a number in the teens. It is a very simplistic way to subtract.
Having a firm foundation of their addition facts and an algorithm that makes use of that foundation is invaluable in subtraction. Teaching students’ subtraction with the Austrian algorithm builds on the relationship between addition and subtraction and is consistently quick and simple.
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