This is because 8 and 2 are complements of 10. The complement method uses the knowledge of our base 10 numbering system for addition by understanding that to add +8 is the same as adding +10 and subtracting -2. Therefore we focus on teaching the complement method which is how your computer does addition and subtraction.

Although simple, the exchange method is not as efficient and increases the workload for mental calculation. As students count, they simply exchange beads to continue the counting process. The exchange method is a traditional method used that does not require knowledge and use of number complements. Using an abacus there are two main ways students can learn to add and subtract numbers, the exchange method and the complement method.

In parallel as students master counting because of the simplicity of the abacus, students immediately begin to learn addition and subtraction. Grasping our number system concept of reuse and place value launches students understanding of counting and becomes their math basis for understanding all of the arithmetic operations. In this process, students are learning the fundamental property of numbers and the concept of place value as they reuse the same single digits over and over as designed in our numbering system. Next the students learn to use the next adjacent rod on the left to keep track of each counting cycle. As students form each single digit number with the beads they learn the counting sequence from 0 to 9. Students very quickly learn to represent and recognize all 10 single digit numbers on a single rod. So each rod can represent all 10 digits from 0 to 9. Each rod represents a single digit of a base 10 number. The only limitation on how large a number that can be counted is the number of rods. Just like using any other objects to represent numbers and learning to count, the abacus in its simplest form can be thought of as a counting device. The first thing we teach on the abacus is number representation, recognition, and counting.

How to use an abacus