Subtraction of Positive and Negative Numbers: The Difference and Completion Approaches with Chips

Abstract

Diverse contexts such as take away, comparison, and completion give rise to subtraction problems. The take-away interpretation of subtraction has been explored using two-colored chips to help students understand addition and subtraction of integers (Bennett and Musser 1976). This article will show how the difference and completion interpretations of subtraction may be illustrated with colored chips to help students develop a better understanding of the subtraction of negative and positive numbers. Black chips will represent positive numbers, and white chips will represent negative numbers. The basic principle is that chips of different colors will cancel each other when joined together; this pair of chips is called a zero-pair. Several zero-pairs together will still have a zero value. Each collection in figure 1 represents zero.