Task# Why is a Negative Times a Negative Always Positive?

Illustrative MathematicsVaries

The purpose of this task is for students to understand the reason it makes sense for the product of two negative numbers to be positive. The idea is that if the properties of operations with which we are familiar when we do arithmetic with positive numbers are universal, then we have to define multiplication on signed numbers the way we do. The task only works through a single example, but the argument would work for any two negative numbers. Another popular way to explain the rules for multiplying signed numbers involves looking at patterns in multiples of, say, 5.