Even though the task is heavily scaffolded, students might have a hard time figuring out what they are supposed to do. So $$0\times 5 - 5= (-1)\times5$$ This task assumes students know how to add and subtract signed numbers, but isn't very interesting if students already know the rules for multiplying signed numbers since they will likely think to answer the questions by citing the rules rather than thinking about the reason for those rules (which is what the task is trying to get at). Whether we are explicit about this or not, this argument also relies on the distributive property.
If you note that the multiples are decreasing by 5 each time, then the natural way to continue the pattern is to fill in -5, -10, and -15 into the three empty cells in the table. The task only works through a single example, but the argument would work for any two negative numbers.Īnother popular way to explain the rules for multiplying signed numbers involves looking at patterns in multiples of, say, 5.
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 purpose of this task is for students to understand the reason it makes sense for the product of two negative numbers to be positive.
