This past week we had quite the debate in my PLC (Professional Learning Community). We gave students the problem

What is the difference between -15 and -9?

Not a big deal, right? Well, we had two main answers from students. -6 and 6.

So which is it?

Well, when I place the problem on a number line, I see that the two numbers are 6 spaces apart. Also, when I subtract, I start with the larger number and subtract the smaller number. That means -9 – (-15), giving me an answer of 6.

Other teachers in my PLC saw this as a problem in which we are teaching students to subtract the numbers in order, meaning -15 – (-9), which has an answer of -6.

It was quite the discussion. I even looked up some other thoughts to see what was said.

In a math forum with “Dr. Math” we can read the following:

Elementary algebra books tend to twist the English language a bit here, to make things easier for the students. In real life, the difference between a and b is |a-b| (or |b-a|, which is the same); differences are always positive. But that would lead to ugly equations that students would struggle to solve; so they pretend that when we say “the difference of a and b” we mean just a-b–in that order, even though if b were greater than a, the “difference” would be negative.

You can also find another explanation here.

I understand that we teach 7th grade, so it should be interpreted to be the first number subtract the second number. However, if I’m confused, maybe we should rewrite the question.

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