5 replies on “Adding and Subtracting Negative Numbers”

I’ve been playing around with the three numbers chosen for a while and cannot for the life of me figure out how to make them -3. In fact, I just used Excel to verify that no combination of 2, 8, and 5 (either positive or negative) adds up to -3.

However, 2 + -8 = -6, and if you then subtract 5 incorrectly from -8 and at the same time forget that you are subtracting 5 and instead think you are subtracting 3 (incorrectly), then I think you would get -3.

David, this was my student. Unfortunately, I haven’t had the discussion yet to figure out what they were thinking. How about the fact the last two integers could conceivably be construed as -3? No idea why he/she would ignore the first integer.

It looks like the second number got erased a few times. And 2 – 5 is -3. Maybe the student started with the first and third number, and then tried to adjust the second number. The problem is that once you have the first and third numbers that equal -3, it then becomes tricky to find a middle number that will work. (I mean, zero works, but if you’re thinking of “What do I add/subtract?” then zero will seem like it’s not really an option.)

After that, I’m as lost as you guys. Maybe the kid changed the focus to the last two numbers because the focus changed to “What do I put in that second position?” So the problem got changed to the last two numbers.

I had similar thoughts about the “frame” of the first and last terms. I’d argue that the “fallback” skill used here is the additive inverse. If I had a frame that yields -3, then I need to put something in the middle that makes 0. +8 and -8 make zero, so I’ll write that in here as one term.

It’s convoluted, but it makes some sense to me in terms of that scrambling moment of looking for a substitutable skill that we talked about during Global Math Chat. I need a zero here, so I can make one with + and -.

As an aside from this particular student, I did notice while evaluating this assessment question that very few students started with -3 and worked backwards. The typical approach was guess and check. What does that say about the students’ understanding of integers? Or operations for that matter?

## 5 replies on “Adding and Subtracting Negative Numbers”

I’ve been playing around with the three numbers chosen for a while and cannot for the life of me figure out how to make them -3. In fact, I just used Excel to verify that no combination of 2, 8, and 5 (either positive or negative) adds up to -3.

However, 2 + -8 = -6, and if you then subtract 5 incorrectly from -8 and at the same time forget that you are subtracting 5 and instead think you are subtracting 3 (incorrectly), then I think you would get -3.

David, this was my student. Unfortunately, I haven’t had the discussion yet to figure out what they were thinking. How about the fact the last two integers could conceivably be construed as -3? No idea why he/she would ignore the first integer.

It looks like the second number got erased a few times. And 2 – 5 is -3. Maybe the student started with the first and third number, and then tried to adjust the second number. The problem is that once you have the first and third numbers that equal -3, it then becomes tricky to find a middle number that will work. (I mean, zero works, but if you’re thinking of “What do I add/subtract?” then zero will seem like it’s not really an option.)

After that, I’m as lost as you guys. Maybe the kid changed the focus to the last two numbers because the focus changed to “What do I put in that second position?” So the problem got changed to the last two numbers.

I had similar thoughts about the “frame” of the first and last terms. I’d argue that the “fallback” skill used here is the additive inverse. If I had a frame that yields -3, then I need to put something in the middle that makes 0. +8 and -8 make zero, so I’ll write that in here as one term.

It’s convoluted, but it makes some sense to me in terms of that scrambling moment of looking for a substitutable skill that we talked about during Global Math Chat. I need a zero here, so I can make one with + and -.

As an aside from this particular student, I did notice while evaluating this assessment question that very few students started with -3 and worked backwards. The typical approach was guess and check. What does that say about the students’ understanding of integers? Or operations for that matter?