Adding and subtracting negative numbers

It's kind of subtle, but if you've been following along with this blog at all, you may have noticed . . . negative numbers are not in my comfort zone. So the more I learn about them, the better. Today I'm focusing on adding and subtracting negative numbers--which is only fitting, since I started this exploration after getting that problem in our problem set.

Again, this is gonna be a shocker, but . . . we're going to the Khan Academy!

Not surprisingly, they have content that looks like it could be useful. Here's a video on adding and subtracting negative numbers. Let's take a look:

Okay, that wasn't particularly helpful. It's basically the exact same thing I did on my first blog entry about negative numbers. It does make me feel a little better, though, that I couldn't understand in that first entry how to use the number line to show -3 - (-5): The answer is, You can't--not without converting it to -3 + 5, anyway. Which is what he does at 2:40.

Maybe it will help if I can explain why subtracting a negative number is the same as adding a positive number? I was able to get there in my first post on this subject by using examples and logical argument, but truth be told? I still don't understand why subtracting a negative is the same as adding a positive. Maybe this video will help? After all, I'm not a betting man, but it is called  subtracting a negative = adding a positive:

That does help a little. The concept is,

• if Steve has a net worth of negative $3 (so -3, basically),

• and his uncle wants to help him out by taking away that negative net worth (so -3 - [-3], basically),

• then the easiest way to do that is by giving Steve $3 (so -3 + 3, basically).

I'd probably avoid using the term "net worth" with young kids, though. Speaking of which: When are students supposed to learn this? Khan Academy usually has the Common Core standard listed at the top of a lesson, but that's not the case here. Let me do a little digging. . . .

Oh.

That's much later in the curriculum than I thought. Seventh graders should be a lot easier to teach negative numbers to than second- or third graders. I feel better already! I may even feel good enough to move on to another topic. But let me do some practice first--which, Ill admit, I mostly want to do because I want to get to that sweet, sweet Level 2 of Mastery! 

So close!

What can I say?

 I'm feeling a little cocky now, so let me try a problem set with negative numbers but in a way I haven't studied them yet--negative symbol as opposite:

Ouch.

 I'll keep trying!