6a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

It's time your students knew the truth: all numbers have evil twins. (It's almost as though math is some kind of daytime soap!)

Students should know that when we stick a negative sign in front of a number, we effectively travel to the dark side of the number line—the part <em>to the left</em> of 0, where minuses lurk in the shadows and negativity reigns supreme. What we've done is turn our nice, normal, happy-go-lucky number into its identical opposite—a shrouded, demonic figure bent on destroying the mathematical world as we know it. Oh, the horror!

If students fear the army of evil twins hiding behind that 0, they'll never be able to confront 'em. But how will students fare against a throng of negative numbers?

Thankfully, students should know that they can turn an evil negative number by using their own negativity against them. In other words, they should realize that since negative signs shift a number to the exact same place on the opposite side of 0, sticking a negative sign in front of an already negative number should shift things back to the positive half of the number line, where unicorns frolic through flowery fields and the clouds are cotton candy.

Surviving this adventure requires that students understand 0 is smack-dab in the middle of the number line—and that it's the only number that is its own evil twin. (Sounds like a <a href=" /jekyll-and-hyde/" target="_blank">Jekyll and Hyde</a> sitch to us.) Seriously, how much freakier can this negativity business get?