Somewhere over the.. number line

A few days ago, my friend came to me. Her sister, in the seventh grade, was confused with the number line concept, and would I explain it to her? I remember my days back when we were learning it. My teacher scribbling away at the board, and me, trying to catch up helplessly.

I did, eventually, but with difficulty.
So I thought I'd post about it, so it could help more confused souls out there.

The number line can be confusing. It's like an infinite lake, spreading in both directions like a confusing, endless thing. One misstep, and you think you've drowned. That is an exaggeration, but anything to liven this up, right? :-) I'm bad at jokes. 

Moving forward-

The start is easy enough. You have in one hand- a bunch of negative numbers, in the other a bunch of positive numbers and somewhere in between, maybe on your nose or forehead, a zero.

Imagine you're standing. On your left hand, imagine a magical ribbon shooting out. The longer the ribbon, the more negative the number. -10 would be a short one, -100 longer, -10,000 still longer, and negative infinity somewhere out there, endlessly moving forward.

Do the same on your right hand- out shoot the positives, smiley happy things shooting out.

Zero- bang in the middle.

Okay.

Please excuse me if you think I'm going too slowly. It's just that certain visualizations help a good deal. Remember- you'll be stuck with this seemingly innocent number line all your life- you wouldn't want to antagonize it. You'd be bickering for a l000ng time. See what i did there? ;-)

Now we know what the number line is, we've got an idea.

The next, irritating step is the movement. Add this, go right. Do this, slide left. Ah, the rights and lefts! The heres and theres!

Try to remember it like a dance- one of those fluid dances where the numbers are the glittery, fascinating dancers and the number line is the shiny, polished floor. Imagine you have a number, say 2. Add 3 to it. Where do you go from there? Left or right?

Think of 2 as a dancer. 3 is the number of steps she(or he, whatever pleases you), has to take.

Observe the sign. 3 is positive, so move the dancer '2' three steps to the right.

Is it confusing? I hope not. I merely referred to 2 the number as '2' the dancer.

Swish. Swish. Swish.

We reach 2+3=5.

What if the number isn't positive? Take -3.

Now the dancer '2' has to move three steps to the left. Another dance, perhaps a bit faster. They jump instead.

Jump. Jump. Jump.

2+(-3)= -1

here we are.

If you add a negative number to a negative number (in other words,  subtract a positive number from a negative one), what happens? can you visualize the dance?

-2 and -3:

-2+(-3)

The dancer '-2' moves three steps to the left.

-2-3=-5

Now, for an interesting topic-

The additive inverse.

Imagine you're standing in front of a mirror. You look into your image. It is you- it looks like you. But it is different. Imagine you're raising your left hand. Your image raises it's right hand.

What happened here? Lateral inversion in physics. You can think of it as an easy way to invert numbers.

The dancer '8' is looking at it's image '-8'.

The dancer '-3' is looking at it's image '3'.

Is it difficult to comprehend? I hope not. In doubt, think of yourself looking into the mirror. Think inversion.