Are you someone who, every time you saw fractions, you wanted to ask for a hall pass? Did you ever wonder, “Do the numbers ever want hall passes too?” I am here to tell you that numbers want hall passes just as much as the rest of us!
Say you have a super cool 
who really wants to walk down the lower hallway in the club to visit his friend 
. Only, belongs to the upper floor, so in order to get down to the lower level he needs a hall pass. This hall pass is important but unobtrusive. It’s a little dash mark next to his exponent. So when he goes to the other hall becomes 
. While he is visiting his friend they look like 
And once is done hanging out with his friend he heads back upstairs. Of course, once he enters his own hallway, he returns his hall pass and looks like again.
Now, lets say wants to head upstairs to visit . He will, of course, need a hall pass to get upstairs. Upstairs the two friends look like 
.
And now that you know how hall passes work for numbers fractions aren’t so scary that you need a hall pass to run away from it all right?
Spoken like a veteran math teacher. The novice math teacher fantasizes about unfolding the beauty of mathematics until each student says, “Aha, I see it. I grok the logic and grandeur. I will never forget that as long as I live.”
But as some are color blind or tone deaf, others are insensitive to the elegance of mathematics.
Here the experienced math teacher offers mnemonics and songs and dances and stories, and hopes that the lesson will be applied at the proper time, some of the time.
LOVE it! Makes me wish they didn’t move negative fractions to grade 10 as I’d love to give this analogy a whirl. Thanks for sharing!
I always tell them that the reason those exponents are so negative (i.e. sad/gloomy/pessimistic) is that they don’t like where they are living. If they are in the upstairs apartment, they must hate walking all the way up there. If they are in the downstairs apartment, their neighbor upstairs is noisy. Either way, they are unhappy where they live, so they must move apartments so they can be positive and happy again.
Silly, but it seems semi-effective.