When I taught math in Tulsa, one concept my freshmen really struggled to understand was the difference between positive and negative integers. They simply could not get their heads around the idea that -5 was not the same thing as 5, and I despaired of ever making them understand it.
We added and subtracted. We graphed inequalities on number lines made from yardsticks and chalkboard paint. I constructed a walkable number line and had them wander back and forth to solve problems. We wrangled with those integers every day, in every way I could dream up, to no avail: Some kids caught on, but some still would get to the end of a lesson and say, “Isn’t minus three the same thing as three?” until I was ready to pull my hair out.
I decided the lesson would be more memorable if they were emotionally invested in it, so I brought in a bag of Starbursts and started handing them out, a few at a time, with instructions to wait until the end of class to eat them.
As I walked around the room, I’d call out an integer and distribute the corresponding number of candies.
“PLUS FIVE!” I shouted, handing a girl five pieces of candy.
“PLUS THREE!” I gave a boy three Starbursts.
When everybody had a handful of candy, I walked over to the girl who had struggled the hardest to understand the difference between positive and negative.
“MINUS FOUR!” I shouted, taking four Starbursts off her desk.
She looked stricken. I raised an eyebrow. “What difference does it make?” I asked. “It’s still four, right?”
Her jaw dropped.
“PLUS TWO!” I handed two of her Starbursts to another kid.
We went on like this for several minutes. When I was sure everybody understood the difference, we applied the lesson to some problems, using the walkable number line to reinforce the idea of moving left for negative and right for positive.
It wasn’t a terribly complicated lesson, and it didn’t require a lot of prep work, but it got the point across and made an elusive concept a little more tangible.