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.