We had been reviewing percents and so I tossed this on to a quiz. I figured they would use either a proportion or change the percent to a decimal first and then multiply.
However, one young man wrote this: (this is my handwriting, recreating what he wrote)
It was 9 p.m. by the time I got to his paper, so I just wrote: "I think you know what you are doing, but I cannot follow your thinking. Will you explain it to me?"
The next day I got together with him and he explained it to me. It was a simple piece of brilliance.
"First of all," he said, "you have to ignore this." He pointed to the proportion. "I was just thinking about stuff."
"Oh, good," I said, relieved. "You DO know that those are not equivalent, right?"
"Yeah, yeah. So I knew that 8 of every 100 kids were sick. So in 600 kids that would make 6 groups of 8 kids, or 48 kids. Then that also means that in a group of 50 kids, there would be half as many kids sick, so instead of 8 kids, that would be 4 kids. 48 kids and 4 kids would be 52 kids out sick."
I nearly melted. I absolutely LOVE it when kids have these great ways of seeing things.
We also worked all week (in our warm ups and review questions on homework) on taking 10% of a number in our heads, which led to taking 20%, 30%, and even 15% in our heads. One kid asked if we could practice more on finding out how much tip to leave at a restaurant, which also led us to a discussion of why we leave tips, what it means to have a living wage, and the types of bills their parents have to pay. It was an amazing week with those students!