## Sunday, November 19, 2017

### What Was He Thinking?

A few days ago I gave my kiddos this problem:

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!