When I teach this, it's like teaching a foundational skill. There's a specific process for finding the mean, median and mode of a set of numbers, so I would need to be thick in the skull to say "EXPLORE!" They would have no clue what they were looking for.
But even when instructing directly, I love this bit of learning because I can make the direct instruction interactive and fun.
First, I gave every kid a number on a paper. That peaked their interest immediately. The whispers started ... debates over what would be done. "It's centres!" "No, these are our groups!"
I had them tape the number onto their shirts and go to the back wall. So much confusion. It was awesome.
I love confusion, because when I'm in control of it, the confusion breaks like clouds to the sun, and then a quick and clear understanding can emerge, giving the illusion of PURE GENIUS. Read that as: the kids feel so dang smart and successful, that they're set up for success throughout the rest of the lesson.
So once I had them good and rustled up, standing all out of order, I told them, "Okay, so we don't really NEED to learn about mode and median this year (it's not in the curriculum), but to get to the MEAN, I think we need to see what these are. So, I'd like you to get in order, so that you can figure out the mode a little more easily."
They looked confused, but did as I said.
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| How adorable are these mathematicians? |
I said, "The mode is the number that repeats most often. Look at this data set. You guys are the values. You're each a different number. Which number repeats the most often?"
They answered: "FOUR!"
"Excellent. You're BRILLIANT." Uncomfortable laughter.
"Now, find the median. Anyone know what that is?"
STUDENTS: "The number that repeats the LEAST often?" ... "No, no one cares about that number." .... "Maybe it's the biggest number?"
ME: "All great guesses! The median is the middle. If we line you up in order, it's the number in the middle. When I point to you, you're out. You need to squat down." I systematically pointed to the end people on either end until we reached the middle person/number. Fortunately, we have 21 students, so there IS a middle number.
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| Hmmm ... what will the median be? I'm picking them off, one at a time! |
They were able to see the last person standing was the middle number. BOOM. Done. Check.
But what if the middle number is an even number? I took one student out and repeated the process. They were (surprisingly) shocked to find that there was "no" middle number, because there were two people left. And so began the real lesson: how to find the mean, because the mean of those two middle numbers would give them the median number.
Rather than go right into the math demo, I had them go back to their spots and watch this video:
<iframe width="420" height="315" src="http://www.youtube.com/embed/QH2obAPwfqk" frameborder="0" allowfullscreen></iframe>
That was really to grab them even more and brief them on the process. They thought it was funny and cheesy, which it is.
I gave them the demonstration of finding the mean flat-out, no secrets, and did two examples. Then, I asked them to watch another video:
<iframe width="420" height="315" src="http://www.youtube.com/embed/oNdVynH6hcY" frameborder="0" allowfullscreen></iframe>
This was even more clear on the steps: Add up the numbers in the data set, divide the answer by the number of values.
We did another example, this time where I threw in a number to throw off the average. I wanted them to think about the fairness of the average/mean. The numbers were representative of their summer jobs:
Lawn Mowers: $30/day
Babysitters: $25/day
Dog Walkers: $20/day
Loungers: $1/day
The loungers really messed it up. They found (with me guiding the SMARTPen) the mean to be $19/day. I asked them if that really represented what most of them made. The answer was NO! Because, it was less than three of the jobs could earn a day.
So, we removed the loungers and found a mean of $25/day. They agreed that this one made sense.
Then, we talked about averages in school, especially in high school, helping you decide whether or not you will get into certain universities or colleges. We brainstormed eight classes they could take (including "Potato Shop" ... I have some weird kids), and I assigned grades to them all. I asked them to find the mean and tell me whether or not they'd get into their dream school, if they needed to have an average of 85.
For some, it was a one-minute find. For others, it took ten. Some wanted to show everything, including the mode and the median. In general, we're off to a good start. Yahoo!
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