Friday Estimation

On Fridays we estimate. I had been pulling all of my estimation tasks from Estimation180.com until this happened a couple weeks ago:

We did that exponential growth/decay activity with M&M’s. A great task for a wacky schedule due to standardized testing. At one point, a student looked into his cup and said, “Does that look like 97 M&M’s?” Another kid said, “No way! I would have guessed that was more like 30.” The first kid then wondered aloud how many candies are in the packs you buy. Then he suggested we do some estimation tasks with M&M’s.

So that Friday I put out one of the cups that they had used during the activity, and a small container filled with M&M's. It was sitting on a desk in the front of the room and they were allowed to look at and touch the container, but they couldn't open it.

Kids were better able to apply their background knowledge to this since just two days before they'd spent a lot of time counting M&M's and putting them in a cup.

I wish I remember why we talked about the volume of a cylinder... Oh! One student got out a ruler and measured one M&M and the width of the container. He tried to justify his estimate based on those two measurements but his justification didn't make any sense (I really don't remember what that was). So we talked about how you could use the information he measured to make a better estimate using that equation, but we didn't do any actual calculations.

Once we were done discussing a student asked if she could count. She came up to the front of the room and carefully counted out all thirty-six candies. Usually my students are reasonably quiet while we're engaged in a discussion but start chatting as soon as there's a lull. They were so quiet as she counted! Occasionally a student made a relevant comment - Darn! I was too low! - but mostly they just watched and listened to her count. Engagement accomplished.

Yesterday we did a slightly larger small container (which I neglected to photograph). I again put out the cup and the green top container for comparison. What happened next was really interesting - after they'd done all of their estimating, I dumped the M&M's out onto three plates so that people could split up the counting. As soon as I dumped some of them onto the first plate a student yelled out, "Whoa! My estimate was way too low!" I wasn't going to deny them the opportunity to factor in new information, so I finished dumping out the M&M's and then made sure everyone could see the three plates. Then I took new estimates (in red). It was interesting to see how different their understanding of how many M&M's were there when they were spread out on a plate rather than tucked inside a container. It makes sense since they counted M&M's the previous week on a plate, but I didn't expect their intuition to be that accurate! Their second round of estimates was really good.