A million is more than a lot

Last Friday, my colleagues and I planned a culminating math activity. It’s been in the works all school year. The purpose was to have students understand and be able to manipulate a million. To make it real. Not hyperbole. Not just a one followed by six zeros. Could we envision a million of anything? In one space? Have we seen a million of anything?

We choose beans and we counted beans. Bagging them in ziplock sandwich-sized baggies. Each baggie held 1,000. We tacked them to a bulletin board. Each row represented 10,000. The board could showcase 100,000; ten by ten; 100 bags. There was power in that.

Beans amassed, I ran out of space. So I set the bean counting aside. My colleague, however, was committed to seeing it through.  Last Friday, she invited all upper grades to see a million beans spread out on the playground. I was excited to see it but had some concerns as to how my kiddos would react to something that was not of their making. Something that they started and didn’t finish.

We walked out. And saw this.Screen Shot 2018-05-27 at 10.26.31 AM.png

Pretty cool. I thought.

My kiddos measured it.
Counted it.
Had questions.
And some did none of the above.

I brought them inside. Ready to talk about what we found.  They were clearly under-engaged, underwhelmed.

Ok. Let’s talk. What’s the problem? Be honest. You won’t hurt my feelings.

The following three reasons were the most voiced.

It wasn’t ours.
We could have done that.
I hate not completing something. That reminded me of it.

I know some of them got something out of i. There were ahas on the playground. But even with that, the lack of ownership was clear. This isn’t ours.

Ok. That could be remedied. Next year, each class would count a fraction of the total. So much more could be done and earlier in the year. With ownership.

But even with that, there were comments that made me wonder about the transfer.

But the more I asked, I realized, there is more to consider.

When I asked, have you ever seen a million of anything? Their response was sure! At a concert. At a football game. The largest stadium in the world, North Korea’s Rungrado 1st of May Stadium has a capacity of 150,000. The same as 150 baggies of beans. One and a half arrays on the playground.  One and a half bulletin boards. They thought they had all seen a million. Lots of times. But in reality, the concept of a million was still simply a lot. Something that fills the screen. Something that surrounds me.

So what to do? What do students understand about a million? They know it is more than a one followed by six zeros. But is it something other than a lot?

We know we can fit a million beans on the playground.
Could we fit a million baseballs?
A million basketballs?
A million people?
Could a million grains of sand fit in one baggie?
How do you know?
A million is something other than a lot.
It fills spaces in different ways.

61lLfYQKFjL._AC_US200_.jpgOn our journey of understanding, we continue to observe, question, process, adjust, and start the cycle again.

Ah, the joy of learning.