Activity to investigate the relationship between cubic centimeters and milliliters.  Students carefully (or not so carefully) calculate the base area for their container, fill it to various heights (depths) of water, and measure the volume of water in the container.

One group of students recalled a prior teacher told them that one centimeter cubed equalled one milliliter, “because that’s how metric works”. I asked how they knew.

“Our eighth grade teacher told us.”

Another student (10 classes into modeling) responded with, “but our data doesn’t support it!”

So the team of now six students set out to calculate their data both ways. The measured volume expected for their calculated volumes, and what size volume in the shape based in their measured volumes. They quickly determined that neither data set would solve their problem. The only solution would be better data. And the bell rang.  (And I silently laughed an evil laugh.  This group almost tortures themselves with these educational cliffhangers.)

The next day at the start of class, I asked how they thought the previous day of data collection had gone. This group immeadiately spoke up. “Not good. The containers you gave us were terrible.” (They were. I used what I could find. The sides curved. Sorry, kids.)

I asked if they had the chance, if they would like to collect more data – as I put two very square rectangular pans on the lab bench at the front of the room. A student for each pan ran up, grabbed some tools, and got to work.

This is what they produced:

Look at that! A slope of 1 mL/cm^3!

Compared to others:

So, which is better: accuracy, or precision? Turns out students in the 10th grade think these terms are basically the same. I drew the classic three targets on the board: one with a cluster of dots at the center, one with a cluster off center, and one with a cluster that was spread out, but “averaged” to the center. I told them two were precise, and two were accurate.

One student told me her brain exploded. She got it.

The kids almost immeadiately yelled which was which – and I asked, “how do you know the difference between accuracy+precision (the cluster close together at the bullseye), and precise but inaccurate (the tight cluster not at the bullseye)?

And we looped back around to discussing careful measurement and definining variables. And why. Context makes learning so much easier.