## Thursday, January 27, 2011

### Hands-on Exploration of Capacity

Here is how I introduced Volume.

We began with a work station on Monday morning: a variety of containers set out on a mat, all with the milliliter measurements on the side covered over with masking tape. These were containers such as vanilla extract, facial lotion, vinegar, cooking oil, and so on. The students were asked to order them according to how much liquid each container could hold. Then they were to try to find the two that had the same capacity (they were radically different in shape). I found that students were using a lot of mathematical language in their discussion of which of our mystery containers had the greatest capacity. I saw students getting out rulers, and explaining to one another that you had to measure the container in more than one direction to compare their size.

The can of hair spray, being tall and thin, caused the most discussion. Some children were insistent that it held the most simply because it was tallest. Others kept moving it to another spot, because it wasn’t very wide and, they argued, it didn’t hold much. I gave everyone time to visit this station before we had our Morning Meeting.

During Morning Meeting I went around and asked the children to say what item they would move to another place in the line and WHY. We had a wonderful discussion, and I saved taking off the masking tape for the very end, at which point I revealed the correct order of the containers. During the meeting, when a lot of people were saying, “it doesn’t just matter how tall it is, it is how fat it is that matters,” a student pointed out that there were actually three sides that had to be measured, which led us to then working with the volume cubes, and finally learning the formula for calculating the volume of a rectangular prism. One child even became interested in the challenge of measuring the volume of a sphere, and pulled me aside to explain to me some of his ideas for doing that.

After our hands-on exploration with the milliliter, I explained the units of liter and kiloliter, and we referred to the Wooden Hierarchical material again to understand the scale.

By the way, even with colored masking tape over the mL measurements on the containers, I still needed to scribble with Sharpie over it. But the masking tape pulls off nicely in the end, and the Big Reveal is a fun moment.

My two containers of the same capacity were a 250 mL squat glass bottle of maple syrup and a 250 mL aluminum can of La Tourangelle Toasted Pumpkin Seed Oil

Not a single person guessed correctly.