Over the past few weeks we have been dealing with the areas volume of different shapes. After doing a multiple classroom activities, one thing that I noticed along with my classmates was that my spatial reasoning is very poor. One activity where I particularly noticed this was when we were comparing the volumes of pyramids to that of a rectangular prisms. When I was calculating the area of these two volumes with the same base shape and height, I realized that the area was calculated almost the same, except that the area of the pyramid was 1/3 that of the rectangular prism of the same dimensions. I was simply baffled that this was true. In my head I could not see how three of the pyramids that I just measured would ever fit into the rectangular prism right next to it.
This made me think about the education that I got and how little the math related concepts were hands on activities with three dimensional objects. So often in our classes we are taught that the best way for students to learn is through inquiry in the sciences, because it is through this process that the students are able to break apart the system at which they are doing things and figure out why the system works. Why have we not adapted this into the math education as well?
This was the reason that I particularly liked the activity where we calculated the volumes of several three dimensional shapes with water. After being given the hollow shapes, a measuring cup of water and a graduated cylinder, we were told to find out how the volume of each of the shapes in milliliters. After noticing that there were a few different ways that these volumes could be measure we decided that the best way for us to measure the volume would be to fill the shapes, then pour out the water that fit in the shape and measure this amount. Unfortunately, we were disappointed to realize that although this was likely the easiest way to measure the volume, it was not the most accurate as there was a lot of space that was missed in the plastic that was used to create the shape.
What I like most about this activity for elementary age students is the fact that this gets at the heart of what volume is and what it is measuring. Because of this students would definitely walk away with a concrete understanding of what volume is. Another aspect that I really think is great is that this is such a good integration activity between math and science. Measuring these volumes accurately with the tools given can be highlighted as a key skill. Also this leads for discussion of an alternative way to measure the volume by displacement.
I saw this activity, however, to be more versatile than just being able to be used in the elementary to understand volume. I think that this could be a great upper elementary or even middle school activity if you could help guide the students to make connections between the measurements that the make two dimensionally on the shapes to the three dimensional volumes. This would be good practice for students to do unit conversions. I also think that this practice would be great for students to begin to develop and refine their spatial thinking.