## Exploring Volume

This week my third grade class explored volume and surface area concepts. Last week they used centimeter cubes to build a number of structures. Students transitioned from counting centimeter cubes to using a formula to find the volume of a rectangular prism.

The next few math sessions in the week revolved around the concepts of identifying faces, edges, vertices, nets, and how all of those characteristics play a role in the volume of prisms. During the next day I asked students to create a net of a rectangular prism using 1cm grid paper. This was a struggle for some students. Being able to visualize the net, cutting it out and creating a prism was challenging. My class went through a LOT of grid paper during this process.  Students started out using trial-and-error and moved closer to a formula method.  After multiple attempts and some major perseverence, I decided to frame the next few lessons with a project.

I decided to dig into my Evernote account and combined a few projects that I’ve used or found through my PLN. I also spoke with a few colleagues in my school for feedback.  The project was going to take some time. I decided that although the project may take more time than individual lessons it was worth the time and gave students opportunities to learn more about the math concepts that were scheduled to be explored.

The project is called volume city. Students were given directions, a model map, 1 cm grid paper and a rubric. You can find the files that I used here. Essentially, students were asked to create a model city using rectangular prisms as buildings. The city had to have at least four basic buildings and students could add more if they desired. Students were required to write the dimensions of the buildings: length, width, height and volume.

Students then used the grid paper to draw and cut out the net for that particular building.

This was probably one of the more challenging aspects of the project, especially when the building wasn’t shaped like a cube.  Students had trouble drawing nets with different heights. Students were given more grid paper as needed. I think every group had to redraw or recut their nets two or more times. This was good in my mind, because it demonstrated that they made a mistake, but were trying again in an attempt to make improvements. The concept of visualizing the net and the action of creating them accurately started to combine as the project continued. I even had a few students decide to create the largest possible net using the entire grid paper.

So after students created the nets they decorated them and glued/taped them on the map sheet. Students filled out the dimension sheet as they created their prisms. Here’s one that’s almost complete.

Not all of projects are complete, but the next phase of the project is for students to find the total volume of their model city. This will most likely take place as students will start taking the PARCC test next week and our math block is shortened. At some point we’ll also be exploring rates in the next unit. During that time we might use some type of stop-motion video of our model cities to look at the frames-per-second in our film.