6th Graders Expand their Understanding of Volume

Recently, Saklan’s sixth graders worked to expand their understanding of volume beyond the equation: volume = length * width * height.

The students experimented with cubic units as they explored a situation involving offices with unusually shaped bases. They quickly were able to determine that a multiplier could be used to extend the height of the office towers much more efficiently than counting. And after a class discussion of why the area of the office tower’s base was the same as the volume of the office tower when it was one unit high, the sixth graders came up with a better formula. Volume = Area of base * height.

An interesting side note: At a math teaching conference that Saul Zippin, Saklan’s Middle School Math Teacher, went to a few years ago, he attended a session about middle school students finding the volume of a parallelepiped (a parallelogram prism) that had one of the sides weighted so it would stand up, as shown in the image below. 

Researchers from the University of Illinois had filmed their students finding the volume of the prism and their outcomes. All of the students used the V = l X w X h idea. Some found the height from their desk to the top (the correct way), while about half measured the side that was the slant instead of the actual height. When it was time for questions, Saul asked how many of the students found the area of the parallelogram (the base of the prism) and then multiplied that by the height. They said that none of the students in their research did that. Interested in how Saklan students would solve this, Saul made a class set of the 3D shapes, weighted the base and asked the students to find the volume. Every student found the volume correctly! Most turned the parallelepiped on its side, found the area of the base and multiplied by the height. 

Saul noted that when students are taught to think mathematically using manipulatives and class discussions, they have a huge advantage when attempting to solve problems.