Volume: It's Not Just a Setting On Your Television

April 20th, 2016

As I've mentioned before, I'm currently doing Service Learning in a fifth grade class. Today during math, the students were put into groups of three, and each group was given a section out of their math workbook that they were to study and later teach to the rest of the class. Each of the sections dealt with different concepts regarding volume. As I was going around the classroom and observing the groups study the concept they were assigned, I noticed one group struggling with the idea of finding volume using cubes (similar to what is shown in the figure below that can be found here). 

  

 I went over to them to assist them, because I remembered struggling with this same idea when I was in elementary school. One girl, Laura, said, "Miss Haley, I don't understand where the cubes come in. I know the cubes are stacked on top of each other and I know the sides of each cube are each one centimeter long but I don't understand how I can find volume using them." 

I replied, "Imagine the cubes aren't there. Imagine that instead, there's only a container that's in the shape of how the cubes are stacked. Now, count the cubes one at a time and pretend that each time you count a cube, you're putting it into the container." Laura proceeded to do this, and once she finished I asked her how many cubes she "placed" into the container. She responded, "Forty cubes." (There were five layers of cubes, and each layer consisted of two rows of four cubes.) 

I then asked Laura, "What is volume?" She replied, "Volume is the amount of something a container can hold." "Something like cubes?" I asked her. Her face lit up and she exclaimed, "Yeah! Like cubes or maybe water or something like that. I get where the cubes come into it now!" "Good job!" I told her. "What is the length of each side of a cube?" "One centimeter," she replied. "So what would the unit of volume be for this figure?" I asked. She paused for a minute and replied, "One cubic centimeter, because each side is a centimeter long and the figure is a cube." 

Volume was always a tricky subject for me in school. The formulas always confused me, and it was difficult for me to imagine filling a container with something as insubstantial and changeable as water. However, when my teachers began using tools such as cubes, it became easier for me to see where numbers were coming from. Cubes also helped me to understand why volume is measured in cubic units, just as area is measures in units squared. They're an excellent tool for teaching volume, especially in the beginning of teaching it. 

You can find more practice with volume using cubes here.