Conceptual Volume

I’m always a fan of ideas that make learning engaging and fun for my students.  I can’t realistically make EVERY SINGLE LESSON awesome and something the students will talk about years down the road, but I do have some moments when I think we have had an activity worth remembering.

With testing creeping up on us next week, there are a few concepts in my grade 8 classes that I need to expose my students to.  Volume is easy to slip into our weekly plan because it can take just 1-2 days to cover and allow students practice with.  I was initially going to try to flip the classroom and have students watch selected videos on volume of cylinders, cones, and spheres, but once I started watch some videos (here , here and here), I decided on another track.

It really all happened by accident–I woke up in the middle of the night, couldn’t go back to sleep, so I started thinking about the day ahead.  I had in my mind the video with the cute mice and the biscuits (the first one in the list above), and I thought, “How can I get my students to experience this in class today? Do I go buy cookies?  No…they aren’t uniform in shape.  What do I have here that’s circular and uniform in shape?” And it dawned on me: poker chips!

I created this exploratory activity for my students.  I think it was so much more memorable than giving them the formula and telling them to “Go at it!” with a bunch of problems on a worksheet.  YAWN!

My awesome math coach, Karen, came and observed, and as we were tossing ideas around about the cone and sphere demo I wanted to do, she contacted another school in our district and borrowed a geometric volume relationships set (like this one from  She even tracked me down at my son’s school later that day (where I was delivering treats for his birthday) to deliver them!  (LOVE HER!)

My first grade son and I practiced the cone and sphere demo at home that weekend.  He loved it–what kid doesn’t love splashing colored water all over the kitchen?

In the classroom Monday, I gathered students around the demo table at the front (which was really just a commandeered table group–I moved those students out so I could use their space.  They didn’t mind…at least I don’t think they did).  This in and of itself was fun because it was out of the ordinary.  Their eyes were alight with wonder, and for the duration of the demo, they were completely and utterly engaged.  It.  Was.  Awesome.

I didn’t have a script, but I basically showed them the relationships between the cone and the cylinder, and then I filled the cylinder with water.  I then asked them to make predictions about what would happen when I placed the cone in the full cylinder.  Most students used the word “displace” when they talked about how the water would flow out of the cylinder as the cone pushed it out (snaps to our science teacher!) and then when I asked them to predict how much water would be displaced, they gave some good guesses using fractions or percents.  Once they saw about 1/3 of the water was displaced, I asked them what would happen if I poured that displaced water into the cone–most students didn’t believe that it would all fit inside, and they were quite surprised when the cone was filled to the brim with the displaced water from the cylinder.  We talked about what that meant, and they were very accurate about connecting that information with the volume of the cone.  From there they came up with the formula for volume of a cone. And continuing on, we followed the same process for volume of a sphere.

The kids liked it, and now they have something conceptual to visualize when they encounter volume problems in the future. Win-win!


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