I started out the volume unit by handing-out a warm-up worksheet that asked students to count the number of cubes that made up each figure. There was an example at the top of the page that also showed students that it was cubic centimeters so answer with the units cm^3. I got fantastic questions immediately:
Are we counting the faces or are we counting the cubes?
Score 1 for a successful surface area unit yet again. I explained we are counting the CUBES, I saw many students erasing their previous answers. They finished the problems in about 3 minutes once they realized it was simply counting up boxes. We went around the room answering the questions making sure to include the correct units (hey, it’s cm^3 because they’re little cubes!).
Next I directed their attention to my desk, and asked them to turn their warm-up paper over and SILENTLY write down their prediction on which container held more and give a reason why. I stated again the need to not shout out because they don’t want to share their answers with their neighbors. I held up each Tupperware for them and its corresponding name (neighboring high schools).
I asked students to raise their hands for each Tupperware, we started with St. Joes. In the first class nobody raised their hand (interestingly, in the honors class about a third believed it was the biggest which shows they are different kinds of thinkers, but I digress). Instead of just moving on I asked if somebody would raise their hand and explain why they did NOT pick St. Joes. The volunteer’s responses included words like deep and short. I reenforced the word Height and when they explained that it was in fact wide I used the word Base. I continued to use those words over and over until the students started to include them in their own descriptions.
As expected, we became split on Masterman and P E&T and it was time to figure out how we were going to measure this! I held up my marshmallows and explained these were my kind-of-cubic centimeters like in the warm-up activity and we were going to count how many cubes filled it up. I asked why this wasn’t perfect and students explained that they were cylinders, wouldn’t fill up the perfectly, could we have half layers?, smushy, etc. And we agreed upon no smushing and a good estimate. I also asked if I could just dump a bunch in and they emphatically responded NO! I must build a layer on the bottom and build carefully.
I had a student volunteer and a supervisor (both rooting on opposite teams) to come up and measure P E&T while I measured Masterman for the class (it was clear). I found there were 6 marshmallows on the bottom layer and I showed this to students and asked if I could find a shortcut. I decided to look at how many layers could I fit and noticed there were four (I stacked four marshmallows on the side and showed students). About half the class shouted, TWENTY-FOUR MARSHMALLOWS WILL FIT!
Score. How did you get that number? I multiplied. Why? Ummmm. Okay, let’s see if you’re all right! And then I proceeded to fill up the Tupperware and WOW, 24. And then I asked them use the terms base and height to explain their shortcut and they explained they multiplied base by height.
The next awesomeness happened when skinny ol’ P &ET ended up with 25 marshmallows and we were flabbergasted on how the two different shapes could hold such a similar amount! And then students started to realize that maybe ones fatter base made up for the shorter height. The conversation was mind-blowing and it occurred in all three class periods.
So when time to show them the volume formula for rectangular prisms and cubes it was super easy for them to see we just get the area of the base and multiply the height. They wrote down the formulas I put on the board and did the following two pieces of classwork, exit ticket, AND completed their homework. Mind you, we did all this in a short day – which means 38 minutes. WOW.
They continued to show me they understand the concept of volume when we moved onto more figures including cones and pyramids which we compared to cylinders and prisms and saw how their volume was related (I put figures inside of other figures and asked questions like which holds more to reenforce similarity/differences) and thus the formulas would be related. It’s been a very successful and exciting 2 weeks of learning for us!
Unfortunately – I only have 10 days left of student teaching. Which means I am going to do some AWESOME things for the next 10 days to get the most out of the last few days – up next, Pythagorean Theorem (looking for projects!)
Sources: All worksheets (except Molly-made exit ticket) taken from: http://www.superteacherworksheets.com/volume.html