I decided that before jumping into surface area and volume of pyramids, I would get my students to build some pyramids. So I took in the bins of polydron manipulative pieces (I'm sure they have a proper name, but I don't know it) and put this on the board:
Play time! It was interesting to see some students struggling trying to make rectangles into pyramids. They figured out that the sides needed to be triangles and came up with lots of different pyramids.
One group also made a basket for all their pyramids:
Next we talked a little about vocabulary.
We then moved on to volume.
I gave them nets of right pyramids to cut out. Once folded they look like this:
If you put three of them together you can form a prism. I wish I had taken a picture of them (sorry!). It took the groups different lengths of time to get to this point so I walked around and had the same conversation with each group:
Me: "What shape did you create?"
S: "A prism." (some said a cube so we talked about how the height could be different from the side lengths of the base)
Me: "How can that help us figure out the volume of the pyramid?"
S: "We know how to calculate the volume of a prism."
S: "Length times width time height."
Me: "Okay, so what about the pyramid?"
S: "There are three of them so divide by 3?"
Having the prism made of pyramids in my hands was really helpful for showing students who had trouble grasping the relationship.
I thought this was pretty good use of the period so far. They got to do lots of hands-on stuff and hopefully understood how to find surface area and volume without relying on a formula sheet, which they so love to do. We finished up working through another example and will do one where they need to calculate slant height tomorrow.
In case you think my class is all sunshine and roses, it isn't. I found today extremely frustrating and waited several hours before blogging about what we did in order to calm down. However, I think this blog should be about what we are doing in class, not about "issues" that arise along the way that I have to deal with. I still think my students are fantastic, but today was not a good day for some...