Instead of starting with a counting circle today, I had them multiply two binomials. They haven't practiced this lately (and were really doing well with counting circles) so I thought it would be more beneficial. I have 8 of these ready to go on little slips of paper (found here) so we can do one each day this week and again later in the semester.
Next up, pyramids! Alex Overwijk and I had talked about creating a new activity involving tents in the shape of pyramids, but that hasn't happened. This week is crazy for me so I went with some not-very-exciting worksheets. We did start by building pyramids. I brought in the bins of G-O-Frames and asked them to build pyramids. That's all I said. Here is some of the collection:
There were a lot of tetrahedrons and some square-based pyramids. There is one hexagonal-based pyramid and one right-angled triangular-based pyramid. I asked what they noticed about the shapes and they said that the sides are always triangles. The base could be a variety of shapes. I asked how they could find the surface area of a pyramid and took a squared-based one apart. I asked the same question while holding up the one with a hexagon as its base. They seemed to understand the idea of adding up all the areas. I had them work on the first example from this handout and I circulated helping some of them get started.
I showed them the right-angled triangular-based prism and said that if we had three of them we could make a cube. I also showed them this video. I could have done the demo myself, but I would just make a mess and I wasn't up for that first thing on a Monday morning. I tried to really emphasize that to find the volume of a prism you take the area of the base and multiply it by the height because the height represents the number of "layers". To find the volume of a pyramid, you perform that same process and divide the result by 3. Again, I let them work through some of the examples before going over this one together:
Along the way we talked about the difference between vertical height and slant height. They figured out that the slant height of the pyramid is the height of the triangle. They also were able to determine that if you were missing one of the heights in a square-based prism, you could use the sum of squares (Pythagorean theorem) to calculate it.
We will do a little more with pyramids tomorrow and work on some trig again.