Today was task day. They were allowed to use their notes to help them work through a task involving Pythagorean theorem, similar triangles and trig. The premise was that an architect was designing a cottage and the roof truss would like like the one pictured below. They were told that the king post needed to be at least 7' long and that the angle formed by the ridge beam and the rafter had to be between 15°and 45°.
They were then given data on king post length and corresponding rafter length for a constant ridge beam length and were asked to choose a truss design and calculate how much wood was needed for their design.
The immediate reaction was "I don't know what I'm supposed to do." and "This is stupid.". There was a lot of resistance to doing ANYTHING but we persevered (as in, I answered a LOT of questions to get them going) and they got to work. I suggested they start by finding the angle formed by the ridge beam and the rafter for each design. From there they chose a design and calculated all of the other lengths to figure out how much wood (length) would be needed for their design.
They also had to write about the connections between the mathematics involved and the construction of a roof truss.
Many students finished within the period, but some need more time. I also discovered that a few students had written very little and will need to continue tomorrow with some prompting. It's funny how some students will ask a bazillion questions and try to get reassurance for every step they take, while others will sit quietly and have no idea what to do next. I was answering questions for the entire period which is why I didn't notice these few students with very little work done. I will have to do a better job next time...
This task originally was designed for 2 days with the first day being spent exploring roof truss designs in groups with the help of Popsicle sticks and glue. Now I think my students are great but I didn't think that they would get a lot out of that exploration and I also thought that the mess they would create with the glue would not be fun to deal with. I was not up for that kind of "stickiness"! I am all for exploring a concept but I'm not sure that it would have helped them with the individual task. Maybe I'm wrong and maybe I'm not giving them enough credit for being able to explore and connect to the mathematics without getting off task.