Floodlight Shadows

Today, the focus was on modeling a situation with geometric structures. The class started with going through questions on the multiple choice practice problems. The main issues on these questions were those involving given coordinates. For whatever reason, students don't think to sketch out the points. Once they do, answering the question becomes much simpler.

For the modeling problem, I used the Mathematical Assessment Project formative assessment problem Floodlight Shadows. Because of some time constraints, I modified the lesson structure somewhat.

I started by giving students the floodlight shadow task. I told them to work on their own for 10 minutes. As I monitored their progress, I ended up providing some extra time for their individual work. Many students could draw a representation but had difficulty overlaying mathematical structures that would help them. They also were coming up with answers for which they had no justification. I pushed them to justify why their response would be correct.

After, I had students work in groups. I provided a blank sheet of legal-sized paper to record their results.Some groups continued to struggle while others readily started drawing triangles to overlay on their drawings. For those struggling groups, I asked them what structures could be overlaid to help them model the situation. At this point many started to realize the triangular structures that were present.

The groups that originally started using triangles to model the situation also started to use similarity and scale factors to derive answers.

I asked the class to complete work tonight. Tomorrow we'll look at the sample responses provided in the lesson package and share out some of the class' thinking on solutions.