Floodlight Shadows conclusion

Today we wrapped up work on the floodlight shadows. It was interesting to see that students could intuitively express what they believed would happen with the shadows as the person walked away or toward a floodlight but they could not solve the problem. There continued to be guesses about lengths without supporting evidence. A few students knew they would need similar triangles and proportional relationships but didn't know how to proceed.

Even after discussing the situation and sketching out lines and triangles, students still struggled to use mathematical structure to model the situation. There is a distinct lack of understanding of how using math models can help to simplify, to describe, and to explain situations. So, while students made conjectures about the results, they had no way of supporting or confirming their conjectures. As I told the class, I could guess the shadow will be 9 feet long or 4 feet long, but without supporting evidence, it is simply a guess.

We then looked at the three sample solutions. Students discussed these and answered questions about the methods. I asked students to complete their work and self-evaluation forms and collected their work. I'll go through the responses and provide some additional feedback and comments.

Next class will be an assessment of their learning over quadrilaterals and similarity. I have one problem on the test that will draw on the modeling of shadow lengths. I'll be interested to see how students fare on this particular question.

Our next unit moves into right triangle trigonometry. This should be a natural progression from the similarity and triangle work that we have been using.