I recently realized that it's almost that time again in Geometry: TRIG. And with trigonometry comes shadow problems .... and by problems I mean the math kind and the understanding kind. I wrote last year about the fact that something I took for granted (knowing how shadows work) is not necessarily in my students' skill set. In fact, with my new crop of cute little 9th (and 2 8th) graders, I posed the following "pre problem" the other day in class:
1. In your notebooks, draw a line representing the ground.
2. Then draw a stick figure that is you somewhere about a third of the way in from the edge.
3. Then draw a sun high up away from you.
4. Now, draw your shadow as accurately as you can based on 1-3, and draw extra markings on your paper that convince me of what your planning process was.
Then I walked around and just glanced at their papers without saying "yay" or "nay". In my brief pass around the room, I saw all sorts of correct and incorrect thinking.
So, we just had a 3-day weekend, and before it, I assigned the following "project" to them (as a precursor to what they'll need to know later):
Every hour on the hour that the sun is up, measure your shadow as accurately as you can and jot down the time and the length. They then brainstormed, and we shared out ways to do this if you don't have a ruler or such. Then I asked them to jot down some things they thought may happen (to look at later). I told them I was going to do the homework, too.
I haven't had them back in class yet, but I already know some changes I'd possibly make to the assignment for next time: It doesn't necessarily have to be ON the hour, but record the exact time you do it once every hour. Also, a kid had an interesting idea: stand in the same spot and notice the position change in your shadow (seems cool, but it would negate the way I measured my shadow). Coordinate with another geometry class at a different latitude and or "place" in their time zone and see what the differences are (if any) for "same heighted" people.
Anyway, I'm curious what they come back with, and if they've learned anything. I'll have to have some follow up questions and follow up drawings to assess. My plan is to get all the data on a spreadsheet and see what the function looks like. I'm guessing since they probably all fudged the times it will be wonky. I'm also curious what will happen when we get to problems such as:
You are standing such that the end of your shadow coincides with the end of a ______ shadow .......... and how they'll draw the picture THIS year (2 suns? 1 sun?)...