Modeling Shadows - Application, Extension and Success!

 Last time, we began our process of modeling shadows - how and why they're formed, why some parts of the shadow are totally dark and others aren't, and began using diagrams to try to predict shadow composition and size.  The initial diagrams had way too many rays and were difficult to interpret, so they had reading on what we teachers would recognize as "the normal way" to ray trace.

In the past, we'd go through that first day of experimenting and fumbling, creating less than perfect diagrams, etc. all together, with me doing the drawing, and them doing the note-taking.  I've even had them do the experiments to determine the trends, but then when the diagrams started, it was all me.

It was quicker, but they surely couldn't do all of this during the next 45 minutes of class:

Today, they:

• Ray traced an actual-size model of a ball/bulb/wall system
• Determined where the shadow was dark or lighter (remembering the names, too)
• Drew, on a smaller board, an actual-size prediction of what the shadow would look like

 

• Checked that prediction against the demo - success! 

 

• Made an accurate prediction about how this would all be different with a point-sized bulb using ray tracing
• Connected the shadow parts to the types of solar and lunar eclipses
• Determined where the antumbra was, what the light looked like from there, and what that shadow looks like on the wall

Modeling FTW.

Even when I've had kids do the reading before class, they weren't able to actually apply ray tracing (if they in fact learned the mechanics by reading) and understand what it tells them.  That bit about drawing what the shadow will look like on the little boards?  That was a totally new perspective on shadows from the ray tracing they've done, but they were able to do it without skipping a beat.

It's the sequence, and who's doing the work that's the magic.  They modeled shadows last class. They  came up with a (moderately effective) ray tracing method, so they saw the need for a better one. They did some reading with a purpose and enough background to assimilate the reading (assuming that they did the reading - one section almost uniformly did, and everything was awesome.  The other section didn't read at a high rate at all, and it wasn't nearly as rosy.  Nothing works if they don't!).  They made predictions and saw them validated. They did it.  The result? They know it.