# Day 24: Graphical Solutions for cvpm Problems vs. Kinematic Solutions and The Lens Game

This was homecoming week, and homecoming week always culminates with a pep assembly.  This translates into only 42 minutes classes, except for those over our lunch mod — that mod stays the normal length.

So, what did I do in with only 42 minutes?  Well, I did not do much, but my students were pretty engaged.  I explained that they were going to work in small groups to solve 4 constant velocity problems.  Most of them I think thought “Four problems, 42 minutes, in a group , no problem”.  Most groups only finished 2 of them; not because they were super nasty, way too difficult, but because of two requirements I gave them.  Requirement number 1:  Every group member worked on every problem, so each student has his/her own solution, no divide and conquer.  If I am going to collect the assignment, it will be from one group member and I choose the one.  I use this technique often with group work because I think it fosters communication between the group members and it forces all the group members to be engaged. Requirement number 2:  The first two problems had to be solved using a graphical approach and a kinematic approach, and the last two can be solved either way, student choice. The graph could be a position graph or a velocity graph (though the position graph for these is much more appropriate) hopefully generated using Logger Pro.  After all, it is much more than just a graphing program.  This basic plan was developed with the help of my chemistry teaching colleague.

I really want my students to be able to solve problems both ways, it makes them better problem solvers.  Some of these kids (especially some in the more advanced math classes) tend to think they can just grab an equation and use it.  As you all know, some problems are MUCH EASIER to solve with a graph than they are with an equation or two.  The ultimate goal is to get the students to the point where they have a feeling of which approach to use.  Another added benefit is that if they get stuck going down one path, they can try solving it with the other method.  Likewise, if they are unsure of the answer, solve it the other way to verify it.

This idea of dual solutions is not really all that new.  The Minds on Physics-Motion book introduces it with constant velocity problems.  Others (Kelly O’Shea, Casey Rutherford and Mike Pustie) have given presentations and written about using a graphical approach to solve kinematic problems, usually constant acceleration.  I have also required it when we work those problems.  The new part for me was to use it with constant velocity problems. Now when we get to constant acceleration, maybe it will not be as much of an adjustment for the students.

General Physics:

The assigned individual practice last night was to finish the ray diagrams for the lenses.  To check the ray diagrams, we set up the optics benches. There are a number of reasons why we did checked it this way.

1.  Connecting the ‘pictorial representation’ to the physical set up and allowing the students to see the image.

2.  It reinforced the idea that we can see both real and virtual images without the use of a screen, just look back through the lens with your eye in the cone of light.

3. It introduced the optics bench and provided practice with it and locating images before we quantify it with the Thin lens experiment.

As we checked them, the students also completed a chart for their notes that summarized all the possible situations (6 total) for object locations and resulting images.  I see this as the linguistic representation.

In my long class, we finished the day off playing The Lens Game.  An awesome idea from a former colleague (Jeff Elmer) and member of our Share group.  I’ll snap some pictures on Monday when I warm the students up with it, but it is just some big (yet thin) wooden cut outs of lenses, images (real and virtual) and objects that have magnets on the back so they will attach to my whiteboard.  Then we play.  Given this object at this location,  with this lens, what image.  Or, given this object at this location and this image, what lens and where?