Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

["Anthony Lapinski" <Anthony_Lapinski@pds.org>]

I, like most teachers on this list, like these simple thinking problems.
Most students, at least the ones I teach, don't. They can't/don't think
like we do. They don't really care about these ratio/scaling problems
as they find them irrelevant. They feel the same way about most of
what they learn in math classes. In physics, they just want a formula
to solve a problem. Their critical thinking skills are generally poor,
mainly because they are not taught how to critically think in high
school. What courses do this, besides physics? And with all the new
handheld devices these days, students are weaker at fixing things
and solving real problems. However, they can text very efficiently! Sad...
I assume others on this list feel the same way.

I also like the question about making the sides of a square and triangle
two times longer. I might incorporate some of these into my "placement"
survey I give each year to assess kids' thinking skills and whether they
are in
the right physics class (honors or regular).

When I teach electricity, I give each student a battery, bulb, and wire
and ask them to make it light. Most can't initially. I tell them not to
look at their neighbors and what they are doing. I eventually give them
some hints, and they all eventually get it. It's a good thinking activity
for kids
at any level (regular, honors, even middle school). I then show the Harvard
video clip, where the graduates can't do this simple task. These are
"smart"
kids ("engineers") who don't know the basics of electricity. Maybe they
were
never taught?


Phys-L@Phys-L.org writes:
> These type of problems contain so many unknowns that they become one of 
> those mind reading problems.
>
> Are the machines identical, and can they run simultaneously? Are they 
> independent, or does the partially completed widget move from machine to 
> machine in an assembly line fashion?
>
> Can the raw material delivery rate be scaled linearly? Probably not. You 
> size your loading dock, and buy sufficient forklifts to support your 
> current capacity, or maybe a little more.
>
> If you're making widgets at a higher rate, where will you put them, and 
> how fast can you ship them out?
>
> Are humans involved? Are there enough trained humans to run more machines?
>
> Is there a reset time between widgets? I.e., does it take 4 minutes to 
> make the widget, and then another minute to cycle the machinery back to 
> the initial state? That would reduce the time to produce the last group 
> of widgets, which could be post-processed while the machines were 
> resetting for the next day.
>
> Can the machines run continuously, or must they pause every so often to 
> get oiled, have waste removed, blades changed, or be maintained in some
> way?
>
> In the simplistic case of independent machines with unlimited capacity 
> and no reset time, the problem stated below can be interpreted as taking 
> an isolated machine 5 minutes to produce each widget. One machine would 
> take 500 minutes to make 100 widgets. So you just need the original 5 
> machines to produce 100 widgets in 100 minutes, or in fact, N widgets in 
> N minutes, where N is a multiple of 5.
>
> Another interesting question is how long it takes for 5 machines to make 
> 4 widgets, or 20 machines to make 50 widgets. What happens when you 
> divide integers, and end up with a remainder? Do they still teach
> "modulo"?
>
> A super excellent way to solve these classes of problems is not with 
> math or physics, but by writing a program that simulates widget 
> production, and allows you to vary the different parameters. It doesn't 
> have to have complex graphics or controls. It just needs to print a 
> timestamp every time a widget is produced.
>
>
>
> On 1/1/2015 12:00 PM, phys-l-request@www.phys-l.org wrote:
> >       It takes 5 minutes for 5 machines to make 5 widgets.
> >       So, how many machines does it take to make 100
> >       widgets in 100 minutes?
>
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