Parabolic Solar Shoebox Cooker - Math You Can See!

C (age 8) found instructions for a parabolic solar shoebox cooker on BrainPOP Jr., and wanted to give it a try.

The Jr. site is geared toward Kindergarten to 3rd grade, so the instructions were very basic.

First, we gathered supplies:

* a shoebox
* a piece of card stock
* aluminum foil
* glue
* scissors
*a pencil
* and a skewer.









Then, we cut an arch out of one side of the shoebox...

...and used the cut out piece to trace...

...and cut a matching arch from the other side.

We traced, and cut the card stock to fit over the open side of the arch...

...and glued...

...aluminum foil over the cards stock, being careful to keep it as smooth as possible.

Finally, we trimmed off the extra foil, and glued (then taped) the card stock onto the box.

The BrainPOP Jr. instructions said to place the cooker into a sunny spot, put a piece of vegetable (silly BrainPOP people, everyone knows a marshmallow is what you need for this sort of thing) onto a skewer, and "hold it over the bright spot in the cooker".

Of course, trying to decide where the bright spot is, and being certain you have the marshmallow in the right spot is tricky.

There is a formula for finding the focal point (the point where all the reflected light meets):

f = x²/4a

PBS's NOVA has a very good explanation of how this formula works in a Student Handout to go along with their "Saved by the Sun" episode.  I made a copy of it for the older children.  The math was over C's head though, so for her, I tilted the box...

...so the light that reflected off of the aluminum foil shined down onto a black sheet of construction paper, and the focal point...

...was easy to spot.  C touched the spot (briefly), and it was hot...

...hot enough, in fact...

...to melt a chocolate chip, and a marshmallow placed onto the spot, in just a few minutes, even though it was only in the mid-30's outside, at the time (gotta love Montana in May!).

Seeing that the cooker worked, I decide to bring the older children in on the project, to see if the math worked as well.  We used a white crayon to mark the spot where the light appeared to come together on the sheet, as well as...

...the two outer edge points, and the center bottom point of the arch.

The older children measured the distance between the two top points (the diameter of the parabola), and divided it in half to find the radius.

In the focal point formula "x" is the radius of the parabola, and "a" is the distance from the bottom of the arch up to the radius.

So plugging our measurements into the formula, we had 14.75²/4(8.5cm), which meant...

...our focal point should have been 6.4cm from the center of the arch...

...almost exactly where it had appeared to be.

I have to say, I was pretty giddy about the math working out as neatly as it did.  The children were somewhat less impressed...

...but were quite happy to spend an afternoon melting marshmallows, nonetheless.