(note: this post was previously under: Two problems, but it seemed better to split the two problems into separate posts. The other problem is found here.)

How many people where at the Rally to Restore Sanity and/or Fear?

Gave the applied math class this picture:

(thanks to @samjshah for finding this image for me.)

Asked for, and recorded guesses.  The guesses weren’t half bad because many of them tried to compare the crowd to concerts that they’ve been to.

Asked them what information they needed to find the size of the crowd.

• They asked for the size of the crowd.  I played dumb, and asked them what they meant, they said the area that the crowd took up.  We used mapmyride.com to find the approximate dimensions of a rectangle holding the crowd.
• They asked how much space a person takes up.  I googled it, got this which says that the 2006 international building code says “5 square feet & 7 square feet if the person is dancing.”  Asked them if that made sense.  THANKFULLY our school has tiled the classrooms with 1 square ft tiles, so they all looked at the floor, many of them stood up, and held their arms out.  There was some disagreement, but the consensus was 6 square feet.
• Proportions to the rescue again!  And our answer was about 260,000 in the first class and 225,000 in the second class.  I didn’t guide their hand at all in these estimates, they controlled all the variables, and yet our results are on par with CBS estimate of 215,000. They liked the idea that their estimate was so close to the “official” estimates, and yet it only took 30 minutes to calculate.

(addition: Interesting article on the difficulties of counting people in a crowd: http://www.bbc.co.uk/news/magazine-12879582)