This past Sunday, did you see hundreds of photos from the People’s Climate March posted on your friends’ Facebook and kick yourself for having a lazy afternoon on your couch (as I kind of did)?

The New York Times reported that, on September 21, approximately 311,000 people participated in the March in New York City. The article said that the number was “… provided by 35 crowd spotters and analyzed by a mathematician from Carnegie Mellon University…”

There seem to be at least a few different ways of counting crowds, many of which use a basic “area times density” principle. They include the classic technique developed in the 1960s called the Jacobs Method, and updated, more accurate methods such as Yip and Watson’s.

While 311,000 was more than enough to make me wonder why I didn’t join this historic event, the event’s organizer claims that nearly 400,000 marched. There is no way to know whether this discrepancy comes from simple errors, or public relations motives. Or is there?

Professors: Do you think you can use this topic in any of your math classes? If so, in which course and how?

(Photo courtesy of Professor Jonathan Cornick at QCC, who was one of those Facebook friends)

Thanks for your comment, Marina! I agree that estimating numbers is such an important activity/skill to have (and it’s fun to do so!). Once you estimate, you want to know the actual number; that’s human nature. And then, numbers become

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It’s a nice event I guess, love the pict that u share,

Thanks for your comment, Marina! I agree that estimating numbers is such an important activity/skill to have (and it’s fun to do so!). Once you estimate, you want to know the actual number; that’s human nature. And then, numbers become more familiar and you get more comfortable with them!

By the way, how did you end up staying at VIERS? That’s so special and I’d love to hear more about it!

I used activities like this at math circles. Once we estimated the amount of leaves in a big pile (about a million – and six-year-olds were thrilled to actually see a million). Another time we estimated the number of hairs on a kid’s head.

This spring I stayed at VIERS biostation, and the marine biologists there said they gradually grow their math eyes for estimating large numbers of fish. The get very precise, too: at a glance, the last estimate one of them did was 840 and the exact count 843.

I use these tasks for teacher and parent courses, as well – to help people learn about the value of estimation. Here’s one of our mini-posters: http://www.moebiusnoodles.com/2014/01/math-mind-hacks-guesstimate/

This may be a better link to the NPR piece:

http://www.npr.org/2014/10/05/353849607/how-to-measure-a-crowd-without-the-political-numbers

I heard a “numbers expert” from FiveThirtyEight.com talking about this topic on NPR’s Weekend Edition Sunday this morning . The use of social media for crowd-counting is an interesting idea. http://www.npr.org/player/v2/mediaPlayer.html?action=1&t=1&islist=false&id=353849607&m=353849610

Milena, I agree. The basic concept is fairly simple and I’m sure students in remedial courses can tackle this problem. Yes, keep us posted. I’m very curious to learn how it goes!

An assignment like this will be very interesting in courses like Statistics or even developmental math courses to study ratios, areas, and proportions. I am going to try it this term and comment about their response to it. Thanks for the idea.

That sounds like a great idea, Hunter. How about taking students to the Thanksgiving parade this year and having them experience different densities? (Probably not a good idea!)

I remember being asked open ended questions like this for the first time in an undergraduate “math modeling” class. In my case the question was: how many golf balls will fit in this room?

I loved thinking about it, and I also liked the impossibility (inconvenience?) of knowing the right answer. Asking students to brainstorm about this sounds like a wonderful assignment.