>>How was it built and measured out?

By hand, believe it or not. Outer arc measured with a transit and laser range finder, everything else involves lining up premeasured chains.

Your answer, btw, does not match the year for the image. (The red arrow points at my art project that has far outlived my attendance at the event.)

Sorry if this doesn’t help the math at all.

I’m pretty sure the image is from 2010. It probably says a lot about my geek level that I can recognize individual camps from that.

For verification, the base of the central sculpture is different each year, and the shadows from your image match up with the shadows from here.

The difference in actual population between the two years is about 20%, so it actually matters, depending on how accurate you want your guesses to be.

@ColinGraham: I find it funny how you and I did not use any circle math to do our estimates (all regions are equal in our world). I was at about 60 000 people, a bit over! I did not think that finding a precise formula was more important than finding the right number of people per meter (or your favorite area unit).

Do most people solving this problem just guess the number of areas and the number of people per area?

Anybody got better results with a different formula?

For example, let’s say that you have your formula and you just adjust the number of people per meter , we could see who got the best formula in the classroom?

Would it be pertinent to then ask students “who got the best formula” instead of “who got the best people per meter estimate”?

Carl

Since my class had fun being challenged by the area of the Pentagon problem in one of Dan’s slides, I would also ask as a challenge problem for those who finish first… Based on our estimate, what is the maximum number of people who could camp inside the pentagon.

There might be some interesting images of ultra crowded festivals that we could show for fun too.

“”the largest region looks at least 250% bigger than the smallest region.””

Ayup.

The question that the city planners still can’t answer is:

“If the ring roads are 200 ft apart, how much error is there in modeling the blocks as rectangles?”

(And the people who deal with the resulting chaos can’t answer whether the error stays the same or changes as you go further out)

Of course, any classroom will have students who have a wide range of skills. Some students will have high visual intelligence, but some of us will have great difficulty interpreting a complex picture. How would you teach the rest of us how to read a picture in a math class?

Ok, some points…

The burning man was the third of three WCYDWT examples that Dan pushed us through. Knowing, I hope, a little about how Dan thinks, I abandoned my actual knowledge and tried to put myself in the situation of the average 15 yo in a maths class in the UK – not an easy task for maths teachers to do, and we need to remember this!

@Carl I worked on the basis that it would be possible to come up with a reasonable estimate based on treating each of the defined areas as being rectangles or, at least, as being of equal area, since I think most students would make the same assumption. I submitted my results based on this (incidentally none of the other participants did this, so I am not going to get defensive because I have nothing to compare myself against!).

@Dan Yes, I did adopt a “Fermi” approach, if you want to give it that particular label but, in the 4 or 5 minutes we had, I did not consciously think: “Ooh, I can apply a Fermi approach here…”, I just thought “OMG, I have 5 minutes to give this maths teacher geek an answer that doesn’t make me look like a complete moron…” OK, slight exaggeration! And I did at least go as far as qualifying my answer in terms of crowd density, which many/most students would not even bother about…. ;-P

I knew nothing about the burning man, I also knew nothing about the ESPN ‘football’ baby we looked at earlier, as our first problem…. In the UK, football could be rugby or soccer, and rugby could be rugby union or rugby league… This is nteresting from the point of view of other cultural issues that have been raised elsewhere. Is the number of cones on a dancer’s skirt something of cultural significance to me…? No. It’s just another arithmetic/algebra problem, therefore there is no cultural interference… Hmm.

As a maths teacher, would I want to go back and investigate the idea that each of the segments/sectors I assumed in my calculation was of equal size? Yes. Is it important for students to do this in a ‘rough guess’ scenario? No. Does it bother me that I couldn’t give a more exact answer based on using geometric formulae for calculating the areas of each of the individual segment? Yes, but we didn’t have time to do that and, as Barb pointed out, why not just ask the people who sold the tickets how many were there…? Pseudocontext? ;-P

Did I make a comment about the segment at 6 o’clock in the picture being circular, and so disrupting the equilibrium? Yes, but Dan edits the conversations, to distill the essence of what is important about the problem, for his blog entries, which is legitimate, but some of the comments people make here in response to Dan’s blog were already covered in the live session.

What I think is important about these types of “guess the answer” problems is that the majority of students should be within a certain percent, or order of magnitude, when they do the “back of the envelope” calculations. The application of some ‘logic’ to narrow down the crazy maximum and minimum answers is what needs to be identified and, in my view, taught or encouraged.

It’s interesting that we never discussed what would be reasonable or unreasonable answers in any of the three problems we did together, apart from a brief exploration with the “football baby”. “Reasonable” here was very much teacher-led = Dan. Is 60,000 way too high or a near miss for the burning man? How about 25,000… too low? How about challenging assumptions, what effect does that have on calculations? There is a lot of opportunity for exploration here beyond the session we had together.

In the 40 minutes we had with Dan, we went through 3 problems. Not everyone got their calculations right or close or in time, but I’d like to think we all came away with a better understanding of two things: how students might approach this type of problem; and, not everyone gets their “back of the envelope” calculations right under a time constraint (do they, Dan? ;-P )

Colin

@Dan I hardly think this photo was taken at midnight on Friday… whatever hardened attendees might attest…

Yahoo! With this “fix”, 60,000 was not too far :-)

@Dan is it useful to get the students immersed in the scenario with a video, for example:
http://www.youtube.com/watch?v=p9W6uX2AFTI

@Colin Sorry for the meter typo. I’m Canadian, we work with… both units all the time ;-)

“Yes, but we didn’t have time to do that and, as Barb pointed out, why not just ask the people who sold the tickets how many were there…? Pseudocontext? ;-P”

As soon as it becomes truly interesting for the targeted students, I guess the job is done. They could use a web browser and just find the number, but they would not be too *impressed* by that path.

@Dan can we limit the resources of the students? Can students “pretend” if it’s interesting enough to not take the easy path?

Carl

Since the biggest region is about 250% bigger than the smallest… I would want my students to estimage using the size of the middle regions. After that, making this an area problem in the geometry would be where I would be taking it.

Sorry, I am new to following these posts. What does WCYDWT stand for? Great mathematical discourse problems!

I haven’t read all comments, but in just browsing I didn’t see anyone mention where my class ended up taking this. But before I get to that…

I’m hooked. It took me a while to get hooked on this WCYDWT idea, but I officially am. Probably because it took me a while to actually administer a WCYDWT lesson somewhat correctly. Which didn’t happen until the last period of geometry on Friday. Which brings me to…

We squared a circle (circumscribed a square around a circle and used the radius of the circle to find the area of the square). Then pentagoned the circle, then hexagoned the circle, then octagoned, and so on. Eventually the kids see that a regular polygon with an infinite amount of sides is a circle, which is pretty cool because pi gets developed.

So Burning Man was awesome for us. The circle was pentagoned, and even though we didn’t go that route they still recognized the shapes and the beauty of the picture. My first geometry class found out how many people they thought were in the campsite. They didn’t even come close. My second geometry class got much closer. Then it hit me. “How much space do you think those 75,000 people (their estimate) would need to be comfortable?” “Here’s a square foot of space. How much space do you think 75,000 people would need?”

And they were off. Arguing and coming up to the board and drawing and arguing some more. Their guesses weren’t even close (I think the highest guess was 1,000,000 sq ft, when it turned out that the campsite portion of Burning Man was actually 42 mil or something like that). But they found the square footage of the campsite and loved doing it. I even videotaped one of my students, a former drug addict, saying, “I LOVE GEOMETRY!”

Further extensions to come…given the square footage allotted per person at Burning Man 2010, how many people would comfortably fit at the campsite if the “C” were extended to be inscribed inside the pentagon?