## Dy/Dan Teacher Prep Academy — Certification Exam Question #42

Turn this infographic by Sean Kearney into an opportunity for critical thinking, data analysis, and mathematical computation for your students.

EC: Extend the activity to the population of Earth.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

1. #### CalcDave

March 24, 2010 - 11:48 am -

The lead-up pictures/videos could be packing people into tight places (clowns in a car, frat boys in a phonebooth, etc.). Those would raise the question of “stuffing people in small volumes,” but then you could pull back from that by showing pictures of packed clubs or concerts or whatever to introduce the concept of “personal space” into the equation. Lead in to typical NYC photos of masses of people crossing the street to lead the question of population densities. Then relate back to the clown-car and to get them to ask how much room would we need to pack a certain number of people “comfortably.”

2. #### Dan Meyer

March 24, 2010 - 1:37 pm -

Yeah, really nice thoughts there. The big question mark hanging over the whole thing for me was the scaffolding of the concept of “population density,” which isn’t a commonplace measurement for K12 students.

3. #### Katie

March 24, 2010 - 2:51 pm -

maybe give them tape measures and ask them to figure out how big their houses/apartments are (give them more specific instructions)? then divide by the number of people living there to get their own house’s pop. density?

then what if you marked out a 800 sq feet somewhere (outside?) and work through calculations together to see that 35,000 people per square mile is about 1 person per 800 sq feet (this sort of ignores the fact that there’s a lot of other stuff in cities besides where people live, maybe as a class you could agree to halve that for living space?)

then you’d have to talk about how people can live on top of each other, how does that change all the stuff we just calculated

maybe the final result is designing a comfortable city (how many skyscrapers – how tall?) to fit everyone into one state?

4. #### Kathy H

March 24, 2010 - 4:59 pm -

IMP 3 has a whole unit on this – how long will it take for each individual in the world to occupy one square foot of land? You’ve got to figure out usable sq miles of land, convert to sq feet, and evaluate linear, quadratic and exponential functions as population predictors. The derivative is introduced along with e. Overall, a good unit. The kids get a little freaked out when I tell them they’re doing calculus by calculating the slope of the tangent line!

5. #### Tom

March 24, 2010 - 6:32 pm -

Looking at the relative population density of their homes vs their schools/classrooms might be a stepping stone to making things more concrete.

6. #### Richard

March 25, 2010 - 5:14 am -

In Detroit this is not as much a hypothetical. As the population shrinks and whole blocks are abandoned, there is some discussion of having some land revert to farmland. Detroit occupies 140 square miles. How much could be “abandoned” to farms?

7. #### Bea Cantor

March 26, 2010 - 10:54 am -

This could be such a cool cross-disciplinary project. So, beyond just people and square miles, what would traffic look like? Garbage collection? Water treatment and distribution? The electric grid? would we lose our accents, or would they become “micro-accents” based on your neighborhood? I can imagine some really interesting short stories coming out of this sci-fi scenario. Social studies would work on how to administer the place. I would imagine laws would have to change, and kids could discuss how and why. Just think of the redistricting issues…Do we draw the line along city blocks, or along city blocks AND up to a certain level in the skyscraper?

8. #### Touzel

April 13, 2010 - 11:45 am -

Kathy, I also immediately thought about the IMP unit “Small World, Isn’t It?” (http://www.mathimp.org/curriculum/AppendixA.html). I haven’t taught Year 3 yet, but I’m really looking forward to it.

I like the implications of the flier. The student conversations would be fascinating. The pros are obvious, but what detriments are there to living together so closely? What about people that don’t like living so densely? How would we protect ourselves from the increased risk of attack (by having such a concise target)? (Sheesh–I sound like I’m from Orange County).

9. #### James Key

June 1, 2012 - 11:12 am -

How do I apply to dy/Dan Teacher Prep Academy? I will pack up all my worldly belongings *right now* to enroll full-time!