Our friend Alan D-S. asked us a great question: how many buildings are there in the world? And he means everything from teepees to skyscrapers. Well, no one has made a nice neat list of buildings for the whole world. Some countries count them up, while others don’t; even inside the countries who do, it’s usually cities and towns who keep track. But we can use math to make a good guess. The more people stuffed into a town, the more buildings they need – except when it gets so high that lots of people live in one tall building. Out on farmland there might be just 1 building every square mile, but in New York City, one street block 1/20 of a mile wide might have 20 buildings crammed into it. If we run the numbers, we can find a guess at least for the U.S. Just remember that might not work everywhere: we’re pretty sure Antarctica has more penguins than buildings!

*Wee ones:* Look at your home from the outside. Is it taller than it is wide, or wider than its height?

*Little kids:* How many people live in the building you call home? Talk about it with a grown-up! *Bonus:* If a building has 7 floors with 10 people living on each, how many people live there?

*Big kids:* If a square city block has 5 buildings on each edge, how many buildings are on the whole block? (Remember, the corner buildings each sit on 2 sides!) *Bonus:* If 100 people live in each, how many people is that?

*The sky’s the limit:* The U.S. covers about 3,800,000 square miles, and about 1/3 of it has no people. If 1,000,000 have 1 building each square mile, another 1,000,000 have 4 buildings each, and the last 500,000 average 30 buildings each, how many buildings do we have? See if you can remember all the parts!

Answers:

*Wee ones:* Different for everyone…an apartment building is taller than wide, but a house (like a ranch style) could be wider than tall.

*Little kids:* Different again…count just your family for a single-family home, but an apartment building will have many more. *Bonus:* 70 people.

*Big kids:* 16 buildings, since each side adds 4 new ones. Another take: 5 on a side means 2 corner buildings and 3 middle ones; you have 4 of those sets of 3 plus the 4 corners. *Bonus:* 1,600 people.

*The sky’s the limit:* 20 million buildings (1 + 4 + 15). That could be low, as one site says we have more than 5 million office buildings only. Also, New York City has about 1,000,000 buildings for 8 million people; the U.S. has at least 40 times as many people, which would give us 40 million buildings for all of them.

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.