This is part of a series of posts I’m doing on math in the real world.
The first question I thought of when I saw these balloons in my colleagues office was, how many of those would I need to be able to float? Clearly, this is a math problem, and one students can actually test themselves (I would recommend using inert ballast to test student guesses, rather than actual students). Students would first have find out the amount of weight one balloon can lift, and then use division to determine how ballons would be required to lift their weight.
If you want to make this problem much more complicated (and more of a calculus problem), you would point ouf that the density of air decreases as the balloon lifts, lowering its buoyancy, and putting a limit on how far the balloons will actually lift the student.
The shape of the balloons in this picture is also mathematically interesting, as is the shape of other balloons. Why do balloons form the shape that they do? How do the manufacturers of balloons know in advance what shape the balloons will have before they fill them up with helium?
Shawn Urban says:
Oh, come on. You know some of your students are going to try to float themselves. Aren’t we all about engagement?
I like your extension of the question into calculus. So often we seek authentic examples of calculus use that students would recognize and be curious about. I bet after playing with balloons outside, Grade 12s would be in the flow trying to calculate how the balloons behave as their buoyancy changes.
And an interesting extension into balloon shape and manufacture. I would really like to know how the material of the balloon is manipulated to create different shapes. I suspect that calculated material thickness or surface tension is engineered into the balloons, yet another great calculus and research question.
One could also go further and compare balloons of different “sizes” as well, so leading, along with different balloon shapes, to topics of similarity and congruence.
Nice post. Thanks.
September 27, 2011 — 7:09 pm
Chris says:
Thanks for this David. I’ve been trying to figure out how to use this particular video in my classroom http://www.youtube.com/watch?v=nNyzwnQ2Qe8 but yours is a much better experiment I think.
One thing I want to do next year in my Math classes is to introduce Math experiments and this will be a great one. I don’t think we should leave the experiments to science anymore!
Cheers,
Chris.
PS. People interested in this sort of stuff should checkout the following video. I asked my Principal if we could do this experiment 🙂
http://www.youtube.com/watch?v=wtXquYhY7wo
September 27, 2011 — 8:36 pm
David Wees says:
I’ve seen both of those videos! Yes, I agree, they are very interesting to watch. The creativity of people never ceases to amaze me. I’ve done quite a few math experiments in my class over the years. I should probably write them up at some point.
September 27, 2011 — 10:29 pm
Annie St-Pierre says:
Reading your post, I tought about Pixar’s Up, and the experiment that National Geographics did:
http://www.wired.com/wiredscience/tag/pixar/
and
http://gizmodo.com/5778006/the-house-from-up-has-been-built-in-real-lifeand-it-flies
That had “wow” me… I suspect it might do the same with students 🙂 And there’s a lot of good math in that … maybe an extension to your floating student challenge?
(p.s. Sorry if I did mistakes, writing in english… I usually write in french.)
September 28, 2011 — 9:14 am
David Wees says:
Those look like a couple of great resources. Yes, we could look at making anything float! Figuring out how many balloons we would need to lift a house would be very interesting, as it would require students to do some pretty serious research, both into the weight of a house, but also potentially into the structural strength so that the house can be lifted without being destroyed in the process.
Thank you for sharing.
September 28, 2011 — 11:43 am