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?