I adore watching those colorful balloons sail across the clear blue sky. Some people live in areas where they never get a chance to see the beauty of these creatures as they follow the wind while others live in a place that has celebrations where so many fill the sky like stars scattered in the night.
So what maths are used in reference to hot air balloons? If you saw my weekend posters, you've seen two math facts so far, but what other math do hot air balloons use.
Using this site you can find out the measurements and weight for a standard balloon which can then be used in this activity. Although this rubric is actually for student made balloons but with a small adjustment this could be turned into an exercise using the information from the article. It has students find circumference, diameter, volume in inches to feet, weight, and lift potential. There is also enough information to calculate surface area.
For this next one, you will probably end up having to create a worksheet to accompany it but the material in it is great. Overflite has information for calculating the weight of the air and modeling hot air balloon lift. It is full of step by step examples and clear explanations. Its areal life activity and could easily be integrated into a project.
On the other hand, I found a balloon simulator that requires students to take off, fly over to a place where they drop something from the balloon, fly back to the starting point and land. As pointed out by the blog with the information, this is a form of mathematical modeling. It is not just a game because they have to control the burner, watch the altitude, speed, vertical speed, etc just like any pilot. The simulator does require flash to run so it has to be used on a computer or through a site that provides the flash if using an iPad or a android based device.
Even Khan Academy has an eight minute video with a balloon example for the calculus class. So if you are teaching calculus you can slide this in under derivatives. Finally, an upper level example. There is also this 88 page PDF from University of Texas At Austin which looks at hot air balloons, linear functions and linear systems. The first eight or nine pages covers this topic, provides the questions, scaffolding questions and answers so you can easily integrate it into your classroom.
The final link is to the CTE online which has a nice lesson on hot air vs helium balloons. I read this and immediately thought of the mythbusters episode where they used helium balloons tied to a chair to see if they could get the chair to fly with someone in it. That would be a great introduction to this activity.
In this activity, students are going to calculate how much hot air they will need for their balloons and they use a linear equation to help find out how much air they need to lift an object. They calculate the amount of air for a toaster and then extend it to a house. The lesson has everything you need to conduct the lesson from opening to extension to grading rubric. It sounds like fun. One thing is that you might need to join the site to access the lesson but its free and allows you to access all the lessons.
I would like to thank Adam Liss for today's topic. It was a comment he made that inspired this entry because where I live, I never, ever see a balloon in the air.