1. Hot Air Balloons

2. History 220-280 ad China Military Lanterns
Lisbon, Peru First Documented
Paris, France First Manned
1950’s United Kingdom First Successful Flight
Japan to Canada Longest 4767 miles
Bombay, India Highest feet

3. Balloons versus Blimps or Zeppelins

4. How does a Hot Air Balloon Work?
Hot air balloons are based on a very basic scientific principle: warmer air rises in cooler air.
Essentially, hot air is lighter than cool air, because it has less mass per unit of volume.
A cubic foot of air weighs roughly 28 grams (about an ounce).
If you heat that air by 100 degrees F, it weighs about 7 grams less. Therefore, each cubic foot of air contained in a hot air balloon can lift about 7 grams.
That's not much, and this is why hot air balloons are so huge -- to lift 1,000 pounds, you need about 65,000 cubic feet of hot air.

5. Physics of Ballooning

6. Components of a Hot Air Balloon

7. Piloting a Balloon http://science. howstuffworks. com/hot-air-balloon2

8. .
Jacksonville, Florida is approximately 12 feet above sea level. A hot air balloon takes off from Jacksonville to travel to Tampa, Florida. The balloon's position measured over time is modeled by the following formula.

9. Calculus Exemplars
What is the initial velocity? …..the initial height?
Sketch a complete graph of the balloon’s position over time.
When does the balloon reach a maximum height?
When does it reach the ground?
Where is the balloon positioned after 2 minutes?
Find the average rate of change for the first 2 minutes.
What is the instantaneous rate of change at 2 minutes?

10. What could you ask?
Based on your NCSCOS objectives, how could you use the story of the hot air balloon to ask questions from K through 12 mathematics? Write an exemplar, solve it , and create a rubric to assess the necessary mastery.

11. Resources http://www.howstuffworks.com/hot-air-balloon.htm