This picture was found at http://travelsinphotography.com/blog/2012/09/09/crown-of-maine-hot-air-balloon-festival/.
A possible math problem students could be asked relating to this picture is build a model that best fits the relationship between the hot air balloons.
This picture aligns with the following CCSS:
Write a function that describes a relationship between two quantities.*
To solve this problem, students will be given a scale in which dictates the scale from centimeters to meters and then use centimeters to meters to explain the real life formula that would best describe the relationship of the hot air balloons. Then, students will use this scale to draw on their picture a quadrant. Once the quadrant has been drawn, to scale, where one centimeter is equal to a one by one square on the graph, students can then use their knowledge of plotting points to find the x and y coordinates of each of the hot air balloons. At this point, the teacher should also make sure the picture should be in the first quadrant, because both x and y are positive. After the points for each of the hot air balloons has been found, students can their use their knowledge of function models to find the model which best fits the data. Students can use the picture as a resource to draw the “best fit model” and then use their graphing calculator to accurately find the model that best fits describes the relationship the hot air balloons have to one another.
Having students create their own coordinate graph, students are using their prior knowledge of graphing points and finding models that best fit the data in a real life situation. Having a connection to how these applications can be used in real life allow students to take a real life situation, create a ratio problem to decrease the real life numbers to a model, find the function that best fits the data, and then be able to explain what that function model means in regard to the data. Allowing students to see functions in real life and be able to understand how functions explain relationships between quantities.
Another problem the students can solve is figuring out the angle at which the balloon is raised from the ground. The students can make a right-angled triangle and use, CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, to figure out the angle.