MATH Concepts and Skills: Collect, Organize, and Interpret Data Trigonometry,Graphing,Measurement,Estimatio

MATH ACTIVITIES
Prior to the balloon launch day, the students should understand the trigonometry ratios of sine, cosine, and tangent. It would be helpful if, during the trigonometry unit, each math class had one period out of doors to estimate the heights of and then use the theodolite (or clinometer) and measuring tape to measure the heights of such objects as the school building, a flag pole, a tree, and a utility pole.

Each student group of two should record the name of the object, the estimate of the object’s height, the angle reading from the theodolite, and the distance they were standing from the object when they took the reading. The students should use their calculator to multiply the tangent of the angle times the distance from the object to find the height of the object.

On the day of the launch the launching team will record three measurements on the data sheet that is in their plastic balloon bag. The launching team will use the theodolite and record the measure of the angle at the highest height of the balloon. They will also record the time that the balloon left the adult launchers’ hands and the time the balloon-catchers caught the balloon.

After the launch, the launching team will determine the balloon flight’s height and length of time in the air using the data collected at the launch. Then all data sheets will be handed in to the math teacher. After compiling the data, the teacher will distribute a master list of the heights and times of flights of each (identified by number) balloon.

From this master data sheet each student will complete such tasks as:
* Determine the mean, median, mode and range of the heights of the flights.
* Make a bar graph of all of the balloon heights including title, label (and unit if
necessary) for each axis, and appropriate intervals.
* Include a paragraph that explains what the bar graph tells the reader.
* Make a box and whiskers chart of the balloon heights.
* Include a paragraph that explains what the box and whiskers chart tells the
reader.
* Make a circle graph of all the balloon heights.
* Include a paragraph that explains what the circle graph tells the reader.
* Make a scatterplot of the balloon heights over balloon times.
* Draw a trend line, if possible, and in a paragraph explain what the trend line
represents.

Note: If weather conditions were such that the tangent could not be used to determine the height of the balloon, the time of the flights could be used for several of the above tasks. You might also ask the students to write a paragraph addressing the following questions:
* Are you able to calculate the height of your balloon?
* What information do you need to perform the calculation?
* Why do you not have the necessary information to perform the calculation?
* How would you change our balloon launch day in order to insure that all
necessary data is collected accurately and reliably?
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MATH