This activity will have students dynamically change the shape of a right triangle, collect data, and investigate the relationships between the altitude drawn to the hypotenuse and other segments in the triangle.
Before the Activity
The teacher should review how to find the arithmetic mean between two numbers. This will be compared to finding the geometric mean between two numbers after the activity.
During the Activity
The teacher will need to guide some students through finding the model for the scatterplot(s). One model uses y = sqrt(x) while the other uses y = x^2. The teacher may need to model and demonstrate how these are related to each other.
After the Activity
Have students complete finding the geometric mean from various problems sets on worksheets or in textbooks of your choosing.