This activity is an occasion for creative and intuitive thinking about the areas of curves, that could be the opportunity for the learning of Reimann Sums and definite integrals.
Students often find the interpretation of graphs extremely difficult – this has been shown in research and from many stories of interviews with college students and with younger students.
In this activity we invite students to conduct their own version of Galileo’s experiment, enabling them to use derivatives as rates and to consider the differences between average and instantaneous speed.
How do you find the area under a curve? What about the length of any curve? Is there a way to make sense out of the idea of adding infinitely many infinitely small things?