Students use balls and disks to prove the general formulas for sums of squares and cubes.
Tongta Somchaipeng, Tussatrin Kruatong, and Bhinyo Panijpan
Emiliano Gómez and Risa A. Wolfson
In this activity, students gradually fill bottles of different shapes and graph the water level (height) versus the volume of water inside the bottles. Then they explore the relationship between the shape of a bottle and the resulting graph.