Calculus can be quite interactive when applied to the real world. Educators should find unconventionally shaped objects in the class or around the school, such as a modern art sculpture and send the students to it. The assignment for the students is to find the area of the object. Since the objects are not regular geometric shapes, students will learn the importance of integrals in Calculus.
Educators will need a loaf of bread for this activity. The purpose is to show students why they must take cross-section slices to compute volume. The loaf of bread should have slices that are all about the same width. Students can then look at the cross sections (each slice of bread). The educator should explain the need to compute the area of the face of the slice in order to find its volume and that the area of the face of each slice depends on where in the loaf the cut was made. The students should then find the volume of each cross section.
Educators can recycle cans to use for a hands-on calculus activity. Make sure to collect a variety of cans with different heights and radii. Students can have the cans on their desks. The students will observe that since the walls of the cans have a thickness to them. Using the cans, the educator should help the students see that they must find the inner and outer radii to find the volume of the inner cylinder and the outer cylinder to find the volume of the can shell itself. Students will then complete these computations to find the volume of the can shell.
This activity is pertinent to Christmas time. The students can come up with calculus songs that tell of certain lessons and the songs must be to the tune of Christmas carols. The class can then walk around the school singing Calculus Carols to the other math classes in the school. For example, the original carol "Twelve Days of Christmas" can be turned into "Twelve steps of Integrals."