Cavalieri's Principle Manipulative

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Students will be learning about Cavalieri’s principle which states that if two solids have the same altitude and the cross section parallel planes are equal, then the volumes of the two solids are equal. Since this is a difficult topic for students to understand, the best way is for them to learn it using 3D objects. Students will be in small groups, no bigger than 4, and will be given six 3D shapes. They are to first examine the shapes and pair them according to what they believe has the same volume. Then they are to find the volumes of each shape to see if they are correct. To do this for some pieces they may need to find partial volumes and add them together. Have students take notice to the altitudes of pairs and ask them if they are the same, then have them find the area of the bases. Finally, use the volume formula for general prisms to see if they get the same volume for the figure. Once they make that connection explain Cavalieri’s principle.