Volume of Pyramids

Students will solve the 5 guided practice problems.  GP1-GP4 are purely application problem.  GP5, to me, is the main idea of the entire lesson so this will be an important problem for me to use as a check for understanding.  Students should provide a brief explanation for this problem based on evidence from the previous activity (GP3).

This first 6 problems of this section mirror the first 4 of guided practice.  Students should hopefully progress through these 6 problems quickly and spend more time on the extension questions. 

Question #7 requires students to find two possible sets of dimensions for the base of a rectangular pyramid given its volume and height.  Students need to realize that they are looking for a product of 120.  Once they identify this structure (MP7), they should be able to come up with a variety of missing dimensions.  As students get stuck I will ask:  What is the volume of the pyramid?  What did we learn about the volume of pyramids as related to the volume of prisms?  If necessary, I may even ask for students to tell me the volume of a prism having the same base and height.   

Question #8 requires students to reason abstractly (MP2).  They must be able to work with dimensions in variable form to answer the question.  If students are stuck, I may ask them to describe the volume of the prism based on the information given.  Some students may choose to substitute values for the variables and then solve.  This is also okay.

We will quickly go over the answers to problems 1-6 and spend most of our time discussing various solutions to the extension problems. 

I have set the criteria for success to 3 out of 4 on the exit ticket.  This is with the hope that by this part of the lesson, students can pretty easily solve the first 3 problems.  If students miss one problem, the error is probably not one of a lack of understanding, but a lack of being careful.