SWBAT describe the characteristics of surface area and volume functions and to develop methods to find these functions based on descriptions or on data tables.

What generalizations can you make about these new types of functions? What are the key differences between surface area functions and volume functions?

40 minutes

Today’s lesson is a bit shorter so there is no warm-up. I realized after the first two days of this unit that there was enough depth in the surface area and volume problems to design a whole problem set based on those. There are two levels of the problem set — Surface Area and Volume Functions is the basic problem set, and the Surface Area and Volume Functions Organizer includes the same problems but has data tables provided. The Exceeds Problem Set has some problems that are quite challenging and others that are not as challenging, but it turned out to be very engaging for my most advanced students.

The problems gave students the chance to think in two different ways. Some students generated a data table by drawing many different rectangular prisms that fit the given requirements and filling out each row of the table based on the prism. They were able to look at vertical patterns in the surface area and volume columns and create function rules based on these patterns. Other students jumped straight to the algebraic expressions for each entry in a row, and used algebra to manipulate these to create formulas.

We basically spent the entire day working on this investigation—students just jumped right in. Some students used isometric dot paper to draw the solids, others used interlocking cubes to build the solids, and other students were able to work entirely with pencil and paper. Students were expected to complete the investigation outside of class.

5 minutes