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# More Surface Area and Volume Functions

Lesson 3 of 10

## Objective: 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.

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

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.

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Surface Area and Volume Functions
- LESSON 2: More Surface Area and Volume Functions and the Painted Cube Problem
- LESSON 3: More Surface Area and Volume Functions
- LESSON 4: Multiple Representations of Surface Area and Volume Functions
- LESSON 5: Cubic Function Data Tables
- LESSON 6: Graphs of Cubic Functions
- LESSON 7: Roots and Graphs of Cubic Functions
- LESSON 8: More Cubic Function Graphs
- LESSON 9: Cubic Functions Practice Quiz and Review
- LESSON 10: Cubic Functions Summative Assessment