Lesson 15
Distinguishing Volume and Surface Area
Lesson Narrative
This is the first of two lessons where students apply their knowledge of surface area and volume to solve realworld problems. The purpose of this first lesson is to help students distinguish between surface area and volume and to choose which of the two quantities is appropriate for solving a problem. They solve problems that require finding the surface area or volume of a prism, or both. When they choose whether to use surface area or volume, they are choosing a mathematical model for the situation and engaging in MP4.
Learning Goals
Teacher Facing
 Compare and contrast (orally and in writing) problems that involve surface area and volume of prisms.
 Decide whether to calculate the surface area or volume of a prism to solve a problem in a realworld situation, and justify (orally) the decision.
 Estimate measurements of a prism in a realworld situation, and explain (orally) the estimation strategy.
Student Facing
Let’s work with surface area and volume in context.
Required Materials
Required Preparation
Make 1 copy of the Card Sort: Surface Area or Volume blackline master for every 2 students, and cut them up ahead of time.
Learning Targets
Student Facing
 I can decide whether I need to find the surface area or volume when solving a problem about a realworld situation.
CCSS Standards
Addressing
Glossary Entries

base (of a prism or pyramid)
The word base can also refer to a face of a polyhedron.
A prism has two identical bases that are parallel. A pyramid has one base.
A prism or pyramid is named for the shape of its base.

cross section
A cross section is the new face you see when you slice through a threedimensional figure.
For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.

prism
A prism is a type of polyhedron that has two bases that are identical copies of each other. The bases are connected by rectangles or parallelograms.
Here are some drawings of prisms.

pyramid
A pyramid is a type of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.
Here are some drawings of pyramids.

surface area
The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.
For example, if the faces of a cube each have an area of 9 cm^{2}, then the surface area of the cube is \(6 \boldcdot 9\), or 54 cm^{2}.

volume
Volume is the number of cubic units that fill a threedimensional region, without any gaps or overlaps.
For example, the volume of this rectangular prism is 60 units^{3}, because it is composed of 3 layers that are each 20 units^{3}.