# 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 real-world 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 real-world situation, and justify (orally) the decision.
• Estimate measurements of a prism in a real-world situation, and explain (orally) the estimation strategy.

### Student Facing

Let’s work with surface area and volume in context.

### 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.

### Student Facing

• I can decide whether I need to find the surface area or volume when solving a problem about a real-world situation.

### 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 three-dimensional 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 cm2, then the surface area of the cube is $$6 \boldcdot 9$$, or 54 cm2.

• volume

Volume is the number of cubic units that fill a three-dimensional region, without any gaps or overlaps.

For example, the volume of this rectangular prism is 60 units3, because it is composed of 3 layers that are each 20 units3.