Lesson plan

# Lesson 16: Distinguishing Between Surface Area and Volume

teaches Common Core State Standards 6.G.A.4 http://corestandards.org/Math/Content/6/G/A/4

# Lesson 16: Distinguishing Between Surface Area and Volume

In this optional lesson, students distinguish among measures of one-, two-, and three-dimensional attributes and take a closer look at the distinction between surface area and volume (building on students' work in earlier grades). Use this lesson to reinforce the idea that length is a one-dimensional attribute of geometric figures, surface area is a two-dimensional attribute, and volume is a three-dimensional attribute.

By building polyhedra, drawing representations of them, and calculating both surface area and volume, students see that different three-dimensional figures can have the same volume but different surface areas, and vice versa. This is analogous to the fact that two-dimensional figures can have the same area but different perimeters, and vice versa. Students must attend to units of measure throughout the lesson.

Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.

Lesson overview

• 16.1 Warm-up: Attributes and Their Measures (25 minutes)
• 16.2 Optional Activity: Building with 8 Cubes (25 minutes)
• There is a digital applet in this activity.
• 16.3 Optional Activity: Comparing Prisms Without Building Them (20 minutes)
• Includes "Are you Ready for More?" extension problem
• Lesson Synthesis
• 16.4 Cool-down: Same Surface Area, Different Volumes (5 minutes)

Learning goals:

• Comprehend that surface area and volume are two different attributes of three-dimensional objects and are measured in different units.
• Describe (orally and in writing) shapes built out of cubes, including observations about their surface area and volume.
• Determine the surface area and volume of shapes made out of cubes.

Learning goals (student facing):

• Let’s contrast surface area and volume.

Learning targets (student facing):

• I know how one-, two-, and three-dimensional measurements and units are different.
• I can explain how it is possible for two polyhedra to have the same surface area but different volumes, or to have different surface areas but the same volume.

Required materials:

• snap cubes
• sticky notes
• geometry toolkits

Required preparation:

• Prepare solutions to the first question of 1-2-3 Dimensional Attributes activity on a large visual display.
• Prepare sets of 16 snap cubes and two sticky notes for each student.

Glossary:

• 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 units$$^3$$, because it is composed of 3 layers that are each 20 units$$^3$$.

• Access the complete Grade 6 glossary.

Standards

• This lesson builds on the standards:CCSS.3.MD.C.5MS.3.MD.5CCSS.4.MD.A.1MS.4.MD.1CCSS.5.MD.CCCSS.5.MD.C.3.bMS.5.MD.3bCCSS.5.MD.C.4MS.5.MD.4CCSS.5.MD.C.5.aMS.5.MD.5aMO.3.GM.C.9MO.4.GM.C.6aMO.5.GM.B.4bMO.5.GM.B.5MO.5.GM.B.4a

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.