Lesson plan

Lesson 16: Distinguishing Between Surface Area and Volume

teaches Arizona State Standards 6.G.A.4
teaches Common Core State Standards 6.G.A.4 http://corestandards.org/Math/Content/6/G/A/4
teaches Colorado State Standards 6.G.A.4.
teaches Colorado State Standards 6.G.A.2.
teaches Georgia State Standards MGSE6.G.4.
teaches Kansas State Standards 6.G.4.
teaches Minnesota State Standards
teaches New York State Standards NY-6.G.4.
teaches Ohio State Standards 6.G.4.
teaches Pennsylvania State Standards CC.2.3.6.A.1.

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.


  • 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.


  • 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/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.