Unit 1, Lesson 16
Distinguishing Between Surface Area and Volume (Optional)
Grade 6
Preparation
Lesson Narrative
This optional lesson reminds students of the distinctions between measures of one-, two-, and three-dimensional attributes. It reinforces 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.
Students take a closer look at the distinction between surface area and volume. They build or draw representations of polyhedra and then calculate both the surface area and volume. In doing so, 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. Throughout the lesson, students practice attending to precision (MP6) as they consider the geometric attributes being studied and the corresponding units of measurement.
- 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.
Let’s contrast surface area and volume.
Required Preparation
Prepare solutions to the first question of the 1-2-3 Dimensional Attributes activity on a large visual display.
Prepare sets of 16 snap cubes and two sticky notes for each student.
For the digital version of the activity, acquire devices that can run the applet.
Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.
This rectangular prism has 3 layers that are each 20 units3. So, the volume of the prism is 60 units3.