Distinguishing Between Surface Area and Volume

10 min

Teacher Prep
Setup
A quick review of metric and standard units of measurement and of how different units are used to measure attributes of objects. 4–5 minutes of quiet think time, followed by a partner discussion. Prepare to display the answers for all to see.
Required Preparation
Prepare solutions to the first question of the 1-2-3 Dimensional Attributes activity on a large visual display.

Narrative

This activity strengthens students’ awareness of one-, two-, and three-dimensional attributes and the units commonly used to measure them. Students decide on the units based on the attributes being measured and on the size of the units and how appropriate they would be for describing given quantities.

As students work, select a few students to share their responses to the last two questions of the activity (on the quantities that could be measured in miles and in cubic meters). 

Launch

Consider a quick review of metric and standard units of measurement before students begin work. Include some concrete examples that could help illustrate the size of each unit. 

Then, pick an object in the classroom for which surface area and volume could be measured (for example, a desk). Ask students, “What units might we use to measure the surface area of the desktop? What units might we use to measure the volume of a drawer?”  

Clarify the relative sizes of the different units that come up in the conversation. For instance, discuss how a meter is a little over three feet, a yard is three feet, a kilometer is about two-thirds of a mile, a millimeter is one tenth of a centimeter, and so on.

Give students 4–5 minutes of quiet think time and then a couple of minutes to share their responses with a partner. Prepare to display the answers to the first six questions for all to see.

Student Task

For each quantity, choose one or more appropriate units of measurement.

For the last two, think of a quantity that could be appropriately measured with the given units.

Quantities

  1. Perimeter of a parking lot:
  2. Volume of a semi truck:
  3. Surface area of a refrigerator:
  4. Length of an eyelash:
  5. Area of a state:
  6. Volume of an ocean:
  7. ________________________: miles
  8. ________________________: cubic meters

Units

  • millimeters (mm)
  • feet (ft)
  • meters (m)
  • square inches (sq in)
  • square feet (sq ft)
  • square miles (sq mi)
  • cubic kilometers (cu km)
  • cubic yards (cu yd)

Sample Response

  1. Meters, feet
  2. Cubic yards
  3. Square inches, square feet
  4. Millimeters
  5. Square miles
  6. Cubic kilometers, cubic yards
  7. Sample responses: distance between home and school, length of a river
  8. Sample responses: volume of a room, volume of a swimming pool
Activity Synthesis (Teacher Notes)

Display the solutions to the first six questions for all to see and to use for checking. Then, select a few students to share their responses to the last two questions.

Ask students what they notice about the units for area and the units for volume. If not already mentioned by students, highlight that area is always measured in square units and volume in cubic units.

Anticipated Misconceptions

Depending on the students’ familiarity with metric and standard units, there may be some confusion about the size of each unit. Consider displaying measuring tools or a reference sheet that shows concrete examples of items measured in different-sized units.

Standards
Building On
  • 3.MD.5·Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • 3.MD.C.5·Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • 4.MD.1·Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. <em>For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …</em>
  • 4.MD.A.1·Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. <span>For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs <span class="math">\((1, 12)\)</span>, <span class="math">\((2, 24)\)</span>, <span class="math">\((3, 36)\)</span>, …</span>
  • 5.MD.C·Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
  • 5.MD.C·Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.