Teaching Volume of Rectangular Prisms in 5th Grade

Mastering finding the volume of rectangular prisms is an important part of a student’s progression through geometry. It’s a skill that combines multiplication, spatial reasoning, and real-world problem-solving.

This blog post outlines a step-by-step progression for teaching this concept, along with engaging volume activities and resources to support your lessons.

Step 1: Exploring Volume with Unit Cubes

Begin your unit on teaching volume by using unit cubes. Unit cubes give students a hands-on way to explore volume. Unit cubes help students visualize how volume measures the space inside a three-dimensional shape.

Give students practice using examples with rectangular prisms completely filled with unit cubes, and prisms only partially filled. This gives students the opportunity to visualize how volume is built up within each prism.

• What Students Learn:
  • The concept of volume as the total number of unit cubes that fit inside a rectangular prism.
  • How to count unit cubes to calculate volume.
• Why This Step is Important: Using unit cubes builds a strong conceptual foundation and allows students to physically manipulate the shapes they’re measuring.

Teaching Tip: Provide students with rectangular prisms made of interlocking cubes. Have them count the cubes to determine the volume and discuss how the layers are formed.

Step 2: Introducing the Volume Formulas

Once students are comfortable with unit cubes, begin to start teaching volume formulas for calculating volume.

Start with the formula Base x height (B x h). Students find the area of the base (B) by multiplying the length and width of the prism’s base.  Then, students multiply the base area by the height of the prism to get the total volume.

Next, introduce the formula length x width x height (l x w x h). Multiplying the length by the width is essentially finding the area of the base of the prism. Students then multiply by the height to get the total volume of the prism.

• What Students Learn:
  • How to use the two volume formulas to calculate the space inside a rectangular prism.
  • The relationship between multiplication and volume.
• Why This Step is Important: The formula simplifies volume calculations and prepares students for more complex volume skills, like finding the additive volume of composite figures.

Teaching Tip: Give students a volume and have them come up with all of the possible combinations that could create that volume. For example, a prism with a volume of 60 square cm could have dimensions of: 2 cm by 10 cm by 3 cm, or 4 cm by 5 cm by 3 cm, or 15 cm by 2 cm by 2 cm.

Step 3: Solving for a Missing Dimension

The third skill students should learn to be able to master volume and rectangular prisms is solving for a missing dimension when the total volume and two side measurements are given. This skill reinforces students’ understanding of the relationship between dimensions and volume.

To find a missing dimension, divide the total volume by the product of the two known dimensions. For example:  The total volume is 300 square inches. The length is 10 inches and the width is 5 inches. To find the missing side length, divide 300 by 50 (the product of 10 x 5) and you will get 6 inches.

• What Students Learn:
  • Rearrange the volume formula to solve for a missing side:
  • Apply problem-solving strategies to work backward from the given information.
• Why This Step is Important: Solving for a missing dimension builds algebraic reasoning and prepares students for more advanced math concepts.

Teaching Tip: Use real-world examples, like finding the height of a storage box when given the base area and total volume. Encourage students to check their work by recalculating the volume with their solution.

Fun Activities for Teaching Volume in Your Classroom

Here are some engaging activities to make volume practice fun and effective in your classroom:

Mysteries:

Students will love being able to solve a mystery as they work through volume task cards in the Math Task Card Mystery, “Mystery of the Vanishing Chips”.

Games:

Kids love working together and playing games. Use a board game, like the one shown below, and a set of volume question cards to get students excited to work together while practicing finding volume.

Matching Puzzles:

Use a matching puzzle, like the one show below, to help students connect volume with its equivalent visual representation. Perfect for math centers or small groups!

Volume Worksheets and Quizzes:

Use worksheets and Google Forms as a way to give students extra practice or to use as formative assessments throughout your unit. This is a great way to give your students test prep throughout the year.

Why Teaching Volume Matters

Learning to calculate the volume of rectangular prisms is an important math skill. By progressing through unit cubes, formulas, and advanced problem-solving to find missing side lengths, students gain confidence in this foundational geometry concept.

Explore the resources linked in the photos above to enhance your lessons, and watch your students get excited to develop a strong understanding of volume!

You can see all of my resources and activities for teaching volume HERE.