Teaching volume of rectangular prisms typically begins in 5th grade, then extends in 6th to prisms with fractional edge lengths. I have included activities and lessons at both levels. All activities and printables listed are free except for the one extension project noted.
A free 5th grade unit plan for volume is available in PDF form from the Santa Ana Unified School District. This includes preassessment, math talk, 4 complete lessons, unit reflection and summative assessment.
A free 5th grade Georgia Standards of Excellence complete unit on volume and measurement is available here. It includes Big Ideas, Essential Questions, Concepts and Skills, Terms and Symbols, Strategies for Teaching, Tasks, and an Intervention Table.
Introducing Volume With Cubes
I begin teaching volume by letting students free build a variety of sizes of rectangular prisms with connecting cubes, either centimeter cubes or unifix cubes. As they build, I ask them how many blocks they think they used in their structure, and how they could check. The first time I did this, a student amazed me by immediately figuring out the formula for volume. “If it was a rectangle it would be length x width, but this also has height!” she said. Then her whole face lit up- “Is that why it’s called 3D? Length and width and height! I never thought of that! Would we multiply length times width times height?” I suggested we check on the different structures and see if it worked. It was true discovery based learning.
If the students you work with don’t figure it out on their own, you would guide them to count the cubes and record the length, width, height, and volume.Challenge them to build different prisms that have the same volume (use different numbers of cubes.) Jennifer Findley has instructions and free printable recording sheets and mini posters for this activity here (aligned to 5th grade standards.)
Better Lesson has a 5th grade lesson plan for Discovering Volume using cubes.
Teaching With Tiffany has a free option made for a math center for printable volume tasks using cubes. (5th grade aligned)
In a now deleted article, Scholastic suggests asking students if they can find the volume of a shoe box using Unifix cubes.It gives these instructions: “Line the bottom of the box with cubes. How many cover the bottom? What is the area of the base of the box? Now ask how many layers they will need to fill the box. Let students experiment in small groups. Some will want to fill the box entirely with cubes to find the volume, while others may realize they only need to find the height of the box in cubes and multiply it by the area of the base.”
Exploring Volume, from K-5 Math Teaching Resources, has students cut out and assemble nets, then find the volume of the resulting boxes by filling with centimeter cubes.
Extending to 6th grade standards for volume
The Curriculum Corner has free resources for teaching volume at 6th grade standards using unifix cubes including anchor charts, notebook inserts, practice, exit tickets, and task cards.
This sixth grade lesson “How Much Can It Hold?” from CPalms extends understanding of volume of rectangular prisms to using the formula to determine volume of prisms with fractional edge lengths.
Munchy Math Snacks is another activity for 6th/7th graders using fractional edge lengths. Students will create their own mini, regular, and large snack boxes.
Practicing Volume
After working with counting cubes, the next step, also described by Jennifer Findley in her above post, is measuring different boxes with rulers and finding their volumes. It is so important to do this multiple times with real boxes of different sizes before jumping to have students calculate volume just from drawings with measurements. You want them to fully understand the 3D aspect in a physical way.
In another idea from Scholastic on a now deleted article, you can also “introduce the idea that solid containers aren’t the only ones with capacity” by having students soak sponges in water and then squeeze into measuring containers, even measuring the volume before and after squeezing.
What’s the Volume? free printable cards from K-5 Math Teaching Resources take students from concrete to pictorial. Students calculate volume from illustrations of structures made from cubes.
A fun challenge I gave students was giving them a single piece of paper and scissors and asking them to create the container with the biggest possible volume. I filled their containers with popcorn so the larger the volume the more popcorn they got! I have seen similar activities listed as a calculus problem for high school and college, but my elementary kids really impressed me with their hands on solutions! A few of them figured out the best solution was cutting squares from each corner.
Free Printable Practice Resources
- Volume Sort and Practice free printable for 5th grade by Love Learning
- Paper Volume Cubes: Understanding Volume Through Paper Craft
- Build a Cubic Meter from K-5 Math Teaching Resources
- Roll a Rectangular Prism
Free TPT Resources for Volume Word Problems
- Volume Word Problems by Growing Grade by Grade (5th grade standards)
- Volume Word Problems With Graphic Organizers by Exceeding the Core (5th gr)
- Real World Volume Problems (5th grade) by Autumn Hicks
Online Games and Practice
- Volume of Cubes and Rectangular Prisms on mathgames.com
- Cube Perspective on Math Playground
- Cubes interactive on Illuminations
Online Videos for Teaching Volume
Flocabulary: Area and Volume of Prisms. “This song uses the story of Harry Houdini’s escape from a box to teach students how to calculate the area and volume of a prism.”
Khan Academy: Measuring Volume With Unit Cubes
Extension and Enrichment Projects
We Built This City- free complete plans for 2 week hands on math and science project for mastering 5th grade volume standards (and science standards for electricity and magnetism) from the Innovation in Teaching competition. “Students master volume computation and science skills by building model cities. Students first construct 3D cubes and rectangular prisms to deepen their understanding of area within the context of volume. Then, students work cooperatively in teams to build a city and find both the volume and additive volume of their structures. Additionally, students create circuits to use as lights for their buildings to learn elements of circuits, insulators and conductors.”
Volume City is available on TPT but does have a cost of $10 (updated price 2/20/23). “This activity includes a teacher presentation that can be given to students, clear directions, student examples, a city planning project dimension sheet, map template, centimeter grid paper and rubric. A secondary city template is also included. The second city includes nets of pyramids, cylinders and triangular prisms.”