Do you remember learning the volume formula (for rectangular prisms) in school? It was easy–just multiply the length, width, and height! But did you have any understanding of where that formula came from? When I first started teaching 5th grade, I taught my students a lesson on the volume formula, gave them some practice, and then couldn’t figure out why they bombed the test! They didn’t know what to do when they forgot the formula, or when they didn’t have all of the information about the shape.
This was all because I didn’t help my students develop a conceptual understanding of volume. I just expected them to memorize a formula–and they weren’t ready for that yet. That’s why I now use the CRA (Concrete-Representational-Abstract) approach to teaching volume. By starting with hands-on models and visual representations, students build a solid understanding of what volume actually means. This makes the transition to using the formula smoother and more meaningful!
Keep reading to learn more about using this approach to teach your students all about volume!
Building Concrete Understanding of Volume
For students to understand volume of any shape, they need to know that it is the amount of space an object takes up. They also need to understand that volume is measured in cubic units. Start out by having students explore building with cubes or filling in rectangular prisms with cubes. Have them determine the volume of their shape by counting the number of cubes they used. Some great tools to use for this activity are Omnifix cubes (affiliate link) and cardboard boxes!
This “building” stage is what helps students understand the meaning of volume and cubic units. Students who are more visual learners can use their counting skills to help them determine volume!
Once students have an understanding of volume as the number of cubes (or cubic units) inside of a shape, move on to more efficient strategies for finding volume. A slightly more efficient strategy is to count the number of cubes in one layer (the base) and then multiply that number by the number of layers.
To help students determine this, have them build a rectangular prism using cubes. Then they should take it apart to show each layer. Ask students, “How could we use multiplication to help us find the number of cubes?” They should soon figure out that they can multiply the number of cubes in a layer by the number of layers to find the volume!
Volume = # of cubes in a layer x # of layers
Making sure that students have a strong conceptual understanding of “layers” in a rectangular prism will help them make a connection between concrete models and the volume formula later!
Representational Understanding of Volume
Once students have a strong conceptual understanding of volume, it’s time to start using drawn representations! For some students, it’s very hard for them to visualize 3D shapes that are on paper, so they may need to build the shapes that they see to continue to understand. Always make cubes available to students!
Since students won’t be able to see all of the cubes in a drawn shape, stress using the “layers” approach to finding volume. Have students identify the number of cubes in one layer (the base) and multiply it by the number of layers.
One thing I was surprised to see from my students was their confusion about dimensions. Some students struggled to decide where the length, width, and height was on a rectangular prism. This would lead to them making silly mistakes like multiplying the same dimension twice. Focusing a lot of time on their conceptual and representational understanding is the only way to help with this issue. If students have a strong understanding of why they’re multiplying certain numbers, they won’t make as many silly mistakes!
Abstract Understanding – Applying the Volume Formula
When it comes to formulas, simply giving students the formula will almost guarantee they forget it. It’s best if they discover it on their own! One way to do this is to have students find the volume of multiple rectangular prisms. As they do so, chart the dimensions and the multiplication equation students can use to find the volume.
At the end of the activity, ask students “If we wanted to make a rule (formula) for a way to find the volume of rectangular prisms, what could it be?” Have them work in partners and triads to come up with ideas. As they share their ideas with the class, compare them to the chart to see if they are correct. You will want students to come up with the two formulas for volume:
Volume = Length x Width x Height
Volume = Area of the Base x Height
After students have come up with the formulas above, they need lots of practice using them! This will give them a chance to commit them to memory, and to understand when each formula is appropriate to use. This is also the perfect time to give students a chance to find real world examples of volume, such as calculating how much water a fish tank can hold.
Bringing It All Together
By using the CRA method to teach volume, you’re giving students the opportunity to build true conceptual understanding. Instead of jumping straight to a formula, students experience volume with their hands, visualize it through drawings, and finally make sense of the abstract math.
This progression doesn’t just help them remember the steps—it helps them understand why they work. When students discover the volume formula for themselves, they’re far more likely to use it confidently and accurately. So the next time you teach volume, start with the cubes, sketch it out, and watch the math come alive!
Helpful Resources
If you’re feeling overwhelmed with teaching volume, try out some of these resources. They are filled with examples, guided practice, and more to help students master finding volume.
- Guided Notes
These Guided Notes will help you easily scaffold students’ learning. The notes go over what volume is, counting cubes to find volume, finding volume using layers, volume formulas, and composite figures. The notes really come in handy when reinforcing the representational and abstract portion of the CRA method, and you can use the problems in the notes to introduce the concrete stage!
If you love these guided notes, you can grab the entire 5th Grade Math Guided Notes Bundle.
- Interactive Worksheets
If you have students that are struggling with finding volume or need extra help, Volume Interactive Worksheets make it a breeze. Each worksheet includes a QR code that links to a mini-lesson video. These are perfect for sending home for extra practice or helping students be more independent at math centers!
If you love these worksheets, you can grab the entire 5th Grade Interactive Worksheet Bundle.
- Task Cards
Task cards are a low-prep tool that you can use in so many ways! Give your students extra volume practice with these Volume Task Cards. You can use them for a SCOOT game, hang them around the room for a scavenger hunt, or even put in an early finisher bin!
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