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Introducing volume is one of my favourite units of the school year! It’s such a concrete, hands-on math concept that we can really create some fun ways to teach volume. We all understand the importance of fostering a solid conceptual understanding of math in our students.
If you’re looking for some practical strategies for how to teach volume so students really get it, we’ve got you covered.
This blog post will focus on finding the volume of rectangular prisms. However, the same ideas could be applied to other 3D figures. We’ll explore how to teach volume using a logical sequence that builds from hands-on activities to developing a formula to calculate volume. Don’t forget to download the free Volume Anchor Chart while you’re here too!
How to Teach Volume for Conceptual Understanding
I first begin by asking my students ‘What is volume?’. Invariably, someone may mention its reference to sound and there is always confusion between volume and capacity (understandably).
Together, we work our way to the correct definition. Volume is the amount of space occupied by a 3D solid.
Now we’re ready to get started!
1. Start with a Single Cube
The first step in introducing volume is to understand the units we use. Pass out an individual cube to each student and ask them to share everything they notice and anything they wonder.
Share that one single cube has the volume of one unit cubed or one cubic unit. It is a 3D figure, has 3 dimensions so the unit has a little 3.
Explain that the volume of a shape is determined by how many cubic units fit inside.
I like to connect the idea of a square being a 2D shape ➡ find area by counting squares ➡ we use units squared² (or square units).
Then I connect the idea of a cube being a 3D shape ➡ find volume by counting cubes ➡ we use units cubed³ (or cubic units).
2. Introducing Volume with Hands-On Activities
Begin by letting students explore volume by using cubes to build 3D figures and count the volume. We can have some fun mini-challenges with this such as:
💡 Give a specific volume and let students try to build a prism with that volume.
💡 Let students explore freely, deciding their own volume to create or build then find the volume.
💡 Challenge students to build a shape with a volume greater than _ or larger than _.
💡 Challenge students to build as many shapes as they can with the same volume.
3. Use Everyday Objects to Find Volume
After students have had a chance to explore building 3D solids and counting their volume, expand this into find the volume of given everyday objects.
Collect a variety of containers (cracker boxes, juice boxes, milk cartons, game boxes,…) and have students use cubes to fill the shapes and determine the volume.
I find this activity really drives home the meaning of volume. One thing to note is that I prefer to use centimeter cubes as we deal with metric units so it transfers more easily to the following stages. If you use inches, consider using cubes that are a cubic inch. However, if the boxes you have available are quite large, this could become rather tedious.
4. Review and Connect with Area
Now’s the time to build in some of the more abstract mathematical thinking.
Most curriculums will teach volume after area (or surface area) but it’s important to explicitly point out the connection for students and the units for each. It will be the foundation for the next stage of teaching volume.
5. Introduce Volume as Layers of the Base
The one idea that I find has the biggest ‘aha’ moment for my students is building volume as layers of the base.
This allows you to bridge the gap between counting cubes and using a formula. It’s a huge leap between the two strategies otherwise!
Ask your students guiding questions such as:
💡 Is there a quicker way to find the volume than counting all the cubes?
💡 What if you don’t have enough cubes?
Like before, ask students to fill a box with cubes. However, limit the number of cubes they have available. Ask them to brainstorm strategies they could use to find the area when they don’t have enough cubes.
Discuss the idea that volume of a rectangular prism is essentially layers of the base stacked.
Give students some questions where they have to find the volume by covering only the base of the solid then finding out how many layers of that base are needed.
AFTER exploration time, I demonstrate this by building a few layers of a 3×4 rectangle with linking cubes. I can clearly show that the base has an area of 12 cubes and if my prism is 3 layers high, the volume will be 3 layers of the 3×4 rectangle.
6. Develop a Formula to Calculate Volume
Finally, students are ready to turn their understanding into a formula that can be used for any rectangular prism (or any prism really).
Let students develop the formula themselves through trial and error, and collaboration. Ask them to use their knowledge and understanding of volume to create a way to quickly calculate the volume of any prism without needing to use cubes.
After, come back as a class and discuss the various strategies they developed. While they will likely be similar, take note of the differences. These are important to how they see the math and understand what is happening!
Rather than using length x width x height, discuss as a class how using the formula base x height might be useful.
(HINT: it works for any prism, not just rectangular prisms)
Volume Anchor Chart
Anchor charts are an important piece of any math program. As they are co-created, they solidify and reaffirm learning. Then they can be posted in the classroom for quick and easy reference.
Together make an anchor chart for volume that gives the definition and the 3 main ways we’ve looked at for finding volume.
- Counting all the cubes that make the shape.
- Counting the cubes that make the base then multiplying by the layers.
- Using the formula base x height.
You can definitely create the anchor chart together at the end of the above 6 learning steps. However, I actually think it’s really meaningful to create the anchor chart in pieces as you go through each of the learning goals.
Grab this FREE Volume Anchor Chart!
You’ll get 3 versions so you can use them in a variety of ways.
- Print and Post in colour
- Print and Post B/W then colour in
- Project and Trace
- Project, trace and complete together
- Give to students for a guided note.
Activities to Teach Volume
Now your students have a solid conceptual understanding of volume and how to find it, it’s time to build on this with engaging activities to practice and review.
Click here to find a collection of my favourite fun ways to teach volume.
Teaching volume with Manipulatives
Hands on activities are really the easiest way to explain volume, and for students to fully grasp what it means.
Here are my favourite manipulatives to make that happen. (Hopefully you’ve got most of them at your school or around your house but I’ve added some links in case):
✰ Base Ten blocks – the small units are the perfect size to use as unit cubes.
✰ Various rectangular prisms (cracker, cereal, soap boxes…)
✰ Centimetre Cubes (for metric) or Linking Cubes (for imperial).
I really feel this is the best way to teach volume. Students are able to build a conceptual understanding of what volume actually is and why the formula works!
Let me know below if you have any other strategies you or your students use!
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