Volume can be a difficult concept for students. Fifth-grade students are expected to understand the concept of volume, calculate volume by counting cubes and by using a formula, and understand that volume is additive. Here are my tried and true tips for teaching volume.
1. Review Area Concepts
Before tackling volume it is important to make sure that students understand the concept of area. Students that are clear on what area is and how to calculate it will have a much easier time understanding volume. I review the concept of area, the area formula (A = l x w), and why we use square units when talking about area.
2. Define Volume
Many students come to math class without knowing the mathematical definition of volume. So, I begin by explaining volume. Volume can be defined as the amount of space a three-dimensional object takes up or volume is the measure of how much space a solid object takes up. My students record the definition of volume in their math notebooks. We add in additional information as we continue through the unit. I have also used a digital version of the notebook. You can check that out here.
Spend time looking at two dimensional and three dimensional objects. This will help students to see the difference between them.
3. Hands-On Practice with Non-Standard Units
Hands-on activities help students make sense of mathematical ideas. I begin my volume unit by investigating rectangular prisms. I collect a variety of small boxes for students to explore. Empty tea boxes, paper clip boxes, and granola bar boxes work perfectly. I place 2 or 3 different boxes, a set of pattern blocks, a container of marbles, and some dollar spot erasers at one of my math stations. Students investigate how many of each unit it takes to fill the boxes.
We discuss the observations that were made while filling the containers. Students will discover that the pattern block shapes, marbles, and erasers did not fill the boxes as they expected and that gaps and overlaps were noticed.
Next, students are asked to fill the same boxes with cubes. I use centimeter cubes and Unifix cubes for this activity. Unifix cubes are great for boxes that are bigger in size. Once students have filled the boxes with cubes we discuss their observations. This leads to a discussion on cubic units.
My classroom floor is made up of square tiles. I explain that we can find the area of the classroom floor by counting the square foot tiles. Then, I explain that we could find the volume of the classroom by using cubic feet. I use rulers to help students understand what a cubic foot looks like. I place one ruler along the length of a tile, one along the width of a tile, and use a third ruler to show the height. Then I add construction paper to make a cubic foot. This really helps my students to see what it means to measure with a cubic unit.
Next, model how to find the volume of a rectangular prism by filling and counting cubes. Nets are perfect for this. Students fill the nets with cubes and count the total to find the volume.
This leads to a discussion of using multiplication to calculate the volume of objects. From this discussion, the formulas for volume can be introduced. I teach my students two different formulas:
- V = length x width x height or V = l x w x h
- V = area of the base x the height or V = B x h (B = l x w)
5. Practice, Practice, Practice
The best way for students to master the concept of volume is to practice. Begin by practicing with cubes and then have students shift to using formulas to calculate volume. This can be done digitally or by using paper-based practice sheets. You can check out my favorite resources to practice volume here.