Learning Volume with Cubes

By: Mary Kienstra on: March 3, 2015  in: Engagement, volume

The best way to introduce volume to fourth graders is to play with cubes.  This week my students are learning volume, one cube at a time, by building rectangular prisms with little wooden cubes.  At first glance, it appears they are “playing” with kindergarten blocks, but in reality, they are learning to calculate volume.  Learning volume with cubes helps students move from concrete to the abstract understanding.


A pile of cubes and a table of information help students find all the possible combinations

The lesson began with an explanation that each little wooden cube is equal to one cubic inch.  Next, I placed two cubes side by side and explained that this figure is 2 cubic inches.  I continued with three cubes to equal 3 cubic inches and 4 cubes in what I called a “tower” which equaled 4 cubic inches.  Then I rearranged those 4 cubes to a 2 x 2 x 1 arrangement and asked what the volume was.  Of course, the volume was still 4 cubic inches.

At this point we created a table with the headings “base,” “side,” “height.” and “volume.”  Students worked to find all the ways to create a rectangular prism with a volume of 8 cubes and then I differentiated their work to include volumes of 12, 24, and 36 cubes.  We discussed how the label of volume has to be “cubes” or “cubic inches” since they are counting cubes.  It was all making sense.

As they created a table to record the dimensions of the boxes they created, they started to see patterns.  They noticed that the dimensions of their rectangular prisms were actually the factors of the volume number.  The discussion was rich as they worked together to determine if they had created all the arrangements of cubes for each volume.  Some groups transitioned from building each figure to using what they knew about factors to find the dimensions.  Some groups were still in the concrete stage, building and calculating.  This hands on approach gave them a solid understanding of the meaning of volume.

These kinds of lessons always remind me how important it is for elementary students to work with manipulatives such as blocks.  They need the experience of arranging the cubes and physically counting them.  Of course we could teach them that base x side x height = volume, but the experience of figuring that out is the most important part of this lesson.

Eventually, these students will find volume from the dimensions of a box, but for now, they will build their boxes using cubes.


How many ways can you arrange a figure where volume = 36 cubes?

IMG_1480 learning volume with cubes

Students create a table to record the arrangements of the cubes













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