The Unit Cube

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The students will be understand volume using a non-standard form of the unit cube.

Big Idea

It's about to get dicey!


15 minutes

In this lesson the students and I begin to dive deeper into the concept of volume by working on the conceptual understanding.  Students will be determining the volume of two boxes using a non-standard unit of measurement and model to determine the volume.  They will also be using isometric dot paper to draw the models they create. 

The practice portion of this lesson involves using dice as a non-standard unit for measuring volume so I begin the lesson by using dice as a warm-up activity.  I take three dice and use them as factors.  Students have to determine the product of the three factors and answer on their whiteboards.  I do a about 10 problems and then move into the practice portion of the lesson.


30 minutes

For this lesson the dice becomes the length of our unit cube.  The activity I use is from the second edition of Teaching Student Centered Mathematics by John Van de Walle. 

Activity 16.15  Box Comparision-Cubic Units

Provide students with a pair of small boxes that you have folded up from cardstock board.  Use unit dimensions that match the blocks that you have for units.  Students are given two boxes, exactly one block, and an appropriate ruler.  (If you use 2-cm cubes, make a ruler with the unit equal to 2cm.)  The students’ task is to decide which box has the greater volume or if the boxes have the same volume. 

Here are some suggested box dimensions (l x w x h):

  • 6 x 3 x 4
  • 5 x 4 x 4
  • 3 x 9 x 3
  • 6 x 6 x 2
  • 5 x 5 x 3

Students should use words, drawings and numbers to explain their conclusions. 

I adapt this activity slightly.

  • I build my boxes using dice as the unit
  • I provide students with base ten cubes to use for creating a model
  • I have the students work in pairs to complete the activity


15 minutes

To wrap up this lesson I introduce students to isometric dot paper and have them recreate the dice box they just explored.  Before having them recreate their models from today we practice together drawing a shape.  I chose to draw a prism that is 2 x 3 x 2.  Most students quickly catch on as to how to use the dot paper. 

Finally, the students complete their drawings we discuss using other units of measuring volume. 

The base ten cube and dice work pretty good for measuring the volume of these boxes.  Would they work for measuring the volume of swimming pool?  What type of unit cube could we use to measure a pool?  A warehouse?