Show students the second Visual Math Talk Prompt video:

Ask students to consider the following:

How many red cubes fit into a white cube?
Make an estimate

Again, students may be able to visually reason that each dimension of the white cube fits four of the red cubes. However, some students may benefit from using wooden cubes or linking cubes to help them think through the problem.

You might then reveal that the side lengths of the red cube is 1 fourth of the length of the white cube and allow students to update their estimates.

Continue playing the video to reveal how many red cubes it takes to ‘fill’ or ‘cover’ the bottom layer of the white cube and once again ask students to:

Update your estimate.

Throughout the duration of this Visual Math Talk Prompt, be sure to encourage students to share their reasoning and to paraphrase the reasoning of others.

As the silent solution animation continues on, students will see that 64 red cubes fit inside 1 white cube.

Some prompts you might consider include:

What is the volume of the white cube?
What is the volume of the red cube?
What connections do you see?

Note that some students might say something like:

The volume of the white cube is 64

This is an important facilitator move to notice and name the fact that they are not referencing the unit of measure (1 red cube). Further, we should note that we often default to using the lesser quantity as a unit of measure (in this case, the red cube). You might consider prompting students to identify the volume of the red cube assuming we are using 1 white cube as the unit of measure by asking:

What is the volume of the red cube using 1 white cube as your unit of measure?

In other words:

How many white cubes can fit in a red cube?

Students may come to realize that the volume of the red cube is 1 sixty-fourth of a white cube since 64 red cubes can fit inside a white cube. 

Other students might apply their understanding of volume to multiply the dimensions of the red cube of  \(\frac{1}{4}\) x \(\frac{1}{4}\) x \(\frac{1}{4}\)  = \(\frac{1}{64}\) .

If students do not mention the connection between the product of the dimensions of the red cube (\(\frac{1}{64}\)) and the number of red cubes that fit into the white cube (64) consider bringing it to their attention at this point.

Ensure that you reiterate the reciprocal relationship when we change our perspective utilizing one of the cubes as the unit of measure to the other (i.e.: the 64 and \(\frac{1}{64}\) relationship).