Calculating Density: Who Cares?

My 8th grade middle school class is studying matter.  One of the properties they are learning about is density.  They have been conducting various experiments to calculate the density of various regular and irregular objects.  They are learning the formula D=M/V (density is equal to the mass of an object divided by its volume).  One of the issues that has arisen is how students learn to manipulate equations.



Many of the students have difficulty thinking outside of a basic formula.  If they are given mass and volume, they mostly seem to be able to calculate density.  They plug the numbers into the formula and use their calculators to solve.  However, as soon as they are presented with a problem in which they have to manipulate the equation differently (for example, if they are given the density and the mass and need to solve for volume), we seem to lose half of the students.  As a result, one of the science teachers came up with a neat tool a few years ago.  It is a graphical representation of the relationship of D,M, and V.  The equation is depicted in a pyramid with three sections:

The student can cover the variable they are trying to solve for and "see" the math involved in the calculation.  So for example, if they are trying to find the mass, they can cover the "M" and see that to solve for mass they need to multiply the density times its volume.  Alternatively, if they want to solve for volume, they would cover the "V" with his finger and see that they need to divide the mass by the density.

While in some ways this is a brilliant tool, I wonder if it ends up being a crutch for students -- allowing them to avoid learning to think through the math involved in manipulating equations.

One of the other issues is that many of the students do not seem fully engaged in this process.  They seem to be just going through the motions without a lot of excitement about what they are learning.  I am wondering how/if it is possible to make this more engaging and relevant to them.