This idea for these popsicle stick manipulatives, to help your students better understand what happens to the different variables in a formula, came from the Bond with James blog, and I found it through Pinterest.
In its original form, this manipulative is used to help students better understand the ideal gas law.
But, since I never did a whole lot of instruction on the gas laws, I immediately began thinking of the equations I did use with my students that fit this pattern (i.e. three variables).
The equations that came to mind were:
Newton's second law: F=ma
Density = mass / volume
Speed = distance / time
The manipulative is simple a popsicle stick, labeled with m (mass), F (force) and a (acceleration). The biggest trick is get the right letters in the right spots.
Once the stick is set up, you can put it to work. For our first scenario, lets say we want to know what happens to an objects acceleration if we decrease its mass, but keep the force constant.
For another example....
What happens to the acceleration of an object when we keep the mass constant, but apply less force to the object?
Here's a manipulative stick for the density equation:
It's used in the same way....
What happens to the density of an object if its mass remains constant but it's volume increases?
Place your finger over the mass, raise the volume end of the stick and observe the density end.
If an objects volume increases without changing the mass, the objects density will decrease. And while I don't have a picture of one.... a stick for the speed equation would have distance in the middle and speed and time on either end. Hopefully with enough practice, your students will begin to internalize these ideas. And when that happens, they will have a much better understanding of whether or not their answers make sense.