First, I'm curious--how old is your son? It sounds like he's in early grades, which is great! Kids who begin to practice the scientific method early in life tend to do better in science in high school and college, and tend to learn and retain more about science.
Now, it seems to me that your idea for your son's science project is to build a lego structure of his same height, and then have him attempt to determine how many pieces are components of the structure. Is that correct?
The next question I have is this--how will he determine that? Will he look at the structure and guess, or will he use math? You said that you have only one size of lego piece to work with, so I suggest that he measure the dimensions of that lego piece (height, width, and depth), then measure those same dimensions of the structure, and see if he can use math to determine how many pieces are in the structure.
If he guessed visually, that would have little to do with science and the scientific method. If he uses math to figure it out, he can say that he is using the scientific method to determine if measurements of small objects can be used to measure large objects. This is something that scientists do all the time--for instance, in my field of aerodynamics, we represent large objects (an airplane we want to design) by reducing it to a small model and testing it in a wind tunnel. A great deal of scientific fields use the concept of modeling (representing large objects with smaller, easier-to-test-and-study objects), and so if your son uses small lego pieces to determine something about a large lego structure, he can report that as a scientific introduction to the idea of modeling, and analysis based on simplifying a complicated object into its simple components.
Does this make sense? My advice is how to make the idea more scientific.
You asked if it would be a good idea to do three different sizes, and I say yes. If your son is using math to simplify the analysis of large structures, then it would be helpful to do three different structures. To make it more complicated, and therefore more impressive and educational, I would suggest three different shapes
. This will make your son need to figure out how to study the large object in creative ways. For example, if the object is a rectangle tower, then it can easily be measured. If it is a pyramid, it's more challenging, and probably too hard. But if it's a structure like a building, with a rectangle of large base underneath a rectangle of smaller base, then he'll have to simplify by analyzing the two different rectangles in the structure, using the small lego piece component--he'd be simplifying the large object twice!
If your son analyzes the large structure in the way I've recommended, then I suggest that the math use be based on the concept of volume: length x width x height. Find the volume of the lego piece, then find the volume of the large object, and divide the large object volume by the lego volume. This will give the number of small lego pieces in the large object, using mathematics!
If this is confusing or doesn't make sense, please let me know. I have offered a suggestion for improvement based on the science of modeling. Below are some additional resources that can help.
To see the Scientific Method as defined by most science fairs around the U.S., click on this link:http://www.sciencebuddies.org/science-f ... thod.shtml
For help with creating, conducting, and presenting a science project, see our list of Project Guides at this link:http://www.sciencebuddies.org/science-f ... ndex.shtml
For a different project involving Legos, which is similar to your idea, please view the following Science Buddies Project Idea, called "Building the Tallest Tower":http://www.sciencebuddies.org/science-f ... p013.shtml
I hope this has been helpful to you! Please let me know if you have any other questions.