Factor Lattice models

Last spring in my number theory class, one of my favorite activities we did was creating 3 dimensional factor lattice models. I'm just about a week away from implementing it with my current students. You use toothpicks (primes) and clay (vertices)to create a 3 dimensional model for a number. I wanted to share this activity because many of us from grades 4-12 are beginning our school year by either teaching or reviewing factors,prime factors and greatest common factor, least common multiple. The activity I will share with you is such a fantastic tool for exploring and making connections across concepts within math and allows students the opportunity to experience these concepts in a very tactile way. There are also endless patterns within the models for students to discover, and a nifty way to tie in technology.
You begin by choosing a number,and finding it's prime factors. Next you start with a vertex from which each prime factor(color-coded toothpick)will extend in a different direction. (Two prime factors will result in a 2 dimensional model, and 3 will result in a 3 dimensional model.) From there, each toothpick represents a multiple of the prime, with a vertex connecting them. Once your model is complete, you can use the primes and vertices to multiply and label all remaining vertices. When finished, the number of vertices is the number of factors, and each factor is labeled on the model. From there you can determine the GCF and LCM of the number by navigating through it.
Students can then create a digital model using Microsoft word, and write about the process. My class did these last year, and we displayed them in the office hallway showcase and had many visitors that wanted to hear about them. The really great thing was that the students could talk about them in detail and relate the math concepts they learned. It was truly a learning experience that allowed all students to explore and experience math in a new way.
I realize that the directions for making these models is not complete in my post, but I just wanted to give enough of a description so that the general idea was clear. If anyone would like step by step directions for this along with a photo of an example, I'd be happy to send that via e-mail.
And finally, I would like to say that this project is just one example of the kinds of exploratory learning we have done during classes in the math program and how beneficial they were to my own understanding, and how easy they were to incorporate into my own classroom. My e-mail for anyone interested in the activity is: jnelson7@lesley.edu Happy Teaching! Jen Nelson