A numerical analysis of the free radical addition polymerization system is described that provides those teaching polymer, physical, or advanced organic chemistry courses the opportunity to introduce students to numerical methods in the context of a simple but mathematically stiff chemical kinetic system. Numerical analysis can lead students to an appreciation of the power of numerical methods applied to chemical systems while providing a better understanding of the steady-state approximation and giving a more complete picture and deeper understanding of reaction dynamics. The description and Mathcad and MATLAB tutorials provided in the Supporting Information offer a variety of levels of student engagement ranging from classroom presentations of numerical and steady-state comparisons to projects requiring students to set up, run, and interpret numerical analyses for a free radical addition polymerization system.