Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation approach to the same equations. The alternative analysis contains regular as well as singular perturbation and shows a simple case where a two-scale singular perturbation solution is insufficient. Additional analyses suitable for student projects are outlined.